Report Overview
Summary of Alignment & Usability: STEMscopes Math | Math
Math K-2
The materials reviewed for STEMscopes Math Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including teacher supports, assessment, and student supports.
Kindergarten
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 3-5
The materials reviewed for STEMscopes Math Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including teacher supports, assessment, and student supports.
3rd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Math 6-8
The materials reviewed for STEMscopes Math Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for usability including teacher supports, assessment, and student supports.
6th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
7th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
8th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 3rd Grade
Alignment Summary
The materials reviewed for STEMscopes Math Grade 3 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and meet expectations for practice-content connections.
3rd Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The materials reviewed for STEMscopes Math Grade 3 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.
Gateway 1
Criterion 1.1: Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.
Indicator 1A
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
The curriculum is divided into 21 Scopes, and each Scope contains a Standards-Based Assessment used to assess what students have learned throughout the Scope. Examples from Standards-Based Assessments include:
Scope 5: Division Models, Evaluate, Standards-Based Assessment, Question 2, “A coffee shop made 36 ice cream cakes and put them on 4 shelves. They put the same number of ice cream cakes on each shelf. How many ice cream cakes did the coffee shop put on each shelf? 12, 9, 32, 40” (3.OA.6)
Scope 7: Multiply by Multiples of 10, Evaluate, Standards-Based Assessment, Question 4, “Sakura buys 10 packages of chocolate cupcakes and 10 packages of vanilla cupcakes for her school carnival. Each package of chocolate cupcakes contains 6 cupcakes. There is a total of 100 cupcakes. Part A What is the total number of vanilla cupcakes? Show your work or explain your reasoning. Park B What is the total number of vanilla cupcakes in each package? Show your work or explain your reasoning.” (3.NBT.3)
Scope 11: Area in Square Units, Evaluate, Standards-Based Assessment, Question 6, students are shown four designs on grid paper labeled, “Jack, Hector, Sinae, and Maren.” “Four students each designed a floor plan for a new classroom. Which two student designs have the same area? (3.MD.6)
Scope 14: Geometry, Evaluate, Standards-Based Assessment, Question 5, “Which three shapes have exactly 4 sides and 4 angles? Quadrilateral, Hexagon, Rectangle, Octagon, Triangle, Rhombus” (3.G.1)
Scope 17: Equivalent Fractions, Evaluate, Standards-Based Assessment, Question 4, “The two figures are each shaded and each represent a fraction.” Students are shown two identical squares. First square is divided into fourths vertically and two are shaded and the second is divided into fourths with a vertical and horizontal line with 2 shaded. “Are the two fractions equivalent? Explain your reasoning.” (3.NF.3b)
Indicator 1B
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials provide extensive work in Grade 3 as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:
Scope 3: Rounding, Explore 1–Round on a Number Line, Explain, Elaborate and Evaluate, engages students in extensive work to meet the full intent of 3.NBT.1 (Use place value understanding to round whole numbers to the nearest 10 or 100.) Explore 1, Round on a Number Line, Student Journal, students toss bean bags on number lines, mark the actual location, and the rounded location. “Part I: Draw where your group’s beanbags landed.” An image of a number line from 0-50 iterated by 10 with midpoints indicated is provided. “Describe where your beanbag landed. Where did your teammates’ beanbags land compared to yours? What number is the exact location of your beanbag? Which multiple of 10 is your beanbag closest to?” Part 2: “Draw where your group’s beanbags landed.” Students are provided with number lines that include a variety of iterations and midpoints to record values on. Explain, Show What You Know–Part 1, Rounding on a Number Line, “An elementary school held a canned food drive during the fall season. 1. The points on the number line show how many cans each grade level collected after two weeks. Estimate how many cans each grade collected: 3rd grade collected about ___ cans. 4th grade collected about ___ cans. 5th grade collected about ___ cans. What place value did you round to? hundreds, tens, ones 2. The points on this number line show how many cans each grade level collected in all.” Evaluate, Decide and Defend, “Jessie and Steven were both treasurers in the Polk Elementary Student Council. During today’s meeting, the student council president asked them how much money they had in their account. Jessie said they had about $500 and Steven said they had about $450. What could the actual amount in their account be? Come up with a number that would make both Jessie and Steven correct. Explain how each of them got to their individual numbers.” Elaborate, As Close as You Can, students engage in a game: “1. The goal of this game is to get a total score as close to 100 as you can without going over. … 3. Each player draws one card from each set to form a number. For example, if you draw a 3 from the ones cards and a 5 from the tens cards, the number formed is 53. Each player writes his or her number on the recording sheet and rounds it to the nearest ten to determine that play’s score. 4. Up to three rounds of this game may take place. Each player must decide whether or not to play another round. a. If a player chooses to play another round, the resulting score gets added to his or her score each time. If a player’s total score is greater than 100, the player is out of the game. b. If a player chooses to lock a score, the player circles the score. Once a score is locked, the player cannot draw any more cards. 5. The winner is the player who gets closest to 100 without going over. In some cases, both players may go over, and the game is a draw.” In Explore 2, “Get ready for your camping trip! You are going on a camping trip for a week! Since this is your first time camping, you need to buy lots of supplies. At each station, estimate how much you will spend. Share your thinking with your group, and record your thinking below.” Cards for stations include: “1. A lantern costs $23, and the supplies to make s’mores cost $28. How much will you spend on both? 2. A flashlight costs $8, and a tent costs $186. How much will you spend on both? 3. You need a sleeping bag and a pillow. The sleeping bag costs $47, and each pillow costs $12. How much will you spend? 4. Cooking gear costs $188, but you have a coupon for $18 off. How much will you spend?...” Evaluate, Skills Quiz, “Round 642 to the nearest ten. 2. Round 289 to the nearest hundred. 3. Which of the following numbers would round to 70 if rounding to the nearest ten? Choose all that apply. 78, 68, 75, 72, 4. Round 250 to the nearest hundred. …”
Scope 6: Multiplication and Division Strategies, Explore 4–Missing Factors and Quotients, Additional Resources, Fact Fluency, engages students in extensive work to meet the full intent of 3.OA.7, (Fluently multiply and divide within 100 using the relationship between multiplication and division or properties of operations.) Explore 4, students are given a set of cards and asked to choose a card and draw a model for the scenario and write an equation to solve. Then they find another scenario that is similar, solve it and write an equation that shows how to solve. During the Explore, students engage in these tasks: “Samantha bought 6 bags of apples at the grocery store. Each bag had 6 apples inside. How many apples did Samantha buy?” Students would be expected to match that scenario to this one: “Leah is a farmer who sells apples. Her crop produced 36 apples. The apples are shipped in cartons that hold 6 apples. How many cartons does Leah need to ship the apples?” Scenario 2: “Zoe is preparing party favors for her 10th birthday party. She packed 4 candies into each party bag. How many bags are needed to pack 20 candies? James is putting together 5 party bags for his birthday party. Each bag will have 4 pieces of candy in it. How many pieces of candy will James need?” Scenario 3: “There are three golf balls in each package. Asha needs 18 golf balls for the annual kids golf tournament. How many packages does Asha need to buy? Jonathan brought six packages of golf balls for the next tournament. If there are three golf balls in each package, how many golf balls did he bring?” Additional Resource, Fact Fluency: Multiplication and Division, students are provided stations for all multiplication facts from 0-9. Station 1 under the 5s facts, “Sandra is in charge of counting the money that her class has collected for a fundraiser. She notices a pattern in the values of nickels and dimes. Fill out the first three rows for 1, 2, and 3 coins. Then, complete the missing boxes to complete the table.” In Scope 5: Division Models, Explore 4, “There will be a total of 24 children attending your party. Each table can seat 6 guests. How many tables do you need to reserve? Use the materials provided to create a model to solve this problem. Draw your model below. Write an equation to match your model. Label the dividend, divisor, and quotient.”
Scope 11: Area in Square Units, Explores 1 and 2, engages students in extensive work to meet the full intent of 3.MD.6 (Measure areas by counting unit squares…) Explore 1, Recognizing Unit Lengths and Tiling Area of Plane Figures, students recognize a unit length and practice tiling area using square units. “The school librarian discovers some old books in the back of a locked cabinet in the library. She sees that the books are in good shape but is worried that since they are older and fragile, they need to be covered for protection. Will you help her protect these books? The Mystery of the Dripping Water Fountain Use the square tiles to measure the cover of the book. Width ___ Length ___ Area ___.” Explore 2, Counting Area in Square Units, students work through a set of task cards to find the area of different shapes by counting the square units. Question 1, “The Fam Games Company is laminating all of their game boards. How many square inches of laminate plastic will they need to laminate this game board? Fam Bam Games will need ___ of plastic laminate.” Question 7, “The school’s annual Field Day is coming up. To invite families, the school wants to hang a large banner at the front of the school with all of the details. How many square meters of space does the banner have to display all of the details? The field day banner has ___ to display information.” Question 8, “Mr. De Avila is creating a class quilt. Each student is getting a square piece of fabric. How many square feet will the quilt be? The class quilt will be___.”
Scope 15: Fractions on a Number Line, Explores 1-2, engages students in extensive work to meet the full intent of 3.NF.2b (Represent a fraction on a number line diagram by marking off a length from 0. Recognize that the resulting interval has size and that its endpoint locates the number on the number line.) Explore 1–Unit Fractions on a Number Line, View Student, Lighting It Up!, “The Bright Idea Light Company needs your help! As a lighting designer, you are creating different lighting options for your clients. To do this, it is important to know how many unit pieces of electrical wires you need to connect individual bulbs and how the string of lights will be partitioned. Let’s get to lighting it up! Label each design box with the number of equal parts that will create each light design. Draw and label the unit fraction parts that represent the light design. ___ parts, Fraction of distance between each light: ___, Numerical equation of the whole string of lights: ___ parts, 3 parts, Unit fraction for each interval: ___, Numerical equation of the whole: ___.” Explore 2, Determine a Given Point, View Student, Building Progress Report, “Use the number lines provided to report how much of each building is complete. Label each brick with the appropriate fraction, and place a dot in the location that shows the completion of the building. Building 1, Two-Story Building, Building Report states the of the reinforcement bricks have been laid for the building. How is each story partitioned? ___, What unit fraction does each partition represent?___, How many whole stories does this building have? ___, What distance from 0 represents the completion of this building? ___.” In Explore 2, Determine a Given Point, Building Progress Report, Use the number lines provided to report how much of each building is complete. Label each brick with the appropriate fraction, and place a dot in the location that shows the completion of the building. Building 3, One Story Building, Building Report states that of the reinforcement bricks have been laid for the building. How is each story [partitioned? ___ What unit fraction does each partition represent? ___ How many whole stories does this building have? ___ What distance from 0 represents the completion of this building? ___.”
Scope 16: Compose and Decompose Fractions into Units, Explore 3–Partitioning Shapes into Fractional Units, Procedure and Facilitation Points and Exit Ticket, engages students in extensive work to meet the full intent of 3.G.2 (Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.) Procedure and Facilitation Points, students work in small groups with the teacher’s guidance to partition shapes into fractions. “1. Place students into groups of 2–4. 2. Distribute a copy of the Student Journal to each student and a bag of pattern blocks to each group. 3. Share the following scenario: Your school is building a new playground! Each part of the new playground is shaped differently and is made up of different-shaped “tiles.” Your job is to help put together the foundation in a specific shape for each part of the playground using the designated tiles. 4. Remind the students that the design they will create is a model and is a smaller version of what the big one is supposed to be. 5. DOK–1 Show the class the 3 triangles in their bag and ask the following question: What do you notice about the triangles? They are all the same size and the same shape; they are all the same kind of triangle. 6. Point out that each group contains shapes that are all the same size as each other, and when they are put together, they make a geometric shape. 7. DOK–1 Ask students the following: When these tiles are put together to make a shape, what fraction does each tile represent? Each equal tile represents of the whole shape. 8. Explain that as a group, they will use the Student Journal to draw models of the foundations for each section of the playground. 9. Ask students to draw the shape of the foundation of the section of the playground and show how they are partitioned by their particular tile. 10. After the Explore, invite the class to a Math Chat to share their observations and learning.” In the Exit Ticket, students independently use what they have learned with a gym floor situation. Students see a rectangular shape to represent the gym floor. “The school has decided to add a basketball court. There are 6 tiles that make up the foundation of the floor for the court. Is each piece the same size with the same area?___, What is the fraction of each piece of the whole?___, What number represents the numerator ? ___, What number represents the denominator ? ___, The fraction each part of the court represents is a___.”
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.
Indicator 1C
When implemented as designed, the majority of the materials address the major clusters of each grade.
The materials reviewed for STEMscopes Math Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.
The instructional materials devote at least 65% of instructional time to the major clusters of the grade:
The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 14 out of 21, approximately 67%.
The number of lesson days and review days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 105 out of 152, approximately 69%.
The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 120 out of 180, approximately 67%.
An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 67% of the instructional materials focus on the major work of the grade.
Indicator 1D
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for STEMscopes Math Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:
Scope 4: Multiplication Models, Skill Basics–Use Story Problems to Represent Multiplication, connects the supporting work of 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the major work of 3.OA.1 (Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each.) Students use story problems to represent multiplication. “Serena’s mother brought home a box of donuts. The box has 3 rows of donuts. There are 8 donuts in each row. How many donuts are in the box? 1. Draw an array that represents the problem. Label the number of rows of donuts and the number of donuts in each row. 2. Write two repeated addition equations. 3. Write the multiplication equation. ___ x ___ = ___. (factor x factor = product)”
Scope 7: Multiply Multiples of 10, Explore 2–Multiplying by Multiples of 10 with Arrays, Exit Ticket, connects the supporting work of 3.NBT.3 (Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., , ) using strategies based on place value and properties of operations.) to the major work of 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that , one knows ) or properties of operations…). Exit Ticket, students are given instructions that require them to make an array of base ten blocks to multiply multiples of 10 by single digits. “Question one: Saturday mornings call for pancake breakfasts! Each box of pancake mix makes 60 pancakes. To make sure you have enough to feed everyone, you get 4 boxes. How many pancakes can you make with the 4 boxes of pancake mix? Make an array with base ten blocks and sketch your model. Solve for the total amount of pancakes. ___ x ___= ___. Question two: Your bed-and-breakfast has a full weekend booked! To entertain the families that visit, you have set up a karaoke sing-along night. You plan on playing 30 songs per hour. Karaoke sing-along night will last for 3 hours on Saturday night. How many total songs will be played? Make an array with base ten blocks and sketch your model. Solve for the total amount of songs. ___ x ___= ___”
Scope 16: Compose and Decompose Fractions into Units, Explore, Explore 1–Unit Fractions in a Whole, Exit Ticket, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas) to the major work of 3.NF.1 (Understand a fraction as the quantity formed by 1 part when a whole is partitioned into b equal parts.) Students create a puzzle with eight equal pieces and write the unit fraction for each puzzle piece on the piece. “Your grandmother loves puzzles, so you have made one for her. Your puzzle has eight equal pieces. Draw your whole puzzle below; then, write the unit fraction of each piece. Define a unit fraction. Define the numerator. Define the denominator.”
Indicator 1E
Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
The materials for STEMscopes Math Grade 3 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.
Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:
Scope 5: Division Models, Explore, Explore 4–Relate Multiplication and Division Equations, Math Chat, connects the major work of 3.OA.A (Represent And Solve Problems Involving Multiplication And Division) to the major work of 3.OA.B (Understand properties of multiplication and the relationship between multiplication and division.) Students apply their knowledge of multiplication facts to help solve related division facts. (Sample answers follow each DOK question.) “DOK-1 In addition and subtraction, there are fact families. Is this the same in multiplication and division? DOK-2 How can recalling multiplication facts help with division? DOK- 2 What is the relationship between multiplication and division?”
Scope 7: Multiply by Multiples of 10, Explore, Explore 1–Multiples of 10, connects the major work of 3.OA.A (Represent and solve problems involving multiplication and division) to the major work of 3.OA.C (Multiply and divide within 100.) Students multiply one-digit whole numbers by multiples of 10 using base-ten rods relating to the number of individual items in a packaged shipping order. Multiplying Multiples of 10, “You just got promoted to regional manager of the country’s biggest warehouse that packs and distributes goods to stores all over the country. As regional manager, your most important job is to make sure all of the orders and shipments are correct and that you have enough items to ship. Each of the 7 stations represents a different shipment. Ensure that you keep precise records of the number of items being shipped. Insulated Coffee Cups, Cozy Coffeehouse has ordered 5 packages of your insulated coffee cups to keep their delicious beverages hot. Each package contains 30 cups. Use the rods below to create a model of your groups of ten. Use the draw tool to complete the model. There are ___ groups of ___ tens = ___ tens. ___ x ___ = ___ or ____ x ___ 10 = ___ There are ___ cups in ___ packages.”
Scope 12: Apply the Area Formula, Explore, Explore 1–Relating Tiling to Multiplication, connects the Operations & Algebraic Thinking domain to the Measurement & Data domain. Students determine the area of a rectangle using the whole-number side lengths by using multiplication of the number of rows by the unit squares in each row. Area of Rectangles, Part 1: Crops of Corn, “A farmer plants crops in equal rows. This picture shows the plan the farmer is making for the corn crops. The plan is not finished yet. Can you help determine the area and how many total crops of corn can be planted in the garden? Use your tiles to create a model of the crops of corn. Draw your model of the garden with crops of corn in the space below. How many rows of corn are in the garden? ___ How many corn plants are in each row? ___ What operation can be used to find the total number of corn plants? Explain. Write an equation that shows how to find the total number of corn plants. ___ Each corn plant takes up 1 square foot. What is the total area of the garden? ___”
Scope 21: Represent and Interpret Data, Explain, Show What You Know Part 1: Picture Graphs and Bar Graphs, connects the Measurement & Data domain to the Operations & Algebraic Thinking domain. “The cafeteria took a survey of 45 students to find out what their favorite lunch was. The results are shown in the table. Create a bar graph to represent the data collected.” A table with the following data is displayed. Pizza: 13, Chicken Nuggets: 7, Mac and Cheese: 20, Nachos: 5. Students are asked to make a bar graph and then answer the questions. “Question 1. “What was the difference between the number of votes for pizza and for chicken nuggets? Explain your reasoning.” Question 2. “How many more students chose mac and cheese than pizza? Explain your reasoning.” Question 3. “How many students chose nachos, pizza, and chicken nuggets? Explain your reasoning.” Question. 4. “Describe something that is different and the same between the two graphs.”
Indicator 1F
Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
The materials reviewed for STEMscopes Math Grade 3 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
Prior and future connections are identified within materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections.
Examples of connections to future grades include:
Scope 4: Multiplication Models, Home, Content Support, Coming Attractions, connects 3.OA.1 (Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects) to future learning. “Students extend this multiplication concept in third grade as they make connections between multiplication and division and apply this knowledge to word problems. In fourth grade, students represent verbal statements of multiplicative comparisons as multiplication equations and solve word problems using drawings and equations with a symbol for the unknown, as well as solve multi-step word problems involving multiplication. Fifth grade advances student learning through evaluating and interpreting expressions, including the use of parentheses, brackets, or braces in numerical expressions.”
Scope 6: Multiplication and Division Strategies, Home, Content Support, Coming Attractions, connects 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that , one knows ) or properties of operations…) to future work. “Fourth-grade students extend multiplication and division to include decimals and fractions. Word problems and equations may be solved using their prior knowledge of place value and properties of operations. Students move to interpreting multiplication equations as statements of comparison. Fifth grade continues the progression of multiplying and dividing whole numbers and decimals to hundredths. They multiply fractions for which the products may be larger or smaller than either factor. Patterns, place value, and properties of operations are essential in their work. The properties and relationships between all operations are crucial to the work in sixth grade as the number system is extended to include rational numbers.”
Scope 9: Multiplication and Division Problem Solving, Home, Scope Overview, Teacher Guide, Future Expectation connects 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities…) to future learning. “Fourth-grade students will solve multi-step problems involving multiplication and division, to include interpreting remainders, with the ability to represent the problem using a symbol for the unknown quantity. They will also multiply or divide to solve word problems involving multiplicative comparisons using a symbol for the unknown quantity.”
Examples of connections to prior grades include:
Scope 8: Arithmetic Patterns, Home, Scope Overview, Teacher Guide, Background Knowledge, connects 3.OA.9 (Identify arithmetic patterns, including patterns in the addition table or multiplication table, and explain them using properties of operations...) to previous work. “In Kindergarten, students begin to understand the relationship between numbers and quantities and connect counting to cardinality (the number of items in a set or group). Kindergarten students notice patterns between added numbers; each successive counting number refers to a quantity that is one larger. In first grade, students relate counting to addition and subtraction and represent such problems with diagrams and equations. In second grade, students use repeated addition to reason about multiplication. Second-grade students apply their understanding of cardinality to add and subtract fluently within 20 using mental math strategies, and they determine if a group of objects contains an even or odd amount.”
Scope 11: Areas in Square Units, Home, Scope Overview, Teacher Guide, Background Knowledge connects 3.MD.6 (Measure areas by counting unit squares, square cm. square m. square ft, and improvised units) to work done prior to 3rd grade. “First-grade students begin measuring length using non-standard units. Second grade continues length measurement using appropriate tools, such as rulers, yardsticks, meter sticks, and measuring tape. Third grade focuses on area measurement, cultivating a conceptual understanding of area. The use of area models to measure square units provides a direct correlation to multiplication and arrays.”
Scope 17: Equivalent Fractions, Home, Content Support, Background Knowledge connects 3.NF.3 (Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size) to work done prior to 3rd grade. “Kindergarten and first-grade students analyze, compose, and partition shapes. First-grade students partition circles and rectangles into two and four equal shares, describing the shares using the words halves, fourths, and quarters. Second grade continues partitioning, adding thirds and the words thirds, half of, and a third of. Students recognize that equal shares of identical wholes need not have the same shape. Second grade partitions circles and rectangles into equal shares using fractional language. Third grade uses concrete models; students investigate and grasp the relationship between unit fractions and the whole. This lays the groundwork for students to work with equivalent fractions.”
Indicator 1G
In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.
The materials reviewed for STEMscopes Math Grade 3 foster coherence between grades and can be completed within a regular school year with little to no modification.
According to the STEMscopes Grade 3 Scope List, there are 21 Scopes, each with between 2 and 4 Explores. In addition, there are materials for Daily Numeracy and Fact Fluency. According to the Teacher Toolbox, Parent Letter, lessons are built by using the research-based 5E+IA model, which stands for Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. The Engage section includes Accessing Prior Knowledge, Foundation Builder, and Hook. With the Explores, there are Virtual Manipulatives and Skill Basics. The Explain Section includes Anchor Charts, Picture Vocabulary, My Math Thoughts, Show What You Know, and Interactive Notebook. The Elaborate section includes Fluency Builder, Spiraled Review, Math Story, Problem-Based Task, Career Connections, Data Science, and Interactive Practice. The Evaluate section includes Standards Based Assessment, Decide and Defend, Technology-Enhanced Questions, and Skills Quiz. The Intervention and Acceleration sections include Small-Group Intervention, Check-up, Supplemental Aids, Math Today, and Create Your Own.
STEMScopes provides a Scope and Sequence for each grade level, “The STEMscopes Math Suggested Scope and Sequence for each grade level is based on a 180-day school calendar. The natural progression of mathematics was the greatest factor in determining the order of scopes.” The Scope and Sequence assigns All Weeks to Daily Numeracy and Fact Fluency.
The STEMscopes Math Suggested Scope and Sequence for Grade 3 provides each scope, name, and number of weeks to be spent on the scope. “STEMscopes Math Suggested Scope and Sequence, The STEMscopes Math program is flexible, and there are variations in implementation within the guidelines provided here. This Scope and Sequence is meant to serve as a tool for you to lean on as you find how STEMscopes Math best meets the needs of the students in your classroom.”
The 3rd-5th Grade Lesson Planning Guide is based on a 90 minute class period. There are 4 different 3rd-5th Grade Guides:
Whole-Group Plan and Small-Group Plan for Scopes with 1-3 Explores show taking 5 days.
Whole-Group Plan and Small-Group Plan for Scopes with 3-5 Explores show taking 10 days.
Each day is segmented into instruction (Whole Group, or Small Group with Stations), which includes activities from the Engage, Explore, Explain, Elaborate, Intervention, and Acceleration sections, and Assessment and Closure which includes Exit Ticket, Show-What You Know, and Standards Based Assessment. Footnotes on the Lesson Planning Guide advise teachers: “The essential elements are highlighted. If time is limited, teach these elements to fully cover the standards. ¹Use (Foundation Builder) as intervention if APK shows foundational gaps. ²Set your pace according to the number of Explores included in this scope. Use Exit Tickets as well as Show What You Know for each Explore completed. ³Choose from the following elements. (Teacher Choice³ All students: Picture Vocabulary, My Math Thoughts, Career Connection, Mastery Level: Decide and Defend, Math Today, Create Your Own, Meets Level: Math Story, Problem-Based Task, Approaching Level: Interactive Practice, Skills Quiz) We have suggested activities for students including recommended tasks for students at each skill level.”
In Grade 3, the STEMscopes Math Suggested Scope and Sequence shows 180 days of instruction including:
132 lesson days
20 scope assessment days
3 days for Pre, Mid, and Post-Assessment
20 review days
5 days for Standardized Testing
Overview of Gateway 2
Rigor & the Mathematical Practices
The materials reviewed for STEMscopes Math Grade 3 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Gateway 2
Criterion 2.1: Rigor and Balance
Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.
Indicator 2A
Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
STEMscopes materials develop conceptual understanding throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Conceptual Understanding and Number Sense, STEMscopes Math Elements, this is demonstrated. “In order to reason mathematically, students must understand why different representations and processes work.” Examples include:
Scope 4: Multiplication Models, Explore 1: Equal Groups, Procedure and Facilitation Points, students develop conceptual understanding as they reason about how a model represents products as the number of groups multiplied by the number in a group. “Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters). DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means… Student answers will vary but may include the following: We see four groups. Each group has three counters. All groups are equal. If we add all the counters together, we can get 12 counters. …Ask students to write a sentence that describes what they see. … Ask students to share how they described the groups on the screen. Ask students to share their sentences and emphasize how each time a group is added, the total increases by the same number. DOK-1 Ask students if they know what mathematical operation that sentence represents. Follow the students’ lead and write a multiplication symbol down. Pose the question, ‘What does this symbol represent?’ It represents “times,” “multiplied by,” “multiplication,” “repeated addition,” and “equal groups of.” Take a marker and under the × symbol write “groups of.” Explain that another way we can think of this multiplication symbol is “groups of.” DOK -2 Have students look back at the model. Ask students, ‘How could you describe the model using the phrase groups of?’ Have students share their ideas. Write down what they say. You should emphasize the student response that means “Three groups of four.” Show how three groups of four can be written as . Repeat this three more times with different equal groups. For each new group of counters, ask students to write the following on their desk using the dry-erase marker:Sketch the model of equal groups on the screen.Write it in word form, using groups of (Example: two groups of three). Translate that into a multiplication sentence (Example: ). Distribute paper plates and counters to each group,and a copy of the Student Journal to each student. Tell students that at each station they will read a scenario, make a model of the problem with plates and counters, write a descriptive sentence, and practice writing multiplication sentences. Break students into groups and have them rotate around the room through the different scenarios. Monitor students as they work, asking them guiding questions: DOK-1 How many equal groups are there? How many are in each group? DOK-1 How can you say it using groups of? After the Explore, invite the class to a Math Chat to share their observations and learning.” (3.OA.1)
Scope 7: Multiply by Multiples of 10, Explore, Skill Basics-Repeated Addition of Multiples of 10, Procedure and Facilitation Points, students develop conceptual understanding of multiplication by multiples of 10 by working with repeated addition. “1. Distribute the base-ten rods to each group. 2. Have groups draw one Multiple of 10 Cards from their bags. 3. Instruct groups to work together using the base-ten rods to make an array that matches their chosen number. Ask the following questions: a. How many base-ten rods did you use to represent your number? Answers will vary depending on the number. b. What does repeated addition mean? Repeated addition means adding the same number over and over. c. What repeated addition sentence do your base-ten rods show that represents your chosen number? Answers will vary depending on the number. 4. Have students write their chosen number and the repeated addition sentence their base-ten rods represent on their Multiples of 10 Work Mats. 5. Repeat steps 2–4 two more times as demonstrated in the following example work mat:, 6. When students have three numbers and addition sentences on their Multiples of 10 Work Mats, ask the following questions: a. How did you form your arrays? Answers will vary. We knew the rods were worth 10, so we put four rods together to make 40. b. What do you notice about your number sentences? They all add 10s. c. How are the number chosen and the number sentence related? The 10s are added the same number of times as the digit in the tens place of the chosen number. 7. Distribute the Student Handouts. Have students use repeated addition sentences to represent numbers that are multiples of 10 and identify multiples of 10 using repeated addition sentences.” (3.NBT.3)
Scope 16: Compose and Decompose Fractions into Units, Engage, Foundation Builder, Part II, students develop conceptual understanding as they demonstrate that a fraction of represents the quantity formed by parts of size . “Distribute the Student Handout to each student. Challenge students to complete the first part (partitioning a shape) in question one independently. Ask them to move around the room and find another student who partitioned their rectangle differently. Have them sketch this way on their Student Handout. Challenge students to complete question two independently. Ask students to use crayons or colored pencils provided.Invite them to compare their answers with their group. Discussion points: How did you shade in one half of a circle if it was divided into fourths? Shading in two fourths is the same as shading in one half of the shape.How would you describe a whole that is divided into two equal pieces? Two halves”. (3.NF.1)
The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade level. Examples include:
Scope 5: Division Models, Show What You Know–Part 1: Equal Groups and Shares, Student Handout, students engage in conceptual understanding as they interpret division problems. “Part 1: Equal Groups and Shares Draw a model and fill in the blanks.” Question One: “Clay has 36 pieces of gum that he wants to share with his 9 friends. How many pieces will each of his friends get? Numbers: ___ ÷ ___ = ___ “ listed under the equation stems: “Words: ___ ___ ___.” Question Two: “Camille works at a dog pound that has 24 dogs that need to be walked. There are 5 other workers who are going to help Camille. How many dogs do the workers each have to walk if they are going to share the job equally? Numbers: ___ ÷ ___ = ___” Listed under the equation stems: “Words: ___ ___ ___” (3.OA.2)
Scope 12: Apply the Area Formula, Elaborate, Fluency Builder-Area Battle, Procedure and Facilitation Points, students play a game (in pairs) to measure area using the formula. “1. Gather students together on a rug or large-group teaching area. 2. Model how to play the game for a few rounds with a student volunteer or volunteers. a. Players shuffle the Area Battle cards and deal them evenly facedown in a pile in front of each player. b. Both players flip over their top card at the same time. c. Players find the area shown on their cards and write their answers on the student recording sheet with the number sentence used to find it. d. The player with the larger area card wins both cards and puts them faceup in a stack next to his or her pile of unplayed cards. e. If there’s a tie, each player keeps the card he or she played and adds it to the faceup stack of claimed cards. f. Continue playing until all cards have been claimed. The player with the most cards after all the cards are claimed is the winner. 3. Divide students into pairs. Mixing students by ability is recommended. 4. Monitor students as they play, and clarify directions for any pair who needs help. 5. Ask students the following questions: a. What is the area shown on your card? b. What is the area shown on your partner’s card? c. How do you know who has the card with the greater area? d. Can you think of another way to find the area shown on this card? e. What operation or operations were you using to find the area? 6. Remind students to record the number sentence and area on their student recording sheet as they play. 7. Students may play more than one round if time allows.” (3.MD.7b)
Scope 18: Compare Fractions, Evaluate, Skills Quiz, students engage in conceptual understanding as they compare fractions by reasoning about their size. Models for the following fractions are given and students asked to complete the inequality: Question one: " " Question two: " ”, Question 3: "___ ". Questions 4-6 ask students to “Write the appropriate comparison symbol (<, >, =) and the correct fractions for each set of models. Question four: models given for and , Question five: models given for and , Question six: models given for and .” (3.NF.3)
Indicator 2B
Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
STEMscopes materials develop procedural skills and fluency throughout the grade level. In the Teacher Toolbox, STEMscopes Math Philosophy, Elementary, Computational Fluency, STEMscopes Math Elements, these are demonstrated. “In each practice opportunity, students have the flexibility to use different processes and strategies to reach a solution. Students will develop fluency as they become more efficient and accurate in solving problems.” Examples include:
Daily Numeracy: Third Grade, Activities, Daily Numeracy–Solve It, Procedure and Facilitation Points, and Slideshow, engages students in adding 2-digit numbers using various strategies. Slide 1, "" “2. Display the slideshow prompt of the day, and ask students to silently think and solve. Instruct students to give hand signals when they are ready to answer. 3. Call on students to give out answers only. Record student answers on chart paper. 4. Ask students to volunteer and to explain the strategies they used to get answers.” … “5. As students share strategies, ask the class if they agree or disagree, and provide sentence stems for their responses. a. I agree because…; b. I disagree because…; c. Can you explain why you …?; d. I noticed that…; e. Could you…?” (3.NBT.2)
Scope 2: Addition and Subtraction Fluency, Explore, Explore 1–Adding Using Base Ten Strategies, Procedure and Facilitation Points, engages students in procedural fluency with teacher support as they add 3-digit numbers. “3. Read the following scenario: ‘A group of friends goes to a flea market to buy used baseball cards and football cards. When the group arrives home, they want to determine which friend bought the most cards. You need to help them figure out who bought the most cards by adding up the total number of cards for each friend.’ Students are given cards with the information about how many baseball cards and football cards each friend bought. 13. After the Explore, invite the class to a Math Chat to share their observations and learning. Question: DOK-3 What do you notice when you look at the value of a number in each place compared to the digit? DOK-3 How did you use each part of a number to combine the two amounts?” (3.NBT.2)
Scope 6: Multiplication and Division Strategies, Explore, Explore 4–Missing Factors and Quotients, Procedure and Facilitation Points, engages students in procedural fluency with teacher support as they use strategies to find cards that represent the relationship between multiplication and division. “Questions: DOK-2 How did you determine the quotient of the division sentence? DOK-2 What did you notice about the matching cards? DOK-3 How did that help you solve the other card?” (3.OA.7)
The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:
Scope 2: Addition and Subtraction Fluency, Explain, Show What You Know–Part 4: Subtracting Using Number Line Strategies, Student Handout, engages students in procedural fluency as they subtract within 1,000. “Model each expression on a numberline and record the difference.” Question one and two, the column labeled “Expression” shows the following expressions: "" and "". Two columns are provided after each expression and labeled “Number Line Model” and “Difference”. Questions 3 and 4 have nothing in the column labeled “Expressions” and have two number line models in the columns labeled “Number Line Model”. The number line for question 3 begins with 125 then shows a jump of 300 to the point 425 followed by a jump of 75 to point 500 then 9 to an unlabeled point. Students are expected to enter the difference in the column labeled “Difference”. The number line for question 4 begins with 230 then shows a jump of 600 to 830 then a jump of 50 to point 880 then a jump of 8 to an unlabeled point. (3.NBT.2)
Scope 6: Multiplication and Division Strategies, Elaborate, Fluency Builder–Products: 1, 2, 3, Procedure and Facilitation Points, engages students in procedural fluency as they play a game determining factors and products of a multiplication equation. “4. The first player places a coin within a circle under a one-digit factor. 5. The second player places the other coin within a circle under a different one-digit factor. Once two coins are on the game board, the first player finds the product of the two marked factors and shades this product on the game board. 6. The second player moves one coin under a one-digit factor to another one-digit factor. The other coin remains where it is. The second player determines the product of the two marked numbers and shades the product on the game board.” (3.OA.7)
Scope 7: Multiply by Multiples of 10, Explore 1-Multiply by Multiples of 10 Using Base Ten Blocks, Exit Ticket, students demonstrate procedural skill and fluency as they multiply a number by a multiple of ten. “Multiply by Multiples of 10 Exit Ticket, Mohammad and Drew created snack bags after their parents went to the grocery store. Help Mohammad and Drew figure out how many snacks their parents bought for them. Complete each number sentence based on the model representation. 1. Drew noticed a box that comes with 30 packages of plain potato chips. His mom bought 3 boxes. How many plain potato chips are there? There are ___ groups of ___ tens = ___ tens, ___ ___ = ___ 2. Mohammad noticed a box of crackers that contained 6 packages with 40 crackers in each package. How many crackers are there in all? There are ___ groups of ___ tens = ___ tens, ___ ___ = ___ 3. Mohammad and Drew’s mom bought 3 cases of water. There are 40 water bottles in each case. How many water bottles did their mom buy? There are ___ groups of ___ tens = ____ tens, ___ ___ = ___.” (3.NBT.3)
Indicator 2C
Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics.
STEMscopes materials include multiple routine and non-routine applications of mathematics throughout the grade level, both with teacher support and independently. Within the Teacher Toolbox, under STEMscopes Math Philosophy, Elementary, Computational Fluency, Research Summaries and Excerpt, it states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful.”
This Math Story activity includes both routine and non-routine examples of engaging applications of mathematics. For example:
Scope 10: Problem Solve Using the Four Operations, Elaborate, Math Story - Crafts, Sweets, and Goodies . . . Oh My!, students solve both routine and non-routine problems with teacher support. Non-Routine: “Read the passage and answer the questions that follow. 7. In the community center, there are 22 booths. Most of the booths have two people working at all times, but a few only have one person. What is a reasonable estimate of how many people are working in the booths? A. About 40 people , B. About 44 people , C. About 20 people , D. About 30 people ; Routine: 8. On Monday, A&M Cupcakes sold 24 vanilla cupcakes. On Tuesday, they sold 48 vanilla cupcakes. On Wednesday, they sold 30 more cupcakes than they did on Monday. Which equation could be used to find c, the number of cupcakes they sold in all three days? A. , B. , C. , D. , 9. At the end of the week, Michael wanted to know the total number of cupcakes they sold. He created this chart to help him. Michael wants to find the total number of cupcakes they sold. Show below any strategy or model that he could use to solve, and write a corresponding equation.” (3.OA.8)
Engaging routine applications of mathematics include:
Scope 6: Multiplication and Division Strategies, Engage, Hook–Appetizers and Toothpicks, Procedure and Facilitation Points, students develop application through a routine problem with teacher support as they use the associative property of multiplication to demonstrate that a multiplication problem can be solved in more that one way and the order in which numbers are grouped does not affect the product. “Part I: Pre-Explore 1. Introduce this activity toward the beginning of the scope. The class will revisit the activity and solve the original problem after students have completed the corresponding Explore activities. 2. Explain the situation while showing the video behind you: a. Your parents are throwing a party. They want you and your sister to make layered desserts. There will be 2 trays, each holding 7 desserts. Each dessert needs 5 ingredients to construct the five layers. Your dad asks you and your sister to construct the desserts in the following way from bottom to top: cookie, marshmallow, chocolate, orange, and a cherry on the top–held together with a toothpick. Your mom asks how many total ingredients you will need to construct the desserts. Your sister says you should multiply the number of trays by the number of desserts per tray and then multiply that product by the number of ingredients per dessert. You argue that you should multiply the number of ingredients per dessert by the number of deserts per tray. Then multiply that product by the number of trays. How many total pieces of ingredients do you need to make the desserts? Who had the correct strategy? Make models to discover who is correct. 3. Ask students, ‘What do you notice? What do you wonder? Where can you see math in this situation?’ Allow students to share all ideas. 4. Discuss the following: a. DOK-3 How will making a model of the desserts help us find how many ingredient pieces are needed to make the desserts? b. DOK-3 How will making a model of the desserts help us determine who had the correct strategy for finding the number? c. DOK-1 What is the associative property of multiplication? 5. Move on to complete the Explore activities. Part II: Post-Explore 1. After students have completed the Explore activities for this topic, show the phenomena video again and repeat the situation. 2. Review the problem and allow students to solve it. 3. Put students in small groups of 4. Give each group of students two pieces of half-sheet-sized graph paper, a box of toothpicks, a bottle of liquid glue, a box of crayons or colored pencils, a piece of lined paper, and a pencil. 4. Instruct students that they need to make models of the desserts. Tell them that each half sheet of graph paper represents the two trays that will be holding the desserts. They will color in squares in certain colors to represent each ingredient in the desserts. Write the colors to represent each ingredient on the board. They are as follows: a. cookie = yellow b. marshmallow = pink c. chocolate = brown d. orange = orange e. cherry = red 5. Students should follow the instructions to start at the bottom and color squares in a vertical line in the following order: cookie, marshmallow, chocolate, orange, and cherry. They can then use liquid glue to glue a toothpick on top of the squares colored on their tray (graph paper) to represent one dessert on the tray. 6. Students should make 7 desserts to go on each serving tray (graph paper). Tell them the desserts should be spaced apart on the tray like they would be at the party. 7. Give students about 10 minutes to create the two trays of desserts and determine how many pieces of ingredients were used to create the desserts. 8. Students should try out both strategies. Instruct students that they can work the problem in their heads if they are fluent in their multiplication facts or they can use the pencil and notebook to figure out the solutions. a. Sister’s strategy: number of trays multiplied by the number of desserts per tray and then that product multiplied by the number of pieces of ingredients per dessert. b. Your strategy: number of pieces of ingredients per dessert multiplied by the number of desserts per tray and then that product multiplied by the number of trays. 9. Students should then count the number of pieces of ingredients to check their answers. Hint: students can count by 5’s. 10. Instruct each small group to tell the class which strategy was right - yours or your sister’s. Did everyone in the class agree? 11. Discuss the following: a. DOK-2 What was the solution for the sister’s strategy? b. DOK-2 What was the solution for your strategy? c. DOK-1 What was the solution you found when you used the model and counted the number of pieces of ingredients needed to make the correct number of desserts? d. DOK-1 Do either of the strategies result in the same solution you got when you counted the number of pieces of ingredients needed to make the desserts? e. DOK-3 Why did both strategies work and result in the same solution? f. DOK-1 Who was correct, your sister or you? g. DOK-1 Is there another way the numbers could be grouped/ordered that would also result in the same solution? h. DOK-2 Is any one of the ways grouped in a way that makes it easier to find the solution?” (3.OA.5)
Scope 8: Multiplication and Division Problem Solving, Explore, Explore 1: Model and Solve One-Step Word Problems, Exit Ticket, students apply multiplication strategies independently to solve a routine problem. “As a way to thank you for your help with the lunchtime orders, the principal is treating 18 people in your class to a field trip! You are excited to be going, but now sack lunches need to be ordered as soon as possible. Your job is to make sure each sack lunch includes three mini cookies for each student. How many cookies do you need to order? Create a model and an equation using a symbol for the unknown that represents the diagram. Then use any strategy to solve the problem.” (3.OA.3)
Engaging non-routine applications of mathematics include:
Scope 4: Multiplication Models, Explore 4–Number Lines and Skip Counting, Procedure and Facilitation Points, students develop application through non-routine problems with teacher support as they determine the total number of objects they have packed for their camping trip by representing multiplication problems using number lines and multiples. “Part I: Counting Equal Groups 1. DOK-1 Begin by asking students to take a minute to look around the class. Ask them to find equal groups of something. 2. Give students 1 or 2 minutes to discuss among themselves and then share with the class. 3. Choose one of the students’ ideas to expand upon. The example below will focus on the number of shoes per student. Distribute a dry-erase marker, eraser, and a meterstick covered by clear tape to each group. 4. DOK-2 Ask students to draw a model of the number of shoes on four people. They can draw the model using a dry-erase marker on their desk (or a small dry-erase board). 5. Allow students to share how they modeled the problem. 6. DOK-1 Ask students to write down a multiplication number sentence for this problem and explain what the equation means. Share with the class: 7. Divide the class in half and have each half stand in a line across from each other. 8. Have students figure out how many shoes there are on the other side of the classroom. Listen for different strategies students used to figure out the total number of shoes. Listen specifically for skip counting. 9. DOK-1 Allow a few students to share how they found the total number of shoes. a. DOK-1 What numbers would you say when you count by twos? b. DOK-1 How many times did you count a group of two? Explain. c. DOK-1 How many shoes are there? d. When we count by a certain number, that is called skip counting! 10. Have students return to their groups and look at the meterstick. Tell students that the meterstick can be used as a number line. 11. Have students practice skip counting by twos as if they were counting groups of students with two shoes. Students should use the dry-erase marker to circle each number they say when they skip sound by twos. 12. Introduce that the numbers circled are called multiples. Since they skip counted by two, each number they said was a multiple of two. Part II: Camping Trip 1. Tell students that they are preparing for a big camping trip and that each group has begun packing a bag (show envelopes). 2. Explain that since they will be staying for several days, they’ve gone shopping for some essentials, and those come in packs. 3. Challenge students to use the meter stick as a tool to find the total number of different types of items. 4. Distribute the camping bag envelopes to each group. 5. Monitor students as they work, asking them guiding questions. a. DOK-1 How many packs are there. How many are in each pack? b. DOK-2 How did you use the number line (meter stick) to model the packs of items? 6. After the Explore, invite the class to a Math Chat to share their observations and learning. 7. When students are done, have them complete the Exit Ticket to assess their understanding of the concept. 8. Return to the Hook and instruct students to use their newly acquired skills to successfully complete the activity. (3.OA.1)
Scope 13: Perimeter, Engage, Hook–2 Gardens and Their Perimeters, Procedure and Facilitation Points, students develop application of area and perimeter on non-routine problems with teacher support. “Part II: Post-Explore, 1. After students have completed the Explore activities for this topic, show the phenomena video again and repeat the situation. 2. Review the problem and allow students to solve it. 3. Put each student in a small group and give each group of students a resealable bag with toothpicks. 4. Instruct students that they need to figure out how many feet of fencing their grandma needs to purchase for each of the two gardens. Students should also determine whether the gardens have equivalent perimeters. Remind students that each toothpick in the resealable bag they were given represents a linear foot of distance. a. Tell students that they must use the dimensions of the gardens given in the scenario when constructing their toothpick models. b. Give students about 10 minutes to create the gardens by building each garden perimeter out of toothpicks. Then students should determine the perimeters of both gardens. c. Instruct each group to tell the class how many feet of fencing each of their gardens required or the perimeters of their gardens. Were the perimeters equivalent for both gardens?” (3.MD.8)
Indicator 2D
The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
The materials reviewed for STEMscopes Math Grade 3 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.
All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, and application include:
Fact Fluency: Multiplication and Division, 9s, Fact Fluency–Station 1, Procedure and Facilitation Points, students develop procedural fluency with multiplication facts. “1. Students will follow the prompt to create a array using counters. Students will answer the following questions on their Student Journal: a. What multiplication sentence does this show? , b. What is the product of ? 50, 2. Next, students will remove one counter from each group of 10. Students can show this on their Student Journal by circling the counters they removed. Students will answer the following questions on their Student Journal: a. How many counters were removed? 5, b. What is the new total? 45, c. What multiplication sentence does this show now? , 3. Repeat the activity modeling an array for . 4. Students will then fill in the table to show their and facts and respond to the following reflection question: How can you use the set strategy to help solve the nines facts? I can use the set strategy to figure out the nines by doing the × 10 fact first, then subtracting one group. Like , do first, which is 80, then subtract one group of 8 and that’s 72. So, .” (3.OA.7)
Scope 2: Addition and Subtraction Fluency, Explain, Show What You Know–Pat 1, students demonstrate application through a routine problem as they solve three-digit addition problems. “Peri baked cookies for her sleepover. She baked 124 chocolate chip cookies and 110 peanut butter cookies. How many cookies does Peri have for her sleepover?” (3.NBT.2)
Scope 15: Fractions on a Number Line, Explore 1–Unit Fractions on a Number Line, Procedure and Facilitation Points, students develop conceptual understanding when they represent a fraction as a number on a number line and define the interval units shown on the number line. “1. Have the students find their one-half tile and make observations about it. 2. Invite students to discuss the following questions with the students around them and share out to class: a. DOK-1 What do you notice about this piece? b. DOK-1 What do you think this piece represents? c. DOK-1 How do you know? d. DOK-1 Do both of these parts represent the same thing? Explain. 3. Explain that each individual equal piece is called a unit, and when we refer to each equal fractions part, it is called a unit fraction. 4. Present the following scenario to the class: a. The Bright Idea Light Company needs your help! As a lighting designer, you are creating different lighting options for your clients. To do this, it is important to know how many unit pieces of electrical wires you need to connect individual bulbs and how the string of lights will be partitioned. Let’s get to lighting it up! 5. Explain that, to light designers, it is important that each light bulb is equally spaced to create an attractive design. 6. Ask students to take out their yarn and line it up above the unit fraction for . 7. Challenge them to discuss the following questions with their group while exploring the yarn and fraction tiles. Have a discussion with the class: a. DOK-2 What do the unit fractions represent for the lighting design? b. DOK-1 How do you know? c. DOK-1 How is the string of lights partitioned? d. DOK-1 How many unit pieces of electrical wire will the whole string be partitioned into? 8. Emphasize that one-half is not the center point but the distance from the start of the line to the end of the first unit, or partition. 9. Encourage students to use the yarn and/or tiles to help determine how this light design can be represented on the number line on their Student Journal. 10. Monitor collaborative groups as they line their tiles and/or strings to the number line provided in the first box of their Student Journal. 11. Access understanding as you are monitoring by using the following questions: a. DOK-2 How do the string/tiles relate to the number line? b. DOK-2 How do you know? c. DOK-2 I see numbers on the tiles. Looking at the models, what do you think they represent? d. DOK-1 How can you draw this light design on a number line? e. DOK-1 What does the space between each tick mark represent? f. DOK-1 How many equal unit pieces of electrical wire will I need for this design? 12. Discuss findings of the first box as a class. 13. Challenge students to create more light designs using the strings and/or tiles and using the number line in their Student Journal to represent their model. 14. Monitor collaborative groups as they complete the rest of the light designs. Use guiding questions above to assess their understanding. 15. After the Explore, invite the class to a Math Chat to share their observations and learning. 16. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.” (3.NF.2)
Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of a single unit of study or topic. Examples include:
Scope 4, Multiplication Models, Explore 1–Equal Groups, Exit Ticket, students apply understanding of arrays and multiplication alongside conceptual understanding as they determine the total number of objects in a scenario by using equal groups. “Look around your classroom. Equal groups are all around you! Sketch two examples of equal groups. Include a real-world problem to go with each sketch, a “groups of” statement, and a multiplication sentence.” (3.OA.1)
Scope 8: Multiplication and Division Problem Solving, Explain, Show What You Know, Part 2: Model and solve two-step Word Problems, students apply their understanding of multiplication strategies alongside procedural fluency to solve a word problem. “Solve each problem: Explain your reasoning using a model or strategy. Write an equation with a variable to represent the problem. Write a solution statement. Multiplication and Division Problem Solving, Part 2, Kelly had a sleepover. She invited 5 friends and made chocolate chip cookies. Each of the 6 girls ate 6 cookies. At the end of the night, there were 11 cookies left. How many chocolate chip cookies did Kelly make for her sleepover?” (3.OA.3)
Scope 19: Time, Explain, Show What You Know–Part 2: Problem Solving with Time on a Number Line, students show conceptual understanding alongside application as students practice problem solving with time using a number line. Students should individually complete the Show What You Know activity that correlates with the Explore activity they just completed. Each Show What You Know piece correlates with the same number Explore. For example, Show What You Know Part 1 will allow students to practice the skills they developed in Explore 1. The problem shows a chart with start time, end time, number line and duration. “The table shows the duration of time students spent in the library last Saturday. Complete the missing information within each row. Start Time: 1:53 p.m., End Time 2:20 p.m., Number Line, Duration___.” (3.MD.1)
Criterion 2.2: Math Practices
Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).
The materials reviewed for STEMscopes Math Grade 3 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).
Indicator 2E
Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the scopes. MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the scopes. Examples include:
Scope 4: Multiplication Models, Explore, Explore 3–Multiplication with Tape Diagrams, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: As students persist in providing a context to different multiplication problems, clear explanations and justifications of their contexts will be required.” Procedure and Facilitation Points, “Part I 1. Introduce the scenario to the class. On your way to school this morning, you counted 9 houses on your neighborhood street. You noticed that every single house has exactly 6 windows. You started to think that you could probably make some money washing windows in your neighborhood. You wished you could figure out a way to see how many windows there are in all without having to count them individually. 2. Challenge students to turn and talk to a partner to describe different ways they can represent the total number of windows that could be washed… 5. Distribute linking cubes to each pair of students. 6. Ask students the following questions: a. DOK-1 What do you need to find? 7. Instruct students to take our 9 linking cubes. Tell them that these represent the houses. 8. DOK-2 Challenge students to turn to their elbow partner and discuss what else we need to do to represent the problem and what we could do to model that. Share 9. Encourage students to find a way to represent this information using the manipulatives. 10. DOK-2 Invite students to share their solutions. 11. Challenge pairs to draw their model and discuss observations. 12. DOK-2 Invite students to turn to a partner to discuss what observations they can make about their model. 13. Explain that the models covered are called tape diagrams. 14. How does a tape diagram represent an equation? 15. DOK-1 Challenge them to write an equation for the tape diagram they created to find the number of windows. How do you know the multiplication sentence is true using the tape diagram? Part II 1. Distribute a copy of the Student Journal to each student and a set of Scenario Cards to each pair. 2. Tell students that they will have 8 scenarios to collaborate with a partner. 3. Encourage students to use linking cubes and dry-erase markers to help build and discuss a tape diagram that represents the problem. 4. Explain that they will record their models and solutions in their copy of the Student Journal. 5. Monitor students as they collaborate on their work, asking the following questions to assess understanding: a. DOK-2 How does knowing the “groups of” help you draw your tape diagram? b. DOK-2 Why should parts of the tape diagram be the same size? c. DOK-1 How would you write the multiplication sentence? d. DOK-1 What are the factors in the tape diagram? e. DOK-1 How does the tape diagram help you find the product? 6. If students have completed the Scenario Cards before classmates are done, challenge them to create their own word problems with their partner and have each other draw a tape diagram and multiplication sentence to match. 7. After the Explore, invite the class to a Math Chat to share their observation and learning. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.”
Scope 12: Apply the Area Formula, Explore, Explore 1–Relating Tiling to Multiplication, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students will analyze the context of a real-world problem involving area, using concrete objects to support conceptualizing the problem.” Area of Rectangles Exit Ticket, “The farmer needs help! The Sun is setting and the pumpkin seeds need to be planted. You need one scoop of seeds per square yard. The farmer gave you the plans below. You need to know how many square yards the section is so you’ll get enough pumpkin seeds!” An image of a rectangle with the 5 squares in the top row and 6 squares in the first column but no other squares in the figure are shown. “How many square yards is the pumpkin section? ____ Write an equation that represents how you found the area of the pumpkin section.”
Scope 19: Time, Explore, Explore 1–Telling Time to the Nearest Minute, Standards of Mathematical Practice, “MP.1 Make sense of problems and persevere in solving them: Students will determine what the problem is asking for, such as the exact time needed for a task or showing a specific time on a clock. Students will also decide whether concrete or representation models, mental mathematics, or equations are the best tools for solving the problem.” Scenario Cards Card, “Science lab is one of our favorite times of the day! First we grab our safety equipment and set up our lab tools to make sure we are ready to explore and experiment. By the time we are all finished setting up, it is eight-twelve in the morning.” Card 3: “After returning from the science lab, we put our science notebooks and materials away and start at our math stations. After the teacher explains what we will focus on, the clock usually reads nine twenty-seven in the morning.”
MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the scopes. Examples include:
Scope 2: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Standards of Mathematical Practice: “MP.2 Reason abstractly and quantitatively: Through the process of bundling numbers into units of tens and hundreds, students use the place values of base ten numbers to compose and decompose in determining sums and differences.” Procedure and Facilitation Points: “Distribute a Student Journal to each student, and a Number Line and a dry-erase marker to each group. Play spy music in the background as you read the following scenario: Around the room, you will find five missions you must complete. You will have 5 minutes to solve each mission. On each mission, there is a “Mission Challenge.” This number challenges your skills to solve the problem in the indicated number of jumps. Remember, agents, the challenge is not an obligation as long as you complete the challenge. Collaborate with your team of agents, but try to complete the final one on your own. Good luck, agents.Invite each group to find a card to start with. Encourage students to use the number lines as needed to work out problems.Inform students that they will complete the missions in order from here. Example: A group starting on mission 3 will continue on to 4.Point out to students that each group of agents will start recording at a different place in their copy of the Student Journal. Allow students about 5 minutes at each mission. While students are working, monitor groups to listen to the discussions. Monitor as students decide on larger jumps versus smaller ones. If students are not adding in the most effective way, guide students by asking the following: DOK-1 How could you decompose the addend? DOK-1 How could you add now that you see the values of the digits?...”
Scope 7: Multiply by Multiples of Ten, Explore, Explore 2–Multiplying by Multiples of 10 with Arrays, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students reason abstractly while using strategies of the associative property to make numbers easier to use. Quantitative reasoning is when students apply base-ten number strategies in multiplication to solve one-digit whole numbers by multiples of ten.” Procedure and Facilitation Points: “Share the following scenario with the students:You and a friend are opening up a bed-and-breakfast! This is a place that is similar to a hotel but typically much smaller with only a few rooms. You are planning a breakfast feast for your guests and want to make sure that they have plenty to eat. In order to ensure that you are all stocked up, you have to take inventory to see how much food you have. Tell students that there are grocery items around the room. Their job is to “take inventory” of each item. Explain that you need a visual model to help you and your friend keep track of all of the items you have, and you will show the total amount of each item using an array. Encourage students to collaborate and use the manipulatives to arrange the best array for each item, and then record the model in their Student Journals. Monitor students as they work, asking the following guiding questions: DOK-2 How did you and your partner set up the array in order to take inventory of the items? DOK-1 Where do you observe equal groups in the models we just built? DOK-2 How could you find the total number of items? ...”
Scope 16: Compose and Decompose Fractions into Units, Explore, Explore 1–Unit Fractions in a Whole, Standards of Mathematical Practice, “MP.2 Reason abstractly and quantitatively: Students make sense of unit fractions and their relationship to the whole. They will connect the unit fraction to how it is written in fractional notation.” Procedure and Facilitation Points, “1. Tell students the following scenario: a. A resale shop has received a bag full of puzzle pieces from someone who told them the pieces belong to five different puzzles. The resale shop has asked you to sort out the pieces into whole puzzles and identify what fraction of the whole puzzle each piece represents. 2. give each group a bag of mystery units. Instruct students to take the pieces out of the bag and place them in a pile on the desk. 3. Tell students they should find matching pieces of the mystery units from the pile, put the pieces together to build a whole puzzle, and identify what the fraction of the whole each mystery piece is. 4. As students are finding matching pieces, monitor student conversations. 5. Encourage student thinking with the following guiding questions: a. DOK-2 How do you know those mystery pieces belong together? b. DOK-1 What is one piece? c. DOK-1 How many pieces do you have? What fractions does each mystery piece equal? d. DOK-2 How many more pieces do you think you need to find to make a whole? How do you know? 6. After students find all the pieces necessary to build each whole puzzle, have them use the whole circles provided on their copy of the Student Journal to generate their report to the shop owner. 7. Students should name each puzzle and partition each circle into the same number of pieces as the original puzzle. 8. Students should also label each piece of their drawing with the fraction of the whole puzzle it represents and identify the unit fractions. 9. After students have built all of the whole puzzles and identified the unit fraction for each puzzle piece, challenge them to work together to develop a definition of a unit fraction. 10. Guide students to identify a unit fraction as one part of the whole, and explain that a whole is divided into two or more equal unit fractions. 11. After the Explores, invite the class to a Math Chat to share their observations and learning. 12. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.”
Indicator 2F
Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials provide opportunities for student engagement with MP3 that are both connected to the mathematical content of the grade level and fully developed across the grade level. Mathematical practices are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. Students construct viable arguments and critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the Scopes. Examples include:
Scope 5: Division Models, Standards for Mathematical Practice and Explore, Explore 1–Equal Groups and Shares, Math Chat, Standards for Mathematical Practice, “MP.3 Construct viable arguments and critique the reasoning of others: Students will have the opportunity to make conjectures and justify their conclusions when determining why division should be the chosen operation to solve. Counterexamples may be given when analyzing the reasoning of others.” Math Chat, “DOK-2 What did you notice about what was happening in the scenarios? DOK-2 What process did you use to divide the totals into their groups? DOK-3 How did you know if the scenario was asking for the number of objects in each group rather than the number of groups? DOK-2 What did you do if the scenario was asking for the number of groups instead of objects in each group? Explain how you did it. DOK-2 Do you think that what you’re doing is related to addition or subtraction? How do you know? DOK-1 Now that you have had some practice, what is division, in your own words?”
Scope 9: Multiplication and Division Problem Solving, Standards for Mathematical Practice and Evaluate: Decide and Defend, Student Handout, Standards for Mathematical Practice: “MP.3 Construct viable arguments and critique the reasoning of others: Students may use concrete objects or drawings to explain their thinking to others as they problem solve. Students will justify their thinking and critique the conjectures of their peers.” Decide and Defend: Game Snacks: “Tyler’s parents bought snacks and drinks for the basketball teams to enjoy after the game. The box of snacks they bought had 36 snack bags in each box. They were not told the number of players on each team, but were told that the 36 snacks were enough for each player to have at least two snacks and that each player would get the same amount. Below you will find the expression they used to find the number of snacks for each player. Draw and describe all the different ways the snacks could have been packed. Explain why the snacks could be grouped in different ways.” Equations are listed: "; ; ; ”.
Scope 16: Compose and Decompose Fractions into Units, Explore, Explore 2–Combining Fractional Units, Standards for Mathematical Practice, Procedure and Facilitation Points, students “Construct viable arguments and critique the reasoning of others: Students will make conjectures and explore their solutions, looking for evidence of proof as they describe the fractional part of an area. Students listen to others asking clarifying questions and expecting feedback. They may provide counterexamples to justify conclusions.” Procedure and Facilitation Points, “1. Place students in groups of 4 or 5. 2. Discuss the following questions: a. DOK-1 Have you had cake on your birthday? How do you serve that cake? b. DOK-1 Does each person eat a whole cake? c. DOK-1 Ask students to remind their shoulder partner what a unit fraction is based on the definition that was agreed upon as a class during Explore 1. 3. Tell students that they are surrounded by unit fractions every day, and that today they will be seeing them in different ways. 4. Explain to students that they will be doing fractional activities at 5 different stations. In each station, they must look for the different unit fractions within the objects they are exploring. 5. Ask students to read the Station Cards and use the objects along with their dry-erase board to model the parts that make up the whole. 6. Encourage students to work together in their groups to decompose the wholes into unit fractions and make a numerical equation that represents the whole. 7. Encourage thinking by asking the following questions, using the objects to help understanding: a. DOK-1 How many equal pieces is this whole partitioned into? b. DOK-1 How would you decompose this whole into its fractional units? c. DOK-1 If I am combining several units together, what operation am I doing? d. DOK-1 When we compose the whole, how would you describe it in a numerical equation? 8. Students should record their models and equations on their copy of the Student Journal. 9. As students rotate through the different stations, monitor for students who may need extra guidance or have misconceptions. 10. Students should complete the challenge at each station, if there is one. 11. After the Explore, invite the class to a Math Chat to share their observations and learning. Math Chat: DOK-2 What are some observations you made through the activities? DOK-3 After having interacted with these fractions in their individual units, how can we define a unit fraction? DOK-1 How can you decompose, or break apart, a fraction? DOK-2 What can you tell me about the fractional pieces in relation to the whole? DOK-2 What do you notice about the fractions that represent each whole? 12. When students are done, have them complete the Exit Ticket to formatively assess their understanding of the concept.”
Scope 19: Time, Evaluate, Decide and Defend, students critique the reasoning of others by creating a model and comparing the effectiveness of two plausible arguments as they work with elapsed time. Given 6 films with times from which to choose, “Abby and Carla want to watch a film at Stem Cinema Theater before going to soccer practice. Abby suggests watching the film Missing Factor at 2:08, because it will conclude before soccer practice. Carla argues that the film Missing Factor will conclude when soccer practice begins at 4:15, because there is a seventeen-minute intermission for the audience to take a break to refresh beverages and snacks. The duration of the films at Stem Cinema Theater is 1 hour and 50 minutes. Who is correct? What time and film are they able to watch before soccer practice begins? Explain your reasoning. Use the number line diagram to represent the problem.”
Indicator 2G
Materials support the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with the support of the teacher and independently throughout the Scopes. Examples include:
Scope 9: Multiplication and Division Problem Solving: Explore, Explore 1–The Commutative Property, Print Files, Exit Ticket, students build experience with MP4 as they create a model to show if the order of the multiplication problem impacts the solution. “Does Order Matter? Create a model of each equation, and fill in the product. ___ ___.” Below each equation is a space for a model and under ___ , is a line. “Circle the word or phrase that best completes the statement. The numbers in each equation are different / the same. The order of the numbers in each equation is different / the same. The products in the equations are different / the same. The order of the numbers being multiplied does/does not matter.”
Scope 11: Area in Square Units, Explore, Explore 1–Recognizing Unit Lengths and Tiling Area of Plane Figures, Print Files, Older Book Station Cards, students build experience with MP4 as they make the connections between the area covered and the square units used to measure. There are ten cards with images of book covers that students must measure with tiles. “Using the square tiles, determine the length and width of this mystery novel. Then, tile the whole cover and count to find the area. Write down your findings on your Book Cover Log.”
Scope 19: Time, Explore, Explore 1–Telling Time to the Nearest Minute, Standards for Mathematical Practices, Procedure and Facilitation Points, Standards for Mathematical Practice, “MP4 Model with mathematics: Students use multiple methods to represent their thinking. They can use concrete models (such as a small clock), representations of time intervals (including number lines, drawings, etc.), or equations to help them find the solution to the problem. In Procedure and Facilitation Points, “1. Hand students the geared clocks. 2. Invite the students to turn and talk to their shoulder partner and talk about what they notice about the geared clocks. … 4. Explain the scenario: Last night there was a storm and ALL of our digital clocks went out, and they are all blinking a big, red 12:00! In order to stay on schedule, we must determine what the analog clock will look like for each part of our day. 5. Place students into groups of three. 6. Explain that they will rotate through the stations with their clocks. 7. Let students know that at each station is a description of the scheduled activity and the time the class usually does it. 8. Explain that they will use the analog clocks provided to determine what the clock should look like as well as write down the corresponding digital time on their copy of the Student Journal. 9. Walk around and observe students working. Be on the lookout for misconceptions like which hand represents hours and which one represents minutes. Ask the following guiding questions: a. Where do you think the hour hand is going to be? b. How will you count the number of minutes described? c. Which direction should we move the hands?”
MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the Scopes. Examples include:
Scope 3: Rounding, Evaluate, Skills Quiz, Question 5, students build experience with MP5 as they use a thermometer to round the temperature in Fahrenheit. Students see a thermometer with both Celsius and Fahrenheit measurements. They need to realize which side of the thermometer is Fahrenheit and then complete the rounding of the number. “Round the temperature to the nearest 10 degrees Fahrenheit. ____”
Scope 13: Perimeter, Explore, Explore 2–Finding the Missing Length, Standards for Mathematical Practice, Procedure and Facilitation Points, Standards for Mathematical Practice, “MP5 Use appropriate tools strategically: Students use non-standard measuring tools, tiles, graph paper, pegboards, rulers, and other resources as appropriate to aid in their understanding of the concept and solving the problem. Procedure and Facilitation Points, “1. Explain that each group will be going to six different stations. At each station, students will read the station card and use the dimensions on the card to build the figure described, with the objects provided. 2. Tell students that each object represents one unit of measurement as described on the station card. a. For example, each craft stick in Station 2 represents 1 foot, each toothpick in Station 4 represents 1 mile, and so on. 3. Have students use sticky notes to label the length of each side. (Note: After groups are finished at their station, have them save the unused sticky notes for use by the remaining groups.) 4. Students will then collaborate to answer the corresponding questions on the Student Journal. 5. Tell students they will have a set amount of time at each station. When the time is up, they will clean up the stations and stack the sticky notes neatly. 6. Assign each group to a station. Monitor and check for understanding. 7. As you walk around, make sure students are counting and labeling the outside of their figures. a. Guide students toward being more efficient by asking the following: What operation could help in finding the remaining length without counting each of the objects? 8. As students get more comfortable, challenge them to make drawings of the figures and use computation instead of building them with the materials…”
Scope 20: Volume and Mass, Explore, Explore 1–Mass (Grams and Kilograms), Student Journal, Part I, students build experience with MP5, recognize the insight to be gained and limitations of using a scale to find the mass of a variety of objects found around the classroom, looking for objects that weigh about a gram and about a kilogram. “Grams vs. Kilograms Find objects around the classroom that are close to the following measurements. Use the scale to test the objects you find. Measurement Object 1 Object 2 Object 3 1 kilogram 1 gram What do you notice about a kilogram? ___ What do you notice about a gram? ___ What tool did you use to measure the weight of each object? ___ Name an object that weighs about 1 kilogram. About how much would five of these objects weigh? ___ Which weighs more: a gram or a kilogram? Explain how you know. ___ Volume and Mass Explore 1 Mass 1 Part II: Pack the Classroom! With your group, help to pack your belongings in boxes. Each box has a maximum limit of 10 kilograms. Estimate which objects you think will have a mass of 10 kilograms first before weighing them. Once you have reached an estimate of 10 kilograms, measure the actual mass to check if you were right! When you reach the limit, draw a line and write “Box #” on the side. Object Estimated Mass (kg) Actual Mass (kg) Quantity Total Mass (kg) Number of Packing Boxes Needed: Volume and Mass Explore 1 2 How did you decide to box up all the materials? ___ Why do you think we should measure the mass in kilograms and not grams? ___ What kinds of objects would make sense to weigh using kilograms? ___”
Indicator 2H
Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP6 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students attend to precision as they work with the support of the teacher and independently throughout the Scopes. Examples include:
Scope 6: Multiplication and Division Strategies, Explore, Explore 3–Distributive Property, Print Files, Exit Ticket, engages students in attending to precision and the specialized language of mathematics. “Distributive Property of Multiplication Exit Ticket: The newly released superhero film is playing at Illumination Theater. Due to its popularity, they are showing the film in six theaters at one time. If each theater can hold 9 customers, how many people will be able to watch the movie at once? Expression: ___ ___ Draw an area model and part of the area model on the grid provided to solve. Fill in the blanks below, using the original equation and information from your area model. ___ ___ ___ (___ ___) ___ ___ ___ ___ ___ (___ ___) (___ ___) ___ ___ ___”
Scope 11: Area in Square Units, Explore, Explore 1–Recognizing Unit Lengths and Tiling Area of Plane Figures, Exit Ticket, students build experience with MP6 as they attend to precision when measuring and drawing a shape,labeling the width, length and area accurately. “You have some leftover fabric from creating all those book covers. You want to create a patch to remember this good deed. Use square tiles to determine the area of the patch in square units. Draw your patch below, and label the width, length, and area. Design it how you want!”
Scope 21: Represent and Interpret Data, Evaluate, Skills Quiz, Question 7, students build experience with MP6 as they attend to precision when creating an accurate bar graph. Exit Ticket, students are given a table of colors and the number of times (frequency) those colors are in a bag of candy. They then create a bar graph to represent that data. “Create a bar graph by using the data in the frequency table. Frequency of Colors in a Bag of Candy, Color Choices, Frequency, Purple 4, Yellow 8, Red 7, Green 9, Blue 5, Orange 4, Title: ___”
Indicator 2I
Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.
Students have opportunities to engage with the Math Practices across the year and are identified for teachers within the Standards of Mathematical Practice within the Explore sections of the Scopes. MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with the support of the teacher and independently throughout the Scopes. Examples include:
Scope 2: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Procedure and Facilitation Points, students build experience with MP7 as they recognize patterns in the structure of base ten numbers. “... 2. Play spy music in the background as you read the following scenario: Around the room, you will find five missions you must complete. You will have 5 minutes to solve each mission. On each mission, there is a “Mission Challenge''. This number challenges your skills to solve the problem in the indicated numbers of jumps. … 3. Invite each group to find a card to start with. 4. Encourage students to use the number lines as needed to work out problems. … 8. While students are working, monitor groups to listen to the discussions. a. Monitor as students decide on larger jumps versus smaller ones. If students are not adding in the most effective way, guide students by asking the following: DOK-1 How could you decompose the addend? DOK-1 How could you add now that you see the values of the digits?”
Scope 8: Arithmetic Patterns, Explore, Explore 2–Evaluating Multiplication Tables, Procedure and Facilitation Points, students build experience with MP7 as they identify patterns involving operational relationships. “Part I: Reading a Multiplication Table…3. Display a multiplication table. Highlight the first row and first column of the multiplication table. 4. Explain that the highlighted row and column are the factors being multiplied. The numbers to the right of the highlighted column and below the highlighted row are the products of those numbers being multiplied. Part II: Packing Boxes 1. Read the following scenario to the class: Fantastic Food Bank received donations from their local community of items that will help those in need. The donation boxes had the same number of objects in each box. The food bank staff recorded the number of items in a table in which, if you multiplied the number of items in each box by the number of boxes, then you could find the total amount of items in all the boxes. Look at the table the staff made and see what patterns you notice. … 3. While students are working, monitor and ask them the following questions to check for understanding. a. DOK-1 What did you notice about the multiplication table? b. DOK-2 What is the pattern of this row or column (point to a row or column)? Why does this pattern make sense? 4. Encourage students to look for similarities and differences between their strategy and the strategies of others. 5. Students can use the counters to model the relationship, if needed. Modeling the relationship can help students see if there are a certain number of equal groups.”
Scope 18: Compare Fractions, Explore, Explore 2–Compare Fractions with Like Numerators, Procedure and Facilitation Points, students build experience with MP7 as they understand the structure of fractions and that the larger the denominator, the smaller the fractional unit. “1. Let students know that today they will serve as judges in court cases regarding fractions…. 4. Have the class stand and repeat the Judge’s Fractional Oath: 1, ___, do solemnly swear that I will administer comparative justice to all fractions, in respect to denominators, numerators, and fraction bars, whether they be greater than, less than, or equal to each other under Mathtitutional Law. 5. Once students have taken their Judge’s Fractional Oath, explain that in order to make a decision in each case, they must use the manipulatives as tools to gather evidence. 6. In each case, the evidence must be presented as words, using symbols in two ways (> and <), using pictorial models (number lines, tape diagrams), as well as sketching how they used the manipulatives. 7. Encourage them to talk about observations they make about the numerators and denominators as they are modeling the fractions. 8. Give students about 30 minutes to make a decision about all four cases. 9. Walk around, encouraging conversation focusing on the inverse relationship between the number of equal pieces (denominator) and the size of the pieces of the whole. 10. For students struggling to see the connection, help them place the manipulatives for each fraction right under each other. a. DOK-1 What do you notice about these two fractions? b. DOK-1 What is different about these two fractions? c. DOK-1 What do you notice about the size of the pieces in fractions with a larger denominator? d. DOK-2 Why would the greater-number denominator give you smaller pieces?”
MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with the support of the teacher and independently throughout the Scopes. Examples include:
Scope 5: Division Models, Explore, Explore 1–Equal Groups and Shares, Procedure and Facilitation Points, students build experience with MP8 as they work to understand the relationship between multiplication and division. “... 3. As a whole group, work through Scenario 1. Read the scenario out loud to the students: a. Mrs. Lopez is making 40 mini cupcakes for her after-school club. She has 8 students in her after-school club. How many mini cupcakes can each student have? 4. DOK-1 Ask students to discuss with their groups, and then share: What information do we have? DOK-1 What do we need to find out? … Ask the following questions: a. DOK-1 What did your plates represent? b. DOK-1 What did your counting objects (cubes, pom-poms, beans, or beads) represent? c. DOK-1 What did you do with the total number of cupcakes? d. DOK-1 What is another word we could use to describe how you divided up the cupcakes? e. DOK-1 How many cupcakes will each student get? How do you know? f. DOK-2 Look at your model again. Does this model make you think of another math operation? Explain your reasoning. g. DOK-1 How could we check our division work by using multiplication?... 9. Discuss the following with students: a. DOK-1 How many cupcakes did we start with?... d. DOK-1 How many groups did we have, and what did each group represent from the scenario? e. DOK-1 How many cupcakes did each student get? f. DOK-3 Is there a way we could change the question in this scenario to find the number of groups instead of the number of objects in each group?”
Scope 10: Problem Solve Using the Four Operations, Explore, Explore 2–Problem Solve Using the Four Operations Part 2, Procedure and Facilitation Points, students build experience with MP8 as they look for generalizations as they solve problems and evaluate the reasonableness of their work. “1. Present the following scenario to the class: Congratulations! You are now the proud owner of a doughnut shop called the Dapper Doughnut. Before you can officially open, you will need to learn some of the basics of the business. Read each problem together with your group and then solve. When you are done, you will attempt to learn more about the business by creating and solving your own word problem. 2. Tell students that each of the posters will designate a station. 3. Explain that they will need to represent each problem with a model, build an equation using a letter for an unknown quantity (maybe even two letters for two unknown quantities), estimate the solution, and then solve. 4. Encourage students to use manipulatives to help create the models that represent the problems. 5. Emphasize collaboration and discussion, since there may be different ways of solving the same problem. 6. Allow sufficient time for students to solve a problem before rotating to the next station. 7. Present the final challenge! Groups will create their own two-step problem for a situation that can arise with their new business. 8. Instruct them to write out the problem and come up with a model to represent it. Ask them to use estimation to find a reasonable answer and, finally, solve the problem. 9. If time permits, allow groups to challenge the class with their own two-step problems. 10. Monitor student collaboration and discussions. Assess for understanding and misconceptions using the following guiding questions: a. What is the question asking you for? b. What information does the problem give you? c. What information is missing? d. How could you model what is happening in the problem? e. What manipulatives could you use to help you visualize the math in the problem?”
Scope 19: Time, Explore, Explore 2–Problem Solving with Time on a Number Line, Procedure and Facilitation Points, students build experience with MP8 as they use patterns discovered in telling time to solve problems. “...3. Give groups the four bags with the Time Interval Cards and the sets of Scenario Cards. 4. Explain to students how to complete the following activity: a. Students will place the Scenario 1 Time Interval cards in the correct positions on the floor number line. b. Student 1 will start as the number line time walker. Student 2 will read the first sentence of the Scenario 1 card. The number line time walker will stand at the starting time on the floor number line. c. Student 3 will read the next sentence, and the group will decide whether the time interval should be added to or subtracted from the starting time. The number line time walker will walk backward or forward to move to the new location. e. As the walker walks on the number line, teammates mirror his or her moves on the analog clock. They can also use the clock to determine which direction to move. f. The number line time walker will state the answer to the question on the scenario card. g. Students will check with you to see if their answer is correct. If the answer is incorrect, groups should repeat the scenario. If the answer is correct, students will move on to the next scenario. h. After Scenario 1 is complete, the students will switch jobs so that when all 4 scenarios are complete, each student will have done each job. i. Scenario answers: i. ___ ii. ___ iii ___ iv ___ 5. Once students have acted out the first four scenarios, have them work together to complete scenarios 5 and 6 without building the number line.”
Overview of Gateway 3
Usability
The materials reviewed for STEMscopes Math Grade 3 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; Criterion 2, Assessment; Criterion 3, Student Supports.
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.
Indicator 3A
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for STEMScopes Math Grade 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Within each Scope, there is a Home dropdown menu, where the teacher will find several sections for guidance about the Scope. Under this menu, the Scope Overview has the teacher guide which leads the teacher through the Scope’s fundamental activities while providing facilitation tips, guidance, reminders, and a place to record notes on the various elements within the Scope. Content Support includes Background Knowledge; Misconceptions and Obstacles, which identifies potential student misunderstandings; Current Scope, listing the main points of the lesson, as well as the terms to know. There is also a section that gives examples of the problems that the students will see in this Scope, and the last section is the Coming Attractions which will describe what the students will be doing in the next grade level. Content Unwrapped provides teacher guidance for developing the lesson, dissecting the standards, including verbs that the students should be doing and nouns that the students should know, as well as information on vertical alignment. Also with each Explore, there is a Preparation list for the teacher with instructions for preparing the lesson and Procedure and Facilitation Points which lists step-by-step guidance for the lesson. Examples include:
Scope 4: Multiplication Models, Explore, Explore 1–Equal Groups, Procedure and Facilitation Points. Teachers do the following: “1. Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters). 2. DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means. 3. Give students 1 or 2 minutes to discuss among themselves, and then invite them to share with the class. 4. Ask students to write a sentence that describes what they see.”
Scope 9: Multiplication and Division Problem Solving, Home, Scope Overview, Teacher Guide, Engage Activities, Assessing Prior Knowledge. Teachers will keep in mind that “to assess student understanding of multiplication and division problem solving, students will be presented with a scenario in which they have to decide if multiplication or division is the way to a solution. After discussing their decisions in small groups or partners, students justify their answer and explain why they were either right or wrong. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this Scope to reinforce ideas presented in the APK.”
Scope 17: Equivalent Fractions, Explore, Explore 2–Modeling Equivalence with Number Lines, Procedure and Facilitation Points. Teachers will do the following: “Part I 1. Distribute the number line and 5 parchment paper strips to each student. Students will put the number line handout under each piece of parchment paper. 2. Ask students to lay the strip on top of the number lines and trace it onto each piece of parchment paper, each with a different color. 3. Explain that each piece will be folded into a different number of equal parts. 4. Model folding the number lines in the following ways: a. Halves, b. Thirds, c. Fourths, d. Sixths, e. Eighths.”
Indicator 3B
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for STEMScopes Math Grade 3 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
Each Scope has a Content Overview with a Teacher Guide. Within the Teacher Guide, information is given about the current Scope and its skills and concepts. Additionally, each Scope has a Content Support which includes sections entitled: Misconceptions and Obstacles, Current Scope, and Coming Attractions. These resources provide explanations and guidance for teachers. Examples include:
Scope 2: Addition and Subtraction Fluency, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states, “In grade four, students extend their work with the base-ten system to become fluent and efficient with computation. Fourth-grade students begin to incorporate the standard algorithm as a representation for the processes of addition and subtraction. Fourth-grade students also use their understanding of place value and properties of operations to represent multiplication and division of multi-digit numbers.”
Scope 8: Arithmetic Patterns, Home, Content Support, Current Scope. It states, “Students identify patterns involving addition and multiplication and explain them using properties of operations. Students examine patterns within even numbers and multiples of even numbers. Students examine patterns within sums and products along the rows and columns of addition and multiplication charts. They observe that the order of two addends or factors does not affect the sum or product (Commutative Property).”
Scope 11: Area in Square Units, Content Support, Misconceptions, and Obstacles. It states “When measuring, the properties of area and perimeter are confused. Students may not cover/construct the complete area with no gaps or overlaps. Area is misunderstood as the length of a line rather than the size of a surface. Students may have difficulty understanding that area is counted in square units.”
Scope 17: Equivalent Fractions, Content Support, Coming Attractions. It states, “Fifth grade continues the progression of equivalent fractions, using equivalent fractions as a strategy to add and subtract fractions. Students will solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Visual models or equations will represent the problem. Benchmark fractions, as well as number sense of fractions to estimate and assess the reasonableness of answers, will be utilized.”
Indicator 3C
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for STEMScopes Math Grade 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.
Correlation information is present for the mathematics standards addressed throughout the grade level and can be found in several places including a drop-down Standards link on the main home page, within teacher resources, and within each Scope. Explanations of the role and progressions of the grade-level mathematics are present. Examples include:
In each Scope, the Scope Overview, Scope Content, and Content Unwrapped provides opportunities for teachers to view content correlation in regards to the standards for the grade level as well as the math practices practiced within the Scope. The Scope Overview has a section entitled Student Expectations listing the standards covered in the Scope. It also provides a Scope Summary. In the Scope Content, the standards are listed at the beginning. This section also identifies math practices covered within the Scope. Misconceptions and Obstacles, Current Scope, and Background Knowledge make connections between the work done by students within the Scope as well as strategies and concepts covered within the Scope. Content Unwrapped again identifies the standards covered in the Scope as well as a section entitled, Dissecting the Standard. This section provides ideas of what the students are doing in the Scope as well as the important words they need to know to be successful.
Teacher Toolbox, Essentials, Vertical Alignment Charts, Vertical Alignment Chart Grade K-5, states, “How are the Standards organized? Standards that are vertically aligned show what students learn one grade level to prepare them for the next level. The standards in grades K-5 are organized around six domains. A domain is a larger group of related standards spanning multiple grade levels shown in the colored strip below: Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations–Fractions, Measurement and Data, Geometry.” Tables are provided showing the vertical alignment of standards across grade levels.
Scope 2: Addition and Subtraction Fluency, Home, Content Unwrapped, states to “Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.” Dissecting the Standard, “Verbs: What should students be doing? Add: To combine two or more numbers to calculate the total (sum) Subtract: To take away a number from another number to calculate the difference Nouns: What concrete words should students know? Algorithm: A step-by-step solution Strategy: A plan of action to find a solution Place value: The numerical value a number has, based on its position within a number Properties of operations: Attributes or characteristics of mathematical processes. Relationship (between addition and subtraction): The way two or more concepts or objects are connectedImplications for InstructionIn the past, students worked on a similar standard of adding and subtracting within 1,000 but were not expected to be fluent. Students have been asked to fluently add and subtract within 100 in the previous year. They have used place value understanding (including partial sums and differences), properties of operations, and the relationship between addition and subtraction. Adding and subtracting fluently implies that students are able to carry out the operations using written methods without relying on concrete objects. However, these can be used as part of an explanation and to continue to build understanding.”
Scope 10: Problem Solve Using the Four Operations, Home, Scope Overview, Teacher Guide, Scope Summary, Vertical Alignment, Background Knowledge, Future Expectations, states the following information: “In this Scope, students will explore problem solving using the four operations, and identifying and explaining patterns in arithmetic. In this Scope, students will master how to solve multi-step word problems using the four operations; represent word problems solved using letters within equations to represent the unknown quantity; and use mental computation and estimation strategies to determine the reasonableness of answers.” Background Knowledge: “Kindergarten students lay the conceptual foundation of the meaning of addition and subtraction: to compose or decompose numbers. First grade develops multiple strategies for adding and subtracting whole numbers. Second grade develops fluency with addition and subtraction, solving one and two-step problems within 100 by applying their understanding of place value and the properties of operations.” Future Expectations: “This acts as the conceptual foundation for third grade, extending problem solving to all four operations. Fourth Grade expands the conceptual development of problem-solving to include multi-step problems using the four operations with whole numbers. Modeling how to interpret remainders is vital as students apply the academic concepts to real-world scenarios. They learn how to multiply or divide word problems involving multiplicative comparisons using drawings and equations with variables to represent the problem. Additionally, problem-solving is extended to the addition and subtraction of fractions and multiplication of fractions by a whole number. They use all four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and measurement conversions.”
Indicator 3D
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for STEMScopes Math Grade 3 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The program provides an initial letter, found in the Teacher Toolbox, that can be used in conjunction with Google Documents to personalize an overview of the program, available in English and Spanish. Teacher Toolbox, Parent Letter: Elementary, states, “STEMScopes is built on an instructional philosophy that centers on children acquiring a conceptual understanding of mathematics through hands-on exploration, inquiry, discovery, and analysis. Each lesson includes a series of investigations and activities to bring mathematics to life for our students so they can learn by doing and fully engage in the process. Intentional cultivation of concepts and skills solidifies our students’ ability to make relevant connections and applications in the context of the real world. Lessons are built by using the research-based 5E+IA model, which stands for Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. Each one of these components of the lesson cycle features specific resources to support not only our students’ understanding of mathematical concepts, but also that of our teachers. STEMScopes Math features many resources for our educators, including Math Stories, Math Today, Writing in Math, Interactives, Online Manipulatives, and much more!”
Each Scope has a corresponding parent letter, in English and Spanish, that provides a variety of supports for families. From each Scope’s Home tab, Parent Letter, states, “The parent is provided a breakdown of the concepts being learned in class, as well as a choice board of activities to practice the concept at home.” A video is provided in How To Use STEMScopes Math that provides guidance on how to use the Scope parent letter. Examples include:
Scope 2: Addition and Subtraction Fluency, Home, Parent Letter, gives a brief overview of the concepts covered in this Scope. “Your child is about to explore addition and subtraction fluency. To master this skill, your child will build on his or her knowledge of adding and subtracting whole numbers from second grade. In second grade, your child learned how to add and subtract whole numbers up to 100 using a variety of strategies. As your child extends his or her knowledge of this concept throughout third grade, he or she will learn the following concepts: Solve with accuracy and efficiency addition and subtraction within 1,000 by applying strategies based on place value, properties of operations, and the relationship between addition and subtraction, Addition by place value uses the place value of each digit to form numbers that are easy to add together. These place value sums are then combined to find the total sum of the addends. Example: What is the value of ? Add hundreds: , Add tens: , Add ones: , Total sum: .”
Scope 5: Division Models, Home, Parent Letter, provides key vocabulary words that can be reviewed. “While working with your child at home, the following vocabulary terms might be helpful in your communication about division models. These are terms your child will be encouraged to use throughout our explorations and during our math chats, which are short, whole-group discussions at the conclusion of each activity. Terms to Know, array: objects or numbers that are arranged into rows or columns, divide: to separate or group a number into equal parts or fair shares, dividend: the number you divide into; the number that is partitioned into equal parts, divisor: the number you divide by; the amount of equal groups that the dividend is partitioned into, factor: a number multiplied with another number to get a product; a factor goes evenly into another number, multiplication: a mathematical operation consisting of repeated addition (through various strategies) to obtain the product (answer), partitive division: solving to determine the number in each group in a problem when the number of groups is known, quotative division: solving to determine the number of groups (unknown) in a problem when the number in each group is known, quotient: the answer to a division problem, tape diagram: a rectangular visual model that represents equal parts, used to solve word problems”
Scope 16: Compose and Decompose Fractions into Units, Home, Parent Letter, provides activities that could be completed with families at home. “Tic-Tac-Toe: Try This at Home, Guessing Unit Fractions, Guess what unit fraction makes up each piece of the whole unit below. Label each piece. Adding Unit Fractions, The equation and the model like the one below show a whole is the sum of the unit fractions. Draw a model of a whole divided into sixths . Write an equation that shows the unit fractions equal to the whole.Yum, Yum, You have a whole pizza to divide among 4 friends. Draw a model below. Label the unit fraction for each piece. Write an equation representing that model. Equation:”
Indicator 3E
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.
The Teacher Toolbox contains an Elementary STEMscopes Math Philosophy document that provides relevant research as it relates to components for the program. Examples include:
Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Learning within Real-World, Relevant Context, Research Summaries and Excerpts, states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of the mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful. “If the problem context makes sense to students and they know what they might do to start on a solution, they will be able to engage in problem solving.” (Carpenter, Fennema, Loef Franke, Levi, and Empson, 2015).
Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, CRA Approach, Research Summaries and Excerpts, states, “CRA stands for Concrete–Representational –Abstract. When first learning a new skill, students should use carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with the physical models, they start to draw a variety of pictorial representations that mirror their work with the concrete objects. Students are then taught to translate these models into abstract representations using symbols and algorithms. “The overarching purpose of the CRA instructional approach is to ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005) “Using their concrete level of understanding of mathematics concepts and skills, students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future.” (Special Connections, 2005).” STEMscopes Math Elements states, “As students progress through the Explore activities, they will transition from hands-on experiences with concrete objects to representational, pictorial models, and ultimately arrive at symbolic representations, using only numbers, notations, and mathematical symbols. If students begin to struggle after transitioning to pictorial or abstract, more hands-on experience with concrete objects is included in the Small Group Intervention activities.”
Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Collaborative Exploration, Research Summaries and Excerpts, states, “Our curriculum allows students to work together and learn from each other, with the teacher as the facilitator of their learning. As students work together, they begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem. Listening to the thinking and reasoning of others allows students to see multiple ways a problem can be solved. In order for students to communicate their own ideas, they must be able to reflect on their knowledge and learn how to communicate this knowledge. Working collaboratively is more reflective of the real-world situations that students will experience outside of school. Incorporate communication into mathematics instruction to help students organize and consolidate their thinking, communicate coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics.” (NCTM, 2000)
Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Promoting Equity, Research Summaries and Excerpts, states, “Teachers are encouraged throughout our curriculum to allow students to work together as they make sense of mathematics concepts. Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students. Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics. They remove the polar separation of being a math person or not, and give opportunities for all students to engage in math and make sense of it. “Teachers can build equity within the classroom community by employing complex instruction, which uses the following practices (Boaler and Staples, 2008): Modifying expectations of success/failure through the use of tasks requiring different abilities, Assigning group roles so students are responsible for each other and contribute equally to tasks, Using group assessments to encourage students' responsibility for each other's learning and appreciation of diversity” “A clear way of improving achievement and promoting equity is to broaden the number of students who are given high-level opportunities.” (Boaler, 2016) “All students should have the opportunity to receive high-quality mathematics instruction, learn challenging grade-level content, and receive the support necessary to be successful. Much of what has been typically referred to as the "achievement gap" in mathematics is a function of differential instructional opportunities.” (NCTM, 2012).” STEMscopes Math Elements states, “Implementing STEMscopes Math in the classroom provides access to high quality, challenging learning opportunities for every student. The activities within the program are scaffolded and differentiated so that all students find the content accessible and challenging. The emphasis on collaborative learning within the STEMscopes program promotes a sense of community in the classroom where students can learn from each other.”
Indicator 3F
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for STEMScopes Math Grade 3 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.
The Teacher Toolbox provides an Elementary Materials List that provides a spreadsheet with tabs for each grade level, K-5. Each tab lists the materials needed for each activity. Within each Scope, the Home Tab also provides a material list for all activities. It allows the teacher to input the number of students, groups, and stations, and then calculates how many of each item is needed. Finally, each activity within a Scope has a list of any materials that are needed for that activity. Examples include:
Scope 3: Rounding, Elaborate, Fluency Builder–Guess My Number, Materials, “Printed, 1 Instruction Sheet (per pair), 1 Guess My Number Chart (per pair), 1 Number Line Sheet (per pair), 1 Student Recording Sheet (per player), Reusable, 1 Dry-erase marker (per pair)”
Scope 9: Multiplication and Division Problem Solving, Explore, Explore 3-Model and Solve One- and Two-Step Problems, Materials, “Printed, 1 Student Journal (per student), 1 Set of Math Hunt Posters (per class), 1 Exit Ticket (per student), Reusable, Manipulatives: Counters, Tiles, Base ten blocks”
Scope 16: Compose and Decompose Fractions into Units, Explore 1–Unit Fractions in a Whole, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 1 Set of Mystery Units (per group), Reusable, 1 Resealable plastic bag (per group)”
Indicator 3G
This is not an assessed indicator in Mathematics.
Indicator 3H
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for Assessment. The materials identify the content standards but do not identify the mathematical practices assessed in assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance, and suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.
Indicator 3I
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for STEMscopes Math Grade 3 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.
The materials identify grade-level content standards within the Assessment Alignment document for the Skills Quiz Alignment and Standards-Based Assessment Alignment. The Benchmark Blueprint document provides grade-level content standards alignment for the Pre-Assessment, Mid- Assessment, and Post-Assessment. While the mathematical practices are identified in each Scope within the Explores, they are not aligned to assessments or assessment items. Examples include:
STEMscopes Math: Common Core Third Grade Teacher Resources, Assessment Alignment, Assessment Alignment, Standards-Based Assessment Alignment, identifies Scope 2: Addition and Subtraction Fluency, Question 1 as addressing 3.NBT.2. Scope 2: Addition and Subtraction fluency, Evaluate, Standards-Based Assessment, Question 1, “William spent $15 on his lunch. Henry spent $17 more than William, and Justin spent $12 less than Henry. How much money did Justin spend? ($44, $14, $20, $10)”
STEMscopes Math: Common Core Third Grade Teacher Resources, Assessment Alignment, Assessment Alignment, Skills Quiz Alignment, identifies Scope 9: Multiplication and Division Problem Solving, Question 3 as addressing 3.OA.3. Scope 9: Multiplication and Division Problem Solving, Evaluate, Skills Quiz, Question 3, “Sam has a total of 49 coins. He wants to put 7 coins in each row. How many rows of coins will Sam have? Use the space below to draw circles to represent a model of what Sam’s coins will look like for the picture. Expression ____ Solution ____.”
STEMscopes Math: Common Core Third Grade Teacher Resources, Assessment Alignment, Benchmark Blueprint, Grade 3 Mid-Assessment, identifies Question 5 as addressing 3.OA.1. STEMscopes Math: Common Core Third Grade Teacher Resources, Resources, Benchmark Assessments, STEMscopes Math Grade 3 Mid-Assessment, Question 5, given six logs with three frogs on each log, “How many total frogs are on the 6 logs?” Students select from, “3 frogs; 6 frogs; 18 frogs; 15 frogs”
Indicator 3J
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for STEMScopes Math Grade 3 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
In Grade 3, each Scope has an activity called Decide and Defend, an assessment that requires students to show their mathematical reasoning and provide evidence to support their claim. A rubric is provided to score Understanding, Computation, and Reasoning. Answer keys are provided for all assessments including Skills Quizzes and Technology-Enhanced Questions. Standards-Based Assessment answer keys provide answers, potential student responses to short answer questions, and identifies the Depth Of Knowledge (DOK) for each question.
After students complete assessments, the teacher can utilize the Intervention Tab to review concepts presented within the Scopes’ Explore lessons. There are Small-Group Intervention activities that the teacher can use with small groups or all students. Within the Intervention, the lesson is broken into parts that coincide with the number of Explores within the Scope. The teacher can provide targeted instruction in areas where students, or the class, need additional practice. The program also provides a document in the Teacher Guide for each Scope to help group students based on their understanding of the concepts covered in the Scope. The teacher can use this visual aide to make sure to meet the needs of each student. Examples include:
Scope 3: Rounding, Evaluate, Standards-Based Assessment, Answer Key, Question 4, provides a possible way a student might complete the problem. Students see a number line with 100, 157, and 200 labeled. “The number line shows the location of 157. What is 157 rounded to the nearest 100? Use the number line to explain your reasoning. (DOK-3), 200 Sample reasoning: 157 rounds to 200 because it is closer to 200 than it is to 100.” (3.NBT.1)
Scope 14: Geometry, Standards-Based Assessment, Answer Key, Question 9 provides a possible solution a student might provide. Students see five shapes labeled A-E. In order, trapezoid, pentagon, rectangle, rhombus, and pentagon. “A group of figures is shown below. Sort the shapes into two groups, Group 1 and Group 2, based on their attributes. List the shapes that are in each group. Explain your reasoning. Write your answers in the box. (DOK-3), Answers vary. Sample response: Group 1: Shapes A, C, and D Group 2: Shapes B and E Shapes in Group 1 are quadrilaterals because they have 4 sides. Shapes in Group 2 are not quadrilaterals because they have 5 sides.” (3.G.1)
Scope 18: Compare Fractions, Intervention, Small-Group Intervention, Procedure and Facilitation Points states, “3. Present different fraction combinations to the students and have them practice writing them in fraction notation. 4. Distribute the Fraction Card Sort. Have the students sort them into three groups: halves, thirds, and fourths. 5. Observe as students work. If students place the non-equal parts into the groups, explain that fractions are made up of equal parts. It would only be considered a half if both pieces are the same size. If they don’t put the non-equal parts into the group, ask them why.”
Indicator 3K
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.
Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:
Scope 4: Multiplication Models, Evaluate, Standards-Based Assessment, Print Files, Student Handout, provides opportunities for students to demonstrate the full intent of the standard 3.OA.1, “Interpret products of whole numbers, e.g., interpret as the total number of objects in 5 groups of 7 objects each…” Item 2: “Charlie saw six flamingos at the zoo. Each flamingo has two legs, as shown below.” Picture of six flamingos shown. “Which expression can be used to find the total number of legs on the six flamingos? A. B. C. D. .” Item 5: “This rectangular array represents multiplication.” A 6 by 5 array is shown. “Which expression corresponds with this array? A. ; B. ; C. ; D. ”. Item 6: “The Sweet Candy Shop has 4 display shelves. Each shelf features 6 candies. Which two statements are true? A. The Sweet Candy Shop displays 6 groups of 4 candies.; B. The Sweet Candy Shop displays 4 groups of 6 candies.; C. The Sweet Candy Shop has a total of 24 candies.; D. The Sweet Candy Shop has a total of 10 candies.”
Scope 12: Perimeter, Evaluate, Standards-Based Assessment, Question 8, provides students with an opportunity to demonstrate full intent of MP2, “Reason abstractly and quantitatively, as they reason abstractly and relate perimeter and area and the differences in their measurements.” “Arnav drew a rectangle with a perimeter of 18 inches. Which two answers could be possible areas for his rectangle? A. 20 square inches, B. 16 square inches, C. 18 square inches, D. 21 square inches”
Scope 19: Time, Evaluate, Skills Quiz, Print Files, Student Handout, provides opportunities for students to demonstrate the full intent of the grade level standard, 3.MD.1, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.” Item two provides a clock and a digital time of 7:18 and asks students to draw the hands of the clock. Item 6 shows an analog clock with the time 3:47 and students are asked to write the digital time. Item 9, “Steven has to set up his project at the science fair by 11:30 a.m. If it takes him 15 minutes to check in and find his table and 30 minutes to set up his display, what time does he need to arrive at the science fair?” Following this question is a number line iterated and labeled every 15 minutes beginning at 9:45 and ending at 11:45.
Indicator 3L
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for STEMScopes Math Grade 3 provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
STEMScopes Math provides assessment guidance in the Teacher Guide within the Scope Overview. “STEMScopes Tip, the Evaluate section, found along the Scope menu, contains assessment tools designed to help teachers gather the data they need to determine whether intervention or acceleration is warranted. From standards-based assessments to an open-ended reasoning prompt, there is an evaluation for every student’s learning style.” Examples include:
Students completing any assessment digitally have several options available to assist with completing the assessment. A ribbon at the top of the assessment allows the student to: change the font size, have directions and problems read which the teacher can turn on and off, highlight information, use a dictionary as allowed by the teacher, and use a calculator. If a paper copy is being used, the teacher can edit the assessment within Google Documents to change the font size and change the layout. Assessments are also available in Spanish. Teachers also can create their own assessments from a question bank allowing for a variety of assessments students can complete to show understanding.
Each Scope provides an Exit Ticket to check student understanding. After reviewing answers, the teacher can use the Intervention tab online either in a small group setting or with the entire class. The Small Group Instruction activity provides more practice with the concept(s) taught within the Scope.
Within the Intervention tab, teachers can click on different supplemental aids that could be used to assist students completing an assessment. Examples of supplemental aids include open number lines, number charts, base tens, place value charts, etc. Teachers can decide to use these aids with students needing additional support.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
Indicator 3M
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for STEMscopes Grade 3 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.
Within the Teacher Toolbox, under Interventions, materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Within each Explore section of the Scopes there are Instructional Supports and Language Acquisition Strategy suggestions specific to the Explore activity. Additionally, each Scope has an Intervention tab that provides support specific to the Scope. Examples include:
Teacher Toolbox, Interventions, Interventions–Adaptive Development, Generalizes Information between Situations, supplies teachers with teaching strategies to support students with difficulty generalizing information. “Unable to Generalize: Alike and different–Ask students to make a list of similarities and differences between two concrete objects. Move to abstract ideas once students have mastered this process. Analogies–Play analogy games related to the scope with students. This will help create relationships between words and their application. Different setting–Call attention to vocabulary or concepts that are seen in various settings. For example, highlight vocabulary used in a math problem. Ask students why that word was used in that setting. Multiple modalities–Present concepts in a variety of ways to provide more opportunities for processing. Include a visual or hands-on component with any verbal information.”
Scope 2: Addition and Subtraction Fluency, Explore, Explore 4–Subtracting Using Number Line Strategies, Instructional Supports, “1. If a student is struggling with creating his or her own number line, provide the student with a premade number line with benchmark numbers labeled. 2.Students might benefit from using alternate models to show their thinking, such as drawing a base ten model. 3. Allow students to use manipulatives, base ten blocks, and place value disks as necessary.”
Scope 18: Compare Fractions, Explore, Explore 2–Compare Fractions with Like Numerators, Instructional Supports, “1. If students are struggling to compare the given fractions, have students explain what they notice about the size of the pieces, such as comparing a third to an eighth. Encourage them to place their models on top of one another. They should notice that even though there are the same number of pieces (numerator), one model will be greater because each piece is larger. 2. Students may have a difficult time understanding that as the denominator gets bigger, the pieces get smaller. Model an example of this inverse relationship using manipulatives, such as and , pointing out the size of the pieces with each denominator. 3. It may be necessary to review key vocabulary, such as ‘numerator’ and ‘denominator’. 4. Some students may have difficulty completing number lines over the given fractions, and may find it helpful to draw a different model or use manipulatives to explain their thinking. 5. It may be necessary to remind students what each comparison symbol represents.”
Indicator 3N
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.
Within each Scope, Scope Overview, Teacher Guide, a STEMscopes Tip is provided. It states, “The acceleration section of each Scope, located along the Scope menu, provides resources for students who have mastered the concepts from the Scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.” Examples include:
Scope 7: Multiply by Multiples of 10, Acceleration, Math Today–Bear Cub Recovery, Question 2 states, “This little cub weighed 8 pounds when she was born. If she will grow to weigh 40 times as much when she is an adult bear, how much will she weigh when fully grown? If , then ___ pounds”
Scope 15: Fractions on a Number Line, Acceleration, Math Today–Concerns About Baby Food, Question 1 states, “Six out of eight toddlers prefer foods that are high in sodium. Locate this quantity on the number line below.” Question 2, “One in four kids is overweight. Locate this quantity on the number line below.” Question 3, “One toddler ate a part of a sugar cookie as shown on the number line below. What fraction of the cookie did the child eat?
Scope 19: Time, Acceleration, Math Today–Ice Swimming, Question 1 states, “Lui Xialong arrived at the ice swimming hole at 8:15. Draw the hands on the clock below to show this time.” Question 2, “If Lui waited for his turn for 30 minutes, what time did he get in the pool? Show your work on the number line below.” Question 3, “Lui jogged and stretched for 15 minutes before getting into the pool. What time did he start jogging and stretching? Show your work on the number line below.”
Indicator 3O
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for STEMscopes Math Grade 3 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Each Scope Overview highlights the potential types of work students will accomplish within the lessons. The Scope Overview states, “What Are Problems? Within the context of a scope, elements that fit into the category of problems expose students to new mathematical concepts by adhering to constructivist principles. Students are expected to explore, question, and attain conceptual understanding through engaging in these elements with teacher facilitation. What Are Exercises? Elements that have been classified as exercises have been designed to provide opportunities for students to apply their understanding to attain mastery. These are carefully sequenced to build upon students’ prior knowledge to support new skills and range in purposes, from building fluency and addressing misconceptions to applying the skill to create a plan or a product in the context of real life.” Examples include:
Teacher Toolbox, Mathematical Practices, Rubrics for Mathematical Practices–Third through Fifth Grades, Third Grade, Rubrics for Mathematical Practices states, “MP.3 Construct viable arguments and critique the reasoning of others. Students may construct arguments by using concrete referents such as objects, pictures, and drawings. They refine their communication skills as they participate in mathematical discussions and discuss and listen to solutions and justifications. Students create arguments and find ways to justify their equations. Teachers may help facilitate by asking questions such as “How did you get that?” “Why is that true?” or “Can you show that another way?” Students explain their thinking to others and respond to others’ thinking. Students ask these questions of their peers. Teachers may encourage the use of language tools such as sentence frames to help students justify their thinking.”
Scope 3: Rounding, Explain, My Math Thoughts states, “Procedure and Facilitation Points 1. Allow students to discuss their thinking with a neighbor before writing their thoughts on paper. 2. Encourage students to persevere through their thinking and to use mathematical tools and models as necessary. 3. Invite students to write their answers in complete sentences using correct spelling, grammar, and punctuation.”
Scope 9: Multiplication and Division Problem Solving, Elaborate, Problem-Based Task–Animal Shelter Antics states, “Congratulations! For your animal shelter’s grand opening, you are hosting an adoption event to help find “fur-ever” homes for your shelter friends. How many animals live at your shelter? Choose a number between 2 and 9 for each type of animal. Your goal is to send each one of your furry friends to their new homes with the same amount of items. Use the inventory below that lists the number of items each dog should get to see if you have enough for each of the dogs in your shelter to go home with the items they need. Inventory, 20 Dog Leashes, 81 Pounds of Dog Food, 27 Dog Collars, 48 Dog Toys, 14 Bowls, 100 Dog Treats.” Given a table with the first 2 columns filled with Item, # Per Dog, Leash 2, Collar 7, Bowls 2, Pounds of Food 9, Toys 8, Treats 10,” students complete the columns labeled “Number Sentence, # of Dogs That Will Receive The Items, Do You Have Enough?”
Indicator 3P
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for STEMscopes Math Grade 3 provide opportunities for teachers to use a variety of grouping strategies.
Suggestions and guidance are provided for teachers to use a variety of groupings, including whole group, small group, pairs, or individual. Examples include:
Scope 7: Multiply by Multiples of 10, Intervention, Procedure and Facilitation Points states, “Part I, a. Ask students to work with a partner”
Scope 13: Perimeter, Engage, Hook–Two Gardens and Their Perimeters, Part II: Post Explore states, “Put each student in a small group and give each group of students a resealable bag with toothpicks.”
Scope 19: Time, Explore, Explore 2–Problem Solving with Time on a Number Line states, “Place students in groups of four. Students should number themselves one through four.”
Indicator 3Q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
Within the Teacher Toolbox, the program provides resources to assist MLLs when using the materials. The material states, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” Examples include but are not limited to:
“Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language.”
“Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates.”
“Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses.”
“Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases.”
“Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe–Try This at Home that students can engage in along with their families. This letter is written in two languages.”
“Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains.”
“Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain.”
“Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills.”
“Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language.”
“Distance Learning Videos – Major skills and concepts are broken down in these student- facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math.”
“My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well.”
Guidance is also provided throughout the scopes to guide the teacher. Examples include:
Scope 2: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Print Files, Printable Math Chat(Spanish) provides support for students who read, write, speak a different language than English to engage in the content. The following questions are written in Spanish on the Math Chat (Spanish) cards: “How did you decide how many jumps to use on the number line? Notice our number lines always started with the first number in our equation. Does it have to be done that way? How would you lead someone else through using this strategy to add?
Scope 6: Multiplication and Division Strategies, Explain, Picture Vocabulary, Student Handout provides support for students who read, write, speak a different language than English to engage in the content. The handout provides visuals and explanations on the meaning of operations such as division where an equation is given, is shown along with a model of 3 circles with 5 dogs in each one and the explanation “To share or separate into equal groups or equal parts”.
Scope 8: Arithmetic Patterns, Explore, Explore 1–Addition Patterns, Language Acquisition Strategy provides support for students who read, write, speak a different language than English to engage in the content. “The following Language Acquisition Strategy is supported in this Explore activity. See below for ways to support a student's English language development. Students utilize personal backgrounds to comprehend English meanings.Ask students to describe three things that they have encountered that are arranged in a pattern. Have them discuss with a partner. Possible questions include the following: What is the item? What does the pattern look like? What math operation is the pattern using?”
Indicator 3R
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
The materials reviewed for STEMscopes Math Grade 3 provide a balance of images or information about people, representing various demographic and physical characteristics.
While there are not many pictures in the materials students use, the images provided do represent different skin tones, hairstyles, and clothing styles. Also, there are a wide variety of names used throughout the materials. Examples include:
Scope 2: Addition and Subtraction Fluency, Evaluate, Standards-Based Assessment, Question 6 states, “Hau got $150 from his friends for his birthday. Then, his grandma gave him $75 more. Finally, Hau spent $57 on a video game. How much money does Hau have now?”
Scope 9: Multiplication and Division Problem Solving, Evaluate, Standards-Based Assessment, Question 6 states, “Josie has gymnastics practice 3 times each week. Each practice lasts 3 hours. What is the total number of hours that Josie will practice in 8 weeks?”
Scope 10: Problem Solve Using the Four Operations, Elaborate, Spiraled Review, Student Handout, shows two cartoon characters depicting the two people in the story. Each person has different qualities. “It was no secret that Darcy’s mom did not enjoy the grocery store. She didn’t complain, but Darcy could see her mom’s shoulders slump when it was time to head to the store every Sunday afternoon. One weekend, Darcy and her twin brother Derek decided to help. They rode to the store together, and Darcy instructed her mom to give them half of the list. Darcy’s mom was hesitant at first, but the twins promised to stay together for safety. Their mom agreed to meet them at the checkout in half an hour. Darcy grabbed the list and Derek grabbed a cart and off they went! Neither understood why their mom did not find this fun. It was going to be a great adventure!”
Indicator 3S
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials reviewed for STEMscopes Math Grade 3 provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The program provides a list of language acquisition tools and resources. All components of the program are offered in both English and Spanish, including the Introductory Parent Letter and the Parent Letters within each Scope. Examples include:
Scope 5: Division Models, Parent Letter, Description states,“The parent is provided a breakdown of the concepts being learned in class, along with the vocabulary they can expect to hear.”
Teacher Toolbox, Multilingual Learners, Linguistic Diversity states, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” These resources include, but are not limited to: Working on Words, Sentence Stems/Frames, Integrated Accessibility Features, and Language Connections.
Indicator 3T
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The materials reviewed for STEMscopes Math Grade 3 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The program is available in Spanish, and includes a number of cultural examples within the materials. Examples include:
Scope 2: Addition and Subtraction Fluency, Elaborate, Spiraled Review–Family BINGO Night states, “Every year on the first day of summer, Jimmy’s family hosted BINGO night for Jimmy’s relatives. He had a LOT of relatives, so it made the start of summer even more fun! His whole family gathered at his house. People brought food and listened to music, danced, laughed, and talked. Everyone got to play BINGO—even little kids. There were prizes for the winners! Each year, Jimmy’s mom came up with a different theme. This year’s theme was the beach, and she let Jimmy design the BINGO cards with numbers up to 100. His siblings collected shells to mark the numbers on the cards Jimmy made. Soon it was BINGO time! Jimmy’s dad began calling out numbers and people began marking their boards, hoping to get a BINGO and win a prize. Jimmy thought it was one of the best days of the year!”
Scope 4: Multiplication Models, Elaborate, Career Connections–James Gosling states. “In 1977, James Gosling received his Bachelor of Science Degree in Computer Science from the University of Calgary. Shortly afterward, he received a doctoral degree (the highest college degree you can get) from Carnegie Mellon University. Gosling started working at Sun Microsystems in 1984. It was here that he would create a product that we still use today. James Gosling created a computer programming language called Java. At first, this program was made for programming home appliances, such as dishwashers and refrigerators. Over time, it has been used to program different applications we use with the internet. Java uses multiplication models to store data. One of the popular multiplication models the programming language uses is arrays. Arrays in Java are used to hold values for certain applications. They can also be used in many other ways in the programming language.”
Scope 5: Division Models, Elaborate, Career Connections–Mindy Weiss states, “Mindy Weiss had a career in making stationery—paper products such as cards and envelopes. The people who used her stationery saw that she was very creative, and they urged her to start an event-planning business. She took their advice and started Mindy Weiss Party Consultants in 1992. As an event planner, or someone who plans celebrations, she often has to use division models. If she is serving dinner at her event, she has to equally divide plates, spoons, forks, napkins, etc. among all her tables. Mindy is also known for her flower arrangements. When she purchases flowers, they come in bunches. She then has to equally distribute them to make different flower arrangements. Event planners use division models to help them decorate events in a way that is pleasing to the eye.”
Indicator 3U
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for STEMscopes Math Grade 3 provide supports for different reading levels to ensure accessibility for students.
The Teacher Toolbox has a tab entitled, Multilingual Learners, Linguistic Diversity, that highlights some of the options to help students at different reading levels. Examples include:
Teacher Toolbox, Multilingual Learners, Linguistic Diversity, Language Acquisition Progression states, “Each student’s journey to acquiring a new language is unique. A common misconception is that language acquisition is linear. However, the process is continuous and open-ended and it differs across language domains (listening, speaking, reading, and writing) depending on factors such as context or situation, with whom the learner is engaging, and how familiar the student is with the topic. The Proficiency Levels by Domain provide an overview of how students are applying language across different domains, as well as methods and tools that can be applied to provide support. The skills and strategies provided are meant to build upon each other as students progress through the levels.
Teacher Toolbox, Multilingual Learners, Linguistic Diversity, Resources and Tools states,“In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning. Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language. Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates. Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses. Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases. Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe –Try This at Home that students can engage in along with their families. This letter is written in two languages. Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains. Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain. Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills. Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language. Distance Learning Videos – Major skills and concepts are broken down in these student-facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math. Skills Quiz – This element utilizes just the numbers! This allows teachers to assess a student’s understanding without a language barrier. My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well. Daily Numeracy – This scope is not only a way for students to work on their flexibility in thinking about numbers and strategies, but it also gives the class an opportunity to listen and discuss math in a structured way as a community of learners.”
In addition, within each Explore in a Scope, Language Supports highlights suggestions to involve different reading levels. Examples include:
Scope 3: Rounding, Explore, Explore 1–Round on a Number Line, Language Acquisition Strategy states, “Students apply various learning strategies to obtain grade-level vocabulary. Park Your Question: Read Explore scenarios as a class. Give each student a sticky note and ask students to "park a question" on the sticky note. Ask them to use one of the following phrases: I understood ___, but ___ confused me. Can you explain ___ better? What is another way of saying ___? After writing the questions, have students trade with a peer and read their questions to each other. If the peer cannot answer the question, have the student stick it to the board to be answered by the teacher.”
Scope 4: Multiplication Models, Explore, Explore 4–Number Lines and Skip Counting, Language Acquisition Strategy states, “Students incorporate newly acquired vocabulary terms into communication within the classroom. Shopping for Multiples: Invite students to go "shopping for multiples." Give each student a sticky note. Invite students to write the following sentence on it: ____ comes in packs of ____. If I bought ____ packs, my multiples would be ____. My factors would be ____ and ____. My product would be ____. Encourage students to pick any one of their packing items during the Explore to fill out their sticky note. They can use the packing item as written, or construct their own. Invite students to share with someone in a different group.”
Scope 11: Area in Square Units, Explore, Explore 2–Counting Area in Square Units, Language Acquisition Strategy states, “Students identify components of the English language in their developing vocabulary. Ask the students what sounds they hear in the words length and width. They should recognize the -th. Relate these words to long and wide, and show students on a rectangle which dimension is which. Ask students if they can think of any other English words that end with -th that have to do with measuring. Examples might include the following words: depth, growth, fourth, fifth, breadth, etc.”
Indicator 3V
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include:
Scope 4: Multiplication Models, Explore, Explore One–Equal Groups, Procedure and Facilitation Points states, “Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters).DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means.Give students 1 or 2 minutes to discuss among themselves, and then invite them to share with the class.Student answers will vary but may include the following: We see four groups. Each group has three counters. All groups are equal. If we add all the counters together, we can get 12 counters.Distribute dry-erase markers and erasers to students.Ask students to write a sentence that describes what they see.Give students a few minutes to write their sentences. Walk around, looking out for students who are struggling.Ask students to share how they described the groups on the screen.Ask students to share their sentences and emphasize how each time a group is added, the total increases by the same number.”
Scope 11: Area in Square Units, Explore, Explore 2–Counting Area in Square Units, Preparation and Print Files, Student Journal, provides for students’ active participation in content through the use of manipulatives. The journal contains 12 rectangles and rectilinear shapes along with square tiles that represent a given square measurement for students to use to find the area of figures by counting. The Preparation section states: “Make one copy of the Student Journal and an Exit Ticket for each student. Make one copy of Task Cards, on card stock if possible. Make one copy of Station Printouts, and laminate or put in a sheet protector for durability. Place the Task Cards around the room in the form of a gallery walk.Place Station Printouts in an accessible place for students to tile.Place a set of square tiles at each station.Group students into pairs. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students.”
Scope 16: Compose and Decompose Fractions Into Units, Intervention, Procedure and Facilitation Points and Supplemental Aids–Fraction Strips, Print Files, Student Handout, Fraction Strips (1, 2, 3, 4, 6, 8) provides for students’ active participation in content through the use of manipulatives. Procedure and Facilitation Points: “The Student Handouts contain a variety of fraction strips. These can be used to reinforce the following fraction concepts:Identifying fractions, Explaining fractional parts, Counting fractional parts, Representing fractions, Composing and decomposing fractions, Finding equivalent fractions, Comparing fractions, Adding and subtracting fractions, Multiplying and dividing fractions. If possible, provide a laminated copy of the fraction strips for each student. The students may then use dry-erase markers to shade and identify various fractions.Encourage students to draw fraction strips at the top of their paper or assessment as a reminder when working with fractions.”
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for STEMscopes Math Grade 3 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and provide teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3W
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for STEMscopes Math Grade 3 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable.
The entire STEMscopes program is available online, and this review was conducted using the online materials. Throughout the Scopes and related activities and lessons, students are able to access the eBook for their grade level. Additionally, any assessments can be completed online. A tab on the website entitled, How to Use STEMscopes Math, provides videos the teacher can watch to learn about a variety of options available online. Virtual manipulatives are available throughout the K-8 program as well. Videos and Powerpoint presentations are available for the teacher to use when teaching a strategy to students. Teachers can also access blackline masters for exit tickets, assessments, and student tools on the website.
Indicator 3X
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for STEMscopes Math Grade 3 include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The program provides an opportunity for students to submit work through the website to the classroom teacher. Additionally, students can complete assessments digitally through the site. This allows some of the work/assessments to be auto scored by the site. Teachers can override any decisions made by the site’s scoring. Teachers also can send feedback on assignments and assessments to each student individually. In the Help section, the program provides a video as well as a handout to guide teachers through assigning and evaluating content. Examples include:
STEMscopes Help, Teacher Tools, STEMscopes Help Series, Assigning Content states, “Once you have classes in your STEMscopes account and your students are in your classes, you can assign material from STEMscopes to your students. They can then access under their own login and submit work to you online. Step 1: Log in and go to the Scopes tab and choose the lesson you want to assign content from. Step 2: Click on the student activity you want to assign. On that page, you will see the green Assign To Students button. Note that when you are in the orange teacher sections, you will not see that button. Click Assign to Students. Step 3: You will see a blank New Assignment page. You can now fill in the drop down menus for all the sections for your account. Then, assign to all or certain individual students within your section. Toggle your start/due dates (not required). Your assignment will not open (students see in their account) until that start date. You can then add labels that can help you/your students find certain assignments (see “Lab” example in help video). You can use your note for students portion (not required) to add notes or even to provide directions/guidance for your assignment and students will see this when they click on the assignment. Click on the green Add this Assignment button to assign. Student View of Content, Step 1: Once students log in, they will see their assignments from their teacher. Note the tags that help them search for a particular assignment. Students can click on an assignment to get started. Step 2: Once in an assignment, students can read, click to type their answers, use a drawing tool to answer questions, and click on multiple choice answers. Note students can enlarge text, use text to speech feature, highlight text, use comments & turn on dictionary mode for assistance. They can click the Save button to save their work and close, or if they’re finished, click the green Turn In button to submit. Teacher View of submitted content, Step 1: Once a teacher logs in, they will see the Student Activity feed on the lower right. It will show the name of the student(s) who completed work, title of the content, and time completed. Teachers can click on the assignment they want to view and/or grade. Step 2: After clicking on the assignment, teachers will see the information related to that assignment. If it was an auto-graded assignment the grade will appear along with how long it took the student to complete the assignment and when they turned it in. Teachers can then see individual results by clicking on the View Results button. Teachers can have students retake assignments by clicking on the Reset button. Teachers can also edit their assignment via the Edit Assignment button or archive the assignment via the Archive button.”
STEMscopes Help, Teacher Tools, STEMscopes Help Series, Evaluating Content states, “... Not all assignments are exactly the same. Some are autograded on the website and some are open-ended and the teacher will have to go in and assign a grade to them. Some are submitted for reference to show that they were done. One example of this is the Picture Vocabulary. Notice that it says “no” for graded, which means Picture Vocabulary doesn’t have anything for students to submit for grading (see the check mark as completed along with time spent and date completed). The Reset button will reassign it to the student and make it reappear on their end. A multiple choice assessment, however, is graded automatically. When a teacher clicks on the assignment, they’ll see all the information about the assignment: 1. Start/due dates; 2. Who assigned to; 3. Autograded checked off; 4. Average for the assignment; 5. The element assigned; 6. Which section is assigned to; 7. Option to view standards; 8. Option to Edit Assignment; 9. Archive the assignment. Teachers will see all students in the section, their status for the assignment, their grade (autograde feature), how long it took them to complete the assessment, when it was submitted, and buttons to see how they performed or to reset their assignment. When viewing results, you’ll notice the correct answers are green and the student in this example chose the correct answer. Teachers can go in and edit the credit awarded by simply clicking on the number and changing the grade (for example, to give partial credit). Teachers can also provide feedback to the students via the Note box. Once the teacher has made all notations, click the green Save button and the blue Close button. For whatever reason, to return the assessment to a student, click the red Return button and you can type in your instructions for the student and click the red Return button again. This student will update in your list with no grade and a gray Returned to student box. In this assignment snapshot, teachers can see all the questions on one screen, the percentage of correct/ incorrect answers, which standard(s) the question is attached to, and which students answered incorrectly. Missed standards will be listed at the bottom of the page. This allows the teacher to quickly see who needs help and which standard(s) may need reteaching/review. For other assignments, there are some things you have to grade by putting in a score or because they are open-ended questions. For example, this student below completed an assignment and submitted it to the teacher. The teacher will see a P in the grade column which means pending. The teacher needs to go in and assign a grade to the student’s work. To do this, click the gray Grade button to pull up the student’s work. There you can assign points based on the correct answers that are provided and make comments for the student. When done, click the green Save button and then the blue Complete button. Where you saw the P in the grade column should now change to a numerical grade based on the student’s answers. Students will not be able to see grades or notes until you click on the green Release Feedback button just above the list of their names on the main assignment page. The button will then turn orange and say Revoke Feedback. If a teacher needs to make changes, edit/add comments they can click that button and complete the process and release feedback when done. Teachers can view assignments given to multiple sections via the Students tab and click on the Assignments tab. Here, you’ll see a master list of assignments and how many sections that the assignment/assessment was given to. You can click on the items on the left to be taken to the main screen for each to begin grading/view performance.
Indicator 3Y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for STEMScopes Math Grade 3 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
There is a consistent design across the K-8 grade levels. For each grade level, the website is formatted in a similar way. Each grade level starts with a link to the Teacher Toolbox, which provides overarching information and guidance. That is followed by a link, STEMScopes Math: Common Core Kindergarten Teacher Resources. This link provides a Scope and Sequence for the grade level, vertical alignment charts, lesson planning guides, as well as assessment alignment documents. The following link, How to Use STEMScopes Math, provides videos for the teacher to view to learn about tools and options available within the program. Launch into Kindergarten provides an overview of the curriculum at the grade level. Fact Fluency and Daily Numeracy links follow. A link to each Scope in the grade level follows. The Scopes are set up with the same tabs: Home, Engage, Explore, Explain, Elaborate, Evaluate, Intervention, and Acceleration. The materials within these tabs are clearly labeled and concise. Assessments can be completely virtually or printed, and both styles provide ample work space.
The Help section of the web page provides guidance to teachers in navigating the site. Help, Curriculum Navigation, STEMScopes Help Series, Curriculum Navigation states, “There are a variety of resources available to teachers here to facilitate the instruction of the content. First of all, STEMScopes is built on the 5E model which is evident on the dropdown toolbar above. There is also I and A for Intervention and Acceleration. Above that you see labels for the lesson topic, grade level, and standard(s). On the right, you’ll see all the essential elements that are available to the teacher for implementing the lesson. The orange Ts are teacher elements, the blue Ss are for student elements, and the ESP means the element is available in Spanish. You can, however, visit some elements (this example is on the Explore tab, Explore Student Materials) and there will be a Ver en español button. Clicking on this will translate most of the page from English to Spanish. Another thing we offer is on the teacher elements. Our content is online where students can read, complete the work, and submit it to teachers within the site, but there are downloadable versions of the content too. This is accessed by clicking on the Print Version button on the right of the page. When you click on it, it will download/open as a digital PDF that you can make copies of or email to parents if needed. Also, you will see the customization bar at the top of every page. It floats down with you as you scroll and can help teachers and students with text sizing, text-to-speech, highlighting text, inserting comments to the page/to text, and defining words. You can get more in-depth tutorials for these features via their individual videos/help sheets. Each teacher element will have the following buttons: Assign to Students: Click to assign the element to your sections to work on in class, as homework or intervention. Add to Planner: Click to add the element to your planner when mapping out how you will teach the Scope. Bookmark Element: Click to bookmark the element to your home page for quick access. 1. Text sizing 2. Text-to-speech 3. Highlighting feature 4. Comment feature 5. Dictionary feature Finally, on the main Scopes page, you will see three resources that you can use. The Teacher Toolbox can help with your planning, lab resources, and lesson matrixes. The Visual Glossary provides a media library of science terminology for teachers and students. STEMcoach in Action is a free professional development resource for teachers. It’s worth noting that not all Scopes look the same and, consequently, some elements may look a little different depending on what grade level you’re subscribed to.”
Students materials are available in printed and eBook form. Both versions include appropriate font size, amount and placement of direction, and space on the page for students to show their mathematical thinking.
Indicator 3Z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for STEMscopes Math Grade 3 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed were digital only. In each grade level, a section entitled, How to Use STEMscopes Math, provides videos teachers can use to learn about the options available online. Each Scope also provides virtual manipulatives for teachers and students to use to enhance learning. Students can also complete assessments throughout the program online. Facilitation Tips within each Scope’s Teacher Guide provide helpful hints to the teacher as they progress through the Scope.