3rd Grade - Gateway 1

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)

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 \frac{a}{b} on a number line diagram by marking off a length \frac{1}{b} from 0. Recognize that the resulting interval has size \frac{a}{b} and that its endpoint locates the number \frac{a}{b} 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 \frac{4}{3} 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 \frac{3}{5} 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 \frac{1}{3} 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___.”

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.

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 5\times7 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., 9\times80, 5\times60) 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 8\times5=40, one knows 40\div5=8) 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 \frac{1}{b} 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.”

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.”

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 5\times7 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 8\times5=40, one knows 40\div5=8) 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.”