2nd Grade - Gateway 1

The materials reviewed for STEMscopes Math Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into 15 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 2: Represent Numbers to 1,000, Evaluate, Standards-Based Assessment, Question 4, “How many hundreds are represented in the number 963? 6, 9, 0, 3” (2.NBT.1a)

• Scope 3: Numbers on a Number Line, Evaluate, Standards-Based Assessment, Question 3, “William drove to a music festival. He drove 25 miles and then stopped to get gas. He drove 13 more miles and arrived at the music festival. Use the number line to find out how many miles WIlliam drove to the music festival. Write your answer in the box below and explain your reasoning.” (2.MD.6) 

• Scope 7: Addition and Subtraction Problem Solving, Evaluate, Standards-Based Assessment, Question 4A, “Hemsworth Elementary had 28 jump ropes in the gym. The coach threw 24 of the ropes away because they were broken. He bought 16 new jump ropes. How many jump ropes does Hemsworth Elementary have now? Part A: Write an equation for the problem in the box. Use the number line below to show how you solved the problem.” (2.OA.1)

• Scope 13: Area, Evaluate, Standards-Based Assessment, Question 8, students are provided with a 12 by 7 grid with 25 square units shaded. “How many square units are shaded in the grid below? Write your answer in the space.”(2.G.2)

The materials reviewed for STEMscopes Math Grade 2 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 2 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 2: Represent Numbers to 1,000, engages students in extensive work to meet the full intent of 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.) Explore, SkillBasics–Different Ways to Write a Number (Standard Form, Word Form, Expanded Form, Pictorial Model), Ways to Write a Number Work Mat, students are given space for “Standard Form, Picture Form, Expanded Form, and Word Form.” Teacher Guide, Procedure and Facilitation Points, Teachers walk the students through writing numbers in these 4 different ways with several examples. “14. After practicing writing numbers in four ways as a whole group, assign each student a partner. Give a set of Number Cards to each pair of students. Instruct students to choose one card at a time. Each card has a number written in one of the four ways they just learned about. Instruct students to write the number in the other three ways on their work mats and then compare their work with their partners to check for understanding. Have students complete all of the Number Cards.” Explore, Explore 3–Representing Numbers in Different Ways, Teacher Guide, Procedure and Facilitation Points,  “10. Give each student a copy of the Student Journal, and ask students to write their numbers in four ways: standard form, pictorial model (of their original blocks or the regrouped version), expanded form, and word form in their group number’s section of the handout. 11. Allow the groups to share their total numbers. As they share their numbers, pause and allow the rest of the students to complete the Student Journal in the appropriate group number’s section with their group.”

• Scope 9: Arrays, Engage, Hook–Making Bracelets, Preparation and Procedure and Facilitation Points, engages students in extensive work to meet the full intent of 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) After the class completes the two Explore lessons for the Scope, students go back to try and solve the problem in the Hook that required them to create an array for the beads used to make a bracelet. Preparation, “Plan to show the video. Part II, Place 9 red, 10 blue, and 12 yellow plastic beads in a resealable bag for each student. Print a copy of the Student Handout for each student.” Procedure and Facilitation Points, Part II: Post-Explore, (DOK questions have sample answers provided after the question), “1. After students have completed the Explore activities for this topic, show the phenomena video again, and repeat the situation. 2. Discuss the following: a. DOK–1 What information do we know? Fiona has a bag of red, blue, and yellow beads. She needs to sort by color and then arrange each color in an array with no more than 5 rows and 5 columns. b. DOK–1 What information do we need to find out? What is the total number of each color bead? 3. Give each student a copy of the Student Handout and a bag of beads. Instruct students to sort the beads by color and then arrange each color into a rectangular array with no more than 5 rows or 5 columns. 4. Ask students to draw a pictorial model of each array and write an equation to find the total number of each color bead on their copies of the Student Handout. 5. Discuss the following: a. DOK–3 What strategy did you use to make counting each color of bead easier? I sorted by color and then arranged the beads in equal rows and columns. b. DOK–1 What are you trying to find? The total number of each color bead, c. DOK–3 How did you make your model? Red = 3 rows of 3; blue = 5 rows of 2 or 2 rows of 5; yellow = 3 rows of 4 or 4 rows of 3. d. DOK–3 How can we use addition to create a number sentence to describe your model? Answers will vary depending on the color of the bead. For example, blue =2+2+2+2+2 or 5+5. e. DOK–3 Is there another strategy you can use to find the total number of beads? I can skip count or just count the beads one at a time. f. DOK–2 How many beads of each color are there in all? There are 9 red beads, 10 blue beads, and 12 yellow beads.”

• Scope 14: Time, engages students in extensive work to meet the full intent of 2.MD.7 (Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.)  Explore, Explore 1–A.M. and P.M., Student Journal, “A.M. and P.M. Use the timeline you created to complete the following table.” Students are given a table labeled A.M. Activities and P.M. Activities. “Reflect: Is noon in the a.m. or p.m.? Explain. ____ Is midnight in the a.m. or p.m.? Explain. ____.” Explore 4 - Digital and Analog Clocks, Student Journal, “Record all the start and end times below by drawing in the clock hands and writing the digital times. Circle a.m. or p.m.” Students are given analog clocks without hands and space for writing the digital time. “Reflect: Look at the time on the clock to the right. How can you write the time 3 ways?” Students are given an analog clock showing 12:45. Time Task Cards, Question 3, “2nd-Grade Jump-Rope Contest. Start. Quarter past 11. End. 10 minutes until 12.”

• Scope 15: Data Analysis, engages students in extensive work to meet the full intent of 2.MD.9. (Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.)  Explore 4– Organizing Data Using Line Plots, Teacher Guide, Procedure and Facilitation Points, “Part I: Collecting Group Data 1.Read the following scenario: Our class has just been entered in a long-jump contest. Each participant will have a chance to see how far he or she can jump. The jumps will be measured to the nearest whole inch. The data will be recorded and used to create a line plot for the contest judges to help with their scoring. Can you collect the data and create a line plot for the judges? … Part II: Collecting Class Data 1. After students have completed Part I, bring the groups together to share their data with the rest of class. Have each group share their collected data with the class. As each group shares, write the lengths on the board or a sheet of chart paper. … Part III: Create a Line Plot 1. Have students create a line plot on Part III of the Student Journal by using the data from Part II. Students should label their horizontal scales in whole units starting with the shortest length and labeling consecutively until the longest length is reached.”

The materials reviewed for STEMscopes Math Grade 2 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 9.5 out of 14, approximately 68%.

• The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 123 out of 180, approximately 68%. 

• The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 123 out of 180, approximately 68%.

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 68% of the instructional materials focus on the major work of the grade.

The materials reviewed for STEMscopes Math Grade 2 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 8: Money, Explain, Show What You Know–Part 5: Solving Word Problems Involving Bills and Coins, connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions…) Students solve word problems involving money. Student Journal, “Part 5: Solving Word Problems Involving Bills and Coins, Solve each problem. Show your work by writing a number sentence with a symbol for the unknown and a number sentence that includes the solution. 3. During December, Jake and Emma earned $57 altogether. If Emma earned $21 in December, how much did Jake earn? Solution: ___”

• Scope 9: Arrays, Explore, Explore 1–Arrays with Concrete Objects connects the supporting work of 2.OA.4. (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) to the major work of  2.NBT.2. (Count within 1000; skip-count by 5s, 10s, and 100s.) Students count squares in a rectangular array, and write an equation. Student Journal, “Part 1, Count the number of objects in the array. Circle the strategy you used to count the objects. Write an equation to represent the total number of objects, and then label the package for the toy factory. Package #1, Counting one by one, Skip counting, Repeated addition, Equation ___”

• Scope 13: Area, Explain, Show What You Know–Part 1: Sorting and Identifying Bills and Coins, connects the supporting work of  2.G.2. (Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.) to the major work of  2.NBT.2. (Count within 1000; skip-count by 5s, 10s, and 100s.) Students count squares in a rectangular array, and mark if the student skip counted. Student Journal, “Area Part 1: Covering Surfaces Area Part 1 1 Part 1: Covering Rectangles with Squares Count the total number of square tiles it takes to cover each rectangle in Dana’s home on the next page. Record the total in the table below.”

The materials for STEMscopes Math Grade 2 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 6: Addition and Subtraction Strategies, Explore, Explore 1–Addition and Subtraction with Two 2-Digit Numbers, Student Journal and Task Cards connects the Number & Operations in Base Ten domain to the Operations & Algebraic Thinking domain as students, “Estimate a solution, and then solve each problem using your mental math strategies. Show your work in each box. Write your solution and explain your strategies in words.” The Task Card 1, “Carlos placed a bag of dog food that costs $25 in the cart. Santos placed a $33 bottle of dog shampoo in the cart. How much have the boys spent on groceries so far?”

• Scope 8: Money, Explore 5–Solving Word Problems Involving Bills and Coins, Procedure and Facilitation Points, connects the supporting work of 2.MD.C (Work with time and money) to the supporting work of 2.MD.D (Represent and interpret data). Students work in groups to solve real-world problems collecting money for purchased items. “1. Read the following scenario: You have been hired by a local fruit stand to collect customers’ money when they buy some delicious fruit. Sometimes the customers pay using only dollar bills, and sometimes they pay using only coins. Can you solve each word problem to determine how much money each customer paid, or how much change they should receive? 2. Direct students’ attention to the Task Cards and the bag of bill and coin manipulatives. Allow students a few moments to discover the manipulatives and experience how they work with their partners. 3. Instruct students to read each Task Card and solve using the bill and coin manipulatives. 4. Monitor and talk with students as needed to check for understanding by using guiding questions. a. DOK-1 What information do you know? b. DOK-1 What information do you need to find out? c. DOK-2 Which manipulatives will you use to solve? d. DOK-3 What strategy could you use to solve? 5. Give each student a copy of the Student Journal. Ask students to show their work in the space provided on the table and then write their solutions. Students can show their work using drawings and/or equations. 6. When students have completed the Task Cards and the Student Journal, bring the class together as a whole group.”

• Scope 9: Arrays, Explore, Explore 1–Array with concrete objects, Station 4, connects the Geometry domain to the Operations & Algebraic Thinking domain as students reason about 3 rows of 2 square tiles and equal groups. Teachers are prompted to monitor students’ thinking to check for understanding with the following questions, “DOK-1 How many objects make up your array? DOK-2 How did you count the objects? DOK-3 Is there another way to count the objects?”

• Scope 12: Length, Explore, Explore 3–Solving Problems with Lengths, Exit Ticket, connects the Measurement & Data domain to the Operations & Algebraic Thinking domain as students measure the sides of a bulletin board and add to find the total perimeter. Students see a bulletin board on the paper they need to measure. “The teacher wants to put a border all around the edges of her classroom bulletin board. How much border is needed? Use a ruler to measure the total amount of border in centimeters the teacher will need to buy. The teacher will need to buy about ___ total centimeters of border to put around the edges of her bulletin board.”

The materials reviewed for STEMscopes Math Grade 2 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 5: Fractions, Home, Content Support, Background Knowledge links 2.G.A to 3.NF.3, “In third grade, students compare two fractions referring to the same whole, with the same numerator or the same denominator according to their sizes, and they acquire an understanding of equivalent fractions. They will explain the equivalence of fractions and compare fractions by reasoning about their sizes or their locations on a number line.”

• Scope 9: Array, Home, Content Support, Coming Attractions, connects 2.OA.4. (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) to work in grade 3.  “In third grade, students use a variety of strategies, such as repeated addition, skip counting, arrays, area models, and jumps on a number line, to solve contextual problems involving multiplication. Third-grade students make connections between multiplication and division and apply this knowledge to word problems. Third graders work with plane figures, covering rectangular shapes with square tiles, and develop an understanding of square units.“ 

• Scope 10: Two-Dimensional Shapes, Home, Scope Overview, Teacher Guide, Future Expectations, connects 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.) to future in grade 3. “In third grade, students use precise language to identify and describe the properties of two-dimensional shapes as they make generalizations about properties that are shared between categories of shapes. Properties are used to determine whether a shape is a quadrilateral, and within that category, students classify and draw subcategories, such as parallelograms, rectangles, and squares.”

Examples of connections to prior grades include:

• Scope 6: Addition and Subtraction Strategies, Engage, Accessing Prior Knowledge, Description and Procedure and Facilitation Points, connects 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method...) to work in grade 1. “Description, Students apply various strategies to solve addition and subtraction problems up to 20. Procedure and Facilitation Points, 1. Give each student a copy of the Student Handout. 2. Read the following scenario: Josiah bought some crickets to feed to his pet lizard. There are already 4 crickets in a jar at home, and Josiah is bringing 12 more from the pet store. Josiah wants to know how many crickets he has to feed his lizard now. You have some counting manipulatives on your table if you need them. I’d like you to use the room on your paper to show me two strategies you would use to solve this problem.3. Circulate around the room and observe student work. Some strategies students might use include:a. Counting out cubes to represent the crickets and finding the total b. Drawing a picture to show how many crickets there are altogether c. Using a number sentence and counting on to put 4 and 12 together d. Applying mental math to add the ones place together and then combining that with the tens place  4. Look out for students who are simply writing the answer, and encourage them to show you how they are arriving at that answer. Students can also be encouraged to show more than two strategies if they are fast finishers.”

• Scope 9: Arrays, Home, Content Support, Background Knowledge, connects 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) to work in grades K and 1. “In kindergarten, students added 2 one-digit numbers within 10. First-grade students investigated the length of an object as the number of same-sized units that, when laid end to end with no gaps or overlaps, reach from one end of the object to the other. First graders used and explained a variety of counting strategies, reasoned about the sums and differences of basic facts through sums of 10, and explored the properties of operations.”

• Scope 12: Length, Home, Scope Overview, Teacher Guide, Background Knowledge, links 2.MD.A (Measure and estimate lengths in standard units.) to 1.MD.A (Measure lengths indirectly and by iterating length units.) “In first grade, students used nonstandard measuring tools to measure length. They illustrated that the length of an object is the number of same-sized units of length that, when laid end to end with no gaps or overlaps, reach from one end of the object to the other.