2nd Grade - Gateway 1

The materials reviewed for Open Up Resources K–5 Math Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The curriculum is divided into nine units, and each unit contains a written End-of-Unit Assessment for individual student completion. The Unit 9 Assessment is an End-of-Course Assessment and includes problems from across the grade. Examples from End-of-Unit Assessments include: 

• Unit 3, Measuring Length, End-of-Unit Assessment, Problem 3, “Here are the heights of some dogs, measured in inches: 20, 13, 16, 25, 20, 19, 20, 14, 16, 1. Label the line plot with numbers. 2. Use the dog heights to complete the line plot.” (2.MD.9)

• Unit 5, Numbers to 1,000, End-of-Unit Assessment, Problem 5, “Fill in each blank with <, =, or > to make a true statement. a. 511 ___151, b. 497+100+100___703, c. 138___118+10+10.” (2.NBT.3, 2.NBT.4)

• Unit 6, Geometry, Time, and Money, End-of-Unit Assessment, Problem 4, “a. Split the circle into 4 equal parts. b. Explain why 4 fourths of the circle is the whole circle.” An image of a circle is provided. (2.G.3)

• Unit 7, Adding and Subtracting within 1,000, End-of-Unit Assessment, Problem 6, “Find the value of each difference. Show your thinking. Use base-ten blocks if it helps. a. 528-315, b. 471-124, c. 600-594.” (2.NBT.7) 

• Unit 9, Putting It All Together, End-of-Course Assessment and Resources, Problem 8, “Diego has 34 cents. Mai has 19 more cents than Diego. How many cents do Mai and Diego have together? Explain or show your reasoning.” (2.NBT.5, 2.OA.1)

The instructional materials reviewed for Open Up Resources K–5 Math Grade 2 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in Grade 2 as students engage with all CCSSM standards within a consistent daily lesson structure. Per the Grade 2 Course Guide, “A typical lesson has four phases: a Warm-up, one or more instructional activities, the lesson synthesis, a Cool-down.” Examples of extensive work include:

• Unit 2, Adding and Subtracting Within 100,Section A, Lesson 4, and Section B, Lessons 5 and 6, engage students in extensive work with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction). Lesson 4, Center Day 1, Warm-up: Number Talk: Subtract 2 Digits, Launch and Student Work Time, students use the addition and subtraction facts they know to develop fluency with addition and subtraction within 100. In Launch, “Display one expression. ‘Give me a signal when you have an answer and can explain how you got it.’ 1 minute; quiet think time.” In Student Work Time, “Record answers and strategy. Keep expressions and work displayed. Repeat with each expression. Student Facing, Find the value of each expression mentally. 6-3, 66-3, 66-30, 66-33.” Lesson 5, Subtract Your Way, Activity 2, Student Work Time, students subtract a one-digit number from a two-digit number using base-ten blocks to represent the starting number and subtract an amount that requires them to decompose a ten, “‘Diego was representing numbers using base-ten blocks. Work with a partner to follow along and see what Diego discovered. Use your blocks first to show what Diego does. Then answer any questions.’ 8 minutes: partner work time. Monitor for students who talk about ‘exchanging’ or ‘trading’ a ten for ten ones.” Lesson 6, Compare Methods for Subtraction, Activity 2, Launch, students subtract numbers within 100 with and without decomposing a ten, “Groups of 2. Give each student a copy of the recording sheet and a set of the number cards. ‘We are going to learn a new way to play Target Numbers. You and your partner will start with 99 and race to see who can get closest to 0. First, represent 99 with base-ten blocks. When it’s your turn, draw a card. Decide whether you want to subtract that many tens or that many ones. Then show the subtraction with your blocks and write an equation on your recording sheet. Take turns drawing a card and subtracting until you play 6 rounds or one player reaches 0. After 6 rounds, whoever is closest to 0 is the winner.’ As needed, demonstrate a round with a student volunteer.”

• Unit 2, Adding and Subtracting within 100, Section C, Lesson 13; Unit 3, Measuring Length, Section A, Lesson 6; Unit 4, Addition and Subtraction on the Number Line, Section B, Lesson 12; and Unit 9, Putting It All Together, Section C, Lesson 10 engage students in the extensive work with 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, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Unit 2, Lesson 13, Story Problems and Equations, Activity 1, Student Work Time, students connect story problems to the equations that represent them and solve different types of story problems. “6 minutes: partner work time, Monitor for students who explain why more than one equation may match a story and how the equations match the quantities in the context of the story problem. 4 minutes: independent work time, Student Facing, a. Match each story problem with an equation. Explain why the cards match. b. Choose 2 story problems and solve them. Show your thinking.” Unit 3, Lesson 6, Compare Reptile Lengths in Story Problems, Activity 1, Student Work Time, students interpret and solve compare problems involving length. “‘Read each story with your partner. Then circle the diagram that matches on your own. When you have both selected a match, compare your choices and explain why the diagram matches the story. Then solve on your own.’ 10 minutes: partner work time Student Facing, 1. Lin's pet lizard is 62 cm long. It is 19 cm shorter than Jada's. How long is Jada's pet lizard? a. Whose pet is longer? b. Circle the diagram that matches the story. (Four tape diagrams are displayed.) c. Solve. Show your thinking. Jada’s pet lizard is ___ cm long. 2. Diego and Mai have pet snakes. Mai’s snake is 17 cm longer than Diego’s. Mai’s snake is 71 cm. How long is Diego’s pet snake? a. Whose pet is shorter? b. Circle the diagram that matches the story. (Four tape diagrams are displayed.” c. Solve. Show your thinking. ​​Diego’s pet snake is ___ cm long.” Unit 4, Lesson 12, Equations with Unknowns, Activity 1, Student Work Time, students solve addition and subtraction problems within 100 with the unknown in all positions. “‘Now you will have a chance to solve riddles to find a missing number, and then represent your thinking on a number line. You and your partner can take turns reading the riddle, while the other person follows along on the number line.’ 12 minutes: partner work time, Student Facing, Solve riddles to find the mystery number. For each riddle: Write an equation that represents the riddle and write a ? for the unknown. Write the mystery number. Represent the equation on the number line. a. I started at 15 and jumped 17 to the right. Where did I end? b. I started at a number and jumped 20 to the left. I ended at 33. Where did I start? c. I started on 42 and ended at 80. How far did I jump? d. I started at 76 and jumped 27 to the left. Where did I end? e. I started at a number and jumped 19 to the right. I ended at 67. Where did I start? f. I started at 92 and ended at 33. How far did I jump?” Each number includes space to write the equation and the mystery number. Unit 9, Lesson 10, What’s the Question? Activity 2, Student Work Time, students work with given numbers and use a story context to determine what question was answered. “‘You are going to look at some student work and figure out what question the student is trying to answer.’ Read the problem. 5 minutes: independent work time, 5 minutes: partner discussion, Student Facing, Clare picked 51 apples. Lin picked 18 apples and Andre picked 19 apples. Here is some student work showing the answer to a question about the apples.” For a, a tape diagram showing 51, 18, 19 above and a question mark below is pictured. The equations 51+19=70 and 70+18=88 are also shown, “What’s the question? Explain how you know.” For b, a double tape diagram is shown with 19, 18, and ? on the top and 51 on the bottom. Equations, 19+18=37 and 51-37=14 are shown, “What’s the question? Explain how you know.“

• Unit 6, Geometry, Time, and Money, Section D, Lesson 18 engages students in extensive work with 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?). Lesson 18, Money Problems, Warm-up: How Many Do You See: Groups of Coins, students use subitizing or grouping strategies to describe the images they see. “Groups of 2. ‘How many coins do you see? How do you see them?’ Flash the image. 30 seconds: quiet think time” In Activity 1, Student Work Time, students solve Add To and Take From problems in the context of money. “‘Lin and Diego went to the school store to get a few supplies. Solve each problem on your own, and then compare with your partner.’ 5 minutes: independent work time, 5 minutes: partner discussion, Monitor for students who cross out the coins needed to find how much was left. Monitor for students who write equations. Student Facing, a chart is provided that shows items and costs: pack of pencils 75¢, pencil sharpener 35¢, eraser 45¢, pens 18¢, 1. Lin has these coins. (1 nickel, 2 quarters, and 3 dimes) a. How much money does Lin have for supplies? b. If Lin buys an eraser, how much money will she have left? Show your thinking. 2. Diego has these coins: (2 nickels, 4 dimes, 5 pennies, and 1 quarter) a. How much money does Diego have for supplies? b. If Diego buys a pack of pencils, how much money will he have left? Show your thinking.” 

The instructional materials provide opportunities for all students to engage with the full intent of Grade 2 standards through a consistent lesson structure. According to the Grade 2 Course Guide, “The first event in every lesson is a Warm-up. Every Warm-up is an Activity Narrative. The Warm-up invites all students to engage in the mathematics of the lesson… After the Warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class… After the activities for the day, students should take time to synthesize what they have learned. This portion of class should take 5-10 minutes before students start working on the Cool-down…The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson.” Examples of meeting the full intent include:

• Unit 4, Addition and Subtraction on the Number Line, Section A, Lesson 1 and Unit 5, Numbers to 1,000, Section B, Lesson 9 engage students with the full intent of 2.MD.6 (Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram). Unit 4, Lesson 1, Whole Numbers on the Number Line, Warm-up: Notice and Wonder: Rulers and Number Lines, Launch, students make sense of a new representation, a number line, and how it is similar to and different from a ruler, “Groups of 2. Display the image. ‘What do you notice? What do you wonder?’ 1 minute: quiet think time.” Unit 5, Lesson 9, Compare Numbers on the Number Line, Warm-up: Estimation Exploration: Hundreds, students practice the skill of making a reasonable estimate for a point on a number line based on the location of other numbers represented, “Groups of 2. Display the image. ‘What number could be represented by the point on the number line? What is an estimate that’s too high? Too low? About right?’ 1 minute: quiet think time.” An image of a number line with 300 and 400 marked on the line is shown.

• Unit 5, Numbers to 1,000, Section A, Lessons 4, 5, and 6 engage students with the full intent of 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form). Lesson 4, Write Three-digit Numbers, Activity 1, Launch and Student Work Time, students write the number from a riddle with hundreds, tens, and ones, and represent the value as a three-digit number. In Launch, “Groups of 2. Give students access to base-ten blocks. ‘I have 4 hundreds, 3 ones, and 2 tens.’ ‘Which of these shows the total value written as a three-digit number? Explain how you know.’ Display 432, 234, 423. 30 seconds: quiet think time, 1 minute: partner discussion, Share responses.” In Student Work Time, “‘You are going to solve number riddles using base-ten blocks.’ As needed, demonstrate the task with a student. ‘Take turns reading the clues, while your partner uses blocks to make the number. Make sure you agree before adding each number to the table.’ 10 minutes: partner work time, If students finish early, ask them to write their own riddles and trade them with other groups to solve. Monitor for students who recognize they need a zero when writing the three-digit number in places where there were no tens or no ones. Student Facing, Solve each riddle and write the three-digit number. Use the table to help you organize the digits. 1. I have 2 ones, 7 tens, and 6 hundreds. 2. I have 3 ones, 5 tens, and 2 hundreds. 3. I have 7 hundreds, 5 ones, and 3 tens. 4. I have 5 hundreds, no tens, and 9 ones. 5. I have 4 ones, 6 tens, and 3 hundreds. 6. I have 8 tens, 1 hundred, and no ones.” Lesson 5, Expanded Form of Numbers, Cool-down, Student Facing, “1. Represent the number 375 as the sum of hundreds, tens, and ones. Expanded form: ___ 2. Represent 200+40+7 as a three-digit number. Three-digit number: ___.” Lesson 6, Represent Numbers in Different Ways, Activity 1, students use words to represent three-digit numbers, “Groups of 2. Display the anchor chart that shows the different forms of 253. Complete the chart together. ‘This number has ___ hundreds, ___ tens, and ___ ones.’ (2, 5, 3) The expanded form of this number is ___. The three-digit number is ___. These other forms can help us think about writing a number using number names. ‘What is this number?’ (two hundred fifty-three) Write the number name as the students say two hundred fifty-three. ‘Fifty-three has a hyphen because numbers with tens and ones representing 21 through 99 use a hyphen to show the 2 parts of a two-digit number.’” In Activity 2: Represent the Numbers, Student Work Time, “‘Each group will be given a number. Work with your group to represent that number in different ways.’ Display the chart from the first activity. ‘Think about how you might organize your representations and make sure that each group member does their fair share. Your group should represent the number as a three-digit number, with a base-ten diagram, using expanded form, and using words.’ Give each group a three-digit number to represent. If time permits, groups can represent the number in the additional ways suggested. 12 minutes: small-group work time, Student Facing, Represent the number on your poster. Be sure to represent the number using: a three-digit number, a base-ten diagram, expanded form, words.” Cool-down: Words and Other Ways, Student Facing, “a. Represent 147 with words. b. Represent 147 in one other way.”

• Unit 8, Equal Groups, Section A, Lessons 3 and 4, and Section B, Lesson 9 engage students in the full intent of 2.OA.3 (Determine whether a group of objects [up to 20] has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends). Lesson 3, Is It Odd or Even, Activity 2, Student Work Time, students are given a set of cards and work in pairs to determine if the number of objects shown on the cards are even or odd, “When it’s your turn, pick a card. Decide whether it shows an even or odd number of objects. Then, explain your choice to your partner. Place each card into the even group or the odd group. If your partner agrees, continue sorting your cards. If your partner disagrees, listen to their explanations and make a decision together about how to sort the card.” Lesson 4, Decompose Even and Odd Numbers, Cool-down, students determine if the number of objects is even or odd, and then create an equation with two equal addends if possible, “1. a. Decide whether the number of dots is even or odd. Circle your choice. Write an equation with two equal addends for each image if you can. 1. even or odd. Dot images. 2 rows of 5. ___=___+___. 2. a. Decide whether the number of dots is even or odd. Dot images. 13 dots. b. Write an equation with two equal addends for each image if you can ___=___+___.” Lesson 9, A Sum of Equal Addends, Activity 3, Student Work Time, students use counters to determine the correct number in the array and then match their solution to expressions that represent that array. “‘Now you will find the total number of counters in arrays using a method that makes sense to you. Then match each array to expressions.’ 6 minutes: independent work time, Monitor for the array that generates the largest variety of different ways students find the total number of counters in each array, including skip-counting or adding on based on the number in each row or column. Student facing, 1.a. How many counters are there in all? (Students see 6 yellow and 6 red counters.) b. Explain how you found the total number of counters. c. Circle 2 expressions that represent the array. 3+3+3+3, 3+3+3, 4+3, 4+4+4, 4+4+4+4. 2.a. How many counters are there in all? (Students see 8 yellow and 6 red counters) b. Explain how you found the total number of counters. c. Circle 2 expressions that represent the array. 2+2+2+2+2+2+2, 6+6, 7+7, 2+2+2+2+2.”

The materials reviewed for Open Up Resources K–5 Math Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65% of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 7 out of 9, approximately 78%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 122 out of 155, approximately 79%. The total number of lessons devoted to major work of the grade include: 114 lessons plus 8 assessments for a total of 122 lessons.

• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 131 out of 134, approximately 98%.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 79% of the instructional materials focus on major work of the grade.

The materials reviewed for Open Up Resources K–5 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. These connections are listed for teachers on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed on a document titled “Scope and Sequence”. Examples of connections include:

• Unit 2, Adding and Subtracting Within 100, Section A, Lesson 1, Activity 1, Student Work Time, connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories…) to the major work of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction). Students use information from a bar graph to compare different methods for solving addition and subtraction problems within 100. Student Facing states, “Use the bar graph to answer the questions. a. What is the total number of students that chose popcorn or pretzels? Show your thinking. b. How many more students chose nachos than chose popcorn? Show your thinking.” A bar graph shows popcorn, pretzels, and nachos with values between 16 and 32.

• Unit 6, Geometry, Time, and Money, Section A, Lesson 3, Activity 2, Launch, connects the supporting work of 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Sizes are compared directly or visually, not compared by measuring. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes) to the major work of 2.MD.1 (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tape). Students recognize and draw shapes that have a specific number of sides, corners, and lengths in order to deepen their understanding that shapes in the same category can share many attributes and look different. The Launch states, “Groups of 2, Give students access to rulers. Display the attribute table. ‘We have been learning about attributes of shapes. This table shows some of the attributes of shapes we have been thinking about, such as number of sides, numbers or types of corners, and specific lengths of sides.’ Draw or display a rectangle with two sides that are 3 inches long. ‘What attributes do you think were picked from this table to draw this shape?’ (4 sides, 4 corners, all corners are square corners, 2 sides are the same length. It’s either 2 sides are 2 inches or 2 sides are 3 inches long). Circle the attributes that students identify on the attribute table.” A table with different attributes is shown.

• Unit 8, Equal Groups, Section A, Lesson 5, Cool-down connects the supporting work of 2.OA.3 (Determine whether a group of objects [up to 20] has an odd or even number of members; write an equation to express an even number as a sum of two equal addends) to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies). Students reason about even and odd numbers and use their knowledge of addition to consider sums without calculating. Student Facing states, “a. Elena has 8 counters. Does she have an even or odd number of counters? Explain or show your reasoning. b. Without adding, explain which one of these expressions represents an odd number. A. 4+4, B. 8+1, C. 8+2.”

The instructional materials for Open Up Resources K–5 Math Grade 2 meet expectations for including 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 can be listed for teachers in one or more of the four phases of a typical lesson:  instructional activities, lesson synthesis, or Cool-down. Examples of connections include:

• Unit 2, Adding and Subtracting within 100, Section A, Lesson 3, Activity 2, Student Work Time, connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Students solve different story problems by adding or subtracting within 100 without composing or decomposing a ten. Student Facing states, “Solve each story problem. Show your thinking. a. There were 65 students in the monkey house. 23 left to see the hippos. How many are still in the monkey house? b. 58 students went to see the bears. 27 students went to see the lions. How many more students went to see the bears than the lions? c. Some birds were in cages outside of the bird house. 34 birds were inside the birdhouse. In all, there were 88 birds. How many were in the cages outside?” 

• Unit 3, Measuring Lengths, Section B, Lesson 11, Cool-down connects the major work of 2.MD.B (Relate addition and subtraction to length) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Students solve subtraction problems within 100 with the unknown in all positions. Student Facing states, “Priya had a piece of ribbon that was 74 inches long. She cut off 17 in. How long is Priya’s ribbon now? Show your thinking. Use a diagram if it helps. Don’t forget the unit in your answer.” 

• Unit 6, Geometry, Time, and Money, Section B, Lesson 9, Activity 2 connects the supporting work of 2.G.A (Reason with shapes and their attributes) to the supporting work of 2.MD.C (Work with time and money). Students work with fractions and compare the fractional amounts to the value of a quarter (money). Student Facing states, “Match each story with the image that it represents. (Students are given 4 fractional pictures.) a. Noah ate most of the pie. He left a quarter of the pie for Diego. ___ b.Lin gave away a half of her pie and kept a half of the pie for herself. ___ c. Tyler cut a pie into four equal pieces. He ate a quarter of the pie. ___ d. Mai sliced the pie to share it equally with Clare and Priya. ___ 2. In Story D, Mai sliced the pie to share it equally with Clare and Priya. a. How much of the pie will they each get? ___ b. How much of the pie will they eat in all? ___ 3. Now you try. a. Partition the circle into four equal pieces. Shade in a quarter of the circle red. Shade in the rest of the circle blue. How much of the circle is shaded? ___ b. Partition the circle into 2 equal pieces. Shade one half of the circle blue. Color the other piece yellow. How much of the circle is yellow? ___ How much of the circle is shaded? ___.”

• Unit 9, Putting It All Together, Section C, Lesson 12, Cool-down connects the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract) to the major work of 2.OA.A (Represent and solve problems involving addition and subtraction). Students create an addition story problem based on a given addition equation. Student Facing states, “Tyler writes the equation 24+37=61 to answer a question about the picture. Write a story problem with a question that Tyler’s equation could answer.”

The instructional materials reviewed for Open Up Resources K–5 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 Course Guide, Scope and Sequence Section, within the Dependency Diagrams which are shown in Unit Dependency Diagram, and Section Dependency Diagram. An arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section. While future connections are all embedded within the Scope and Sequence, descriptions of prior connections are also found within the Preparation tab for specific lessons and within the notes for specific parts of lessons. 

Examples of connections to future grades include:

• Unit 3, Measuring Length, Section B, Lesson 9, Preparation connects the work of 2.MD.2 (Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen) and 2.MD.3 (Estimate lengths using units of inches, feet, centimeters, and meters) to work with unit fractions in later grades and work with measurement unit conversions in grades 4 and 5. Lesson Narrative states, “In an earlier lesson, students were introduced to the inch as a length unit in the customary system. They developed a benchmark for an inch and measured objects with an inch ruler. In this lesson, students use the length of a 12-inch ruler to develop an understanding of the length of 1 foot. They use a ruler as a benchmark for estimating the length of a foot. Throughout the lesson, students make decisions about which tools and which length units to use when measuring (MP5). They compare measurements for the same object in inches and feet and generalize that the more units are needed to measure the same length if you use a smaller length unit. This concept is a foundation for future work with measurement and their work with unit fractions in later grades. Although the activities encourage students to notice that 1 foot is the same length as 12 inches, students are not expected to convert units in grade 2. Students express larger units in terms of smaller units in grade 4 and larger units in terms of smaller units in grade 5.”

• Unit 6, Geometry, Time, and Money, Section B, Lesson 9, Preparation connects the work of 2.G.3 (Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape) to the work with fraction equivalence in Grade 3. Lesson Narrative states, “In previous lessons, students partitioned circles and rectangles into halves, thirds, and fourths and identified an equal piece of different shapes as a half of, third, of, or fourth of the shape. In this lesson, students continue to practice partitioning circles and describe halves, thirds, and quarters of circles using the language a half of, a third of, and a quarter of to describe a piece of the shape. They also use this language to describe the whole shape as a number of equal pieces. Students recognize that a whole shape can be described as 2 halves, 3 thirds, or 4 fourths. This understanding is the foundation for students' work with a whole and fraction equivalency in grade 3.”

• Unit 8, Equal Groups, Section B, Lesson 12, Warm-up connects 2.G.2 (Partition a rectangle into rows and columns of same-size squares and count to find the total number of them) and 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 with concepts of area in 3.MD.C. Narrative states, “The purpose of this Estimation Exploration is to practice the skill of making a reasonable estimate. Students consider how the placement of the first 2 squares can help them think about the total number of squares needed to fill the rectangle (MP7). These understandings will be helpful later when students will need to partition rectangles into equal-size squares.”

Examples of connections to prior knowledge include:

• Unit 1, Adding, Subtracting, and Working with Data, Section A, Lesson 1, Preparation, connects 2.OA.2 (Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.) to the previous work of adding and subtracting within Grade 1. Lesson Narrative states, “Students develop fluency with addition and subtraction within 10 in grade 1. This lesson provides an opportunity for formative assessment of students' fluency within 10, including recognizing sums with a value of 10.”

• Grade 2 Course Guide, Scope and Sequence, Unit 2, Adding and Subtracting Within 100, Unit Learning Goals connect 2.NBT.B (Use place value understanding and properties of operations to add and subtract) to previous work with addition and subtraction in Grade 1. Narrative states, “Previously, students added and subtracted numbers within 100 using strategies they learned in grade 1, such as counting on and counting back, and with the support of tools such as connecting cubes. In this unit, they add and subtract within 100 using strategies based on place value, the properties of operations, and the relationship between addition and subtraction.”

• Unit 5, Numbers to 1,000, Section A, Lesson 1, Preparation connects 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones) to work with place value concepts in Grade 1 and previous work composing and decomposing tens in Grade 2. Lesson Narrative states, ​”In grade 1, students were introduced to a ten as a unit made of 10 ones. They used that understanding to represent two-digit numbers and add within 100. Students used connecting cubes to make and break apart two-digit numbers. In previous units in grade 2, students used the words compose and decompose as they made and broke apart tens when they added and subtracted within 100. In this lesson, students are introduced to the unit of a hundred. Building on the understanding that they can use 10 ones to compose a ten, students learn they can compose a hundred using 10 tens.”