3rd Grade - Gateway 2

The materials reviewed for Open Up Resources K–5 Math Grade 3 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials develop conceptual understanding throughout the grade level. According to the Grade 3 Course Guide, Design Principles, conceptual understanding is a part of the design of the materials. Balancing Rigor states, “There are three aspects of rigor essential to mathematics: conceptual understanding, procedural fluency, and the ability to apply these concepts and skills to mathematical problems with and without real-world contexts. These aspects are developed together and are therefore interconnected in the materials in ways that support student understanding. Opportunities to connect new representations and language to prior learning support students in building conceptual understanding. Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Additionally, Purposeful Representations states, “Across lessons and units, students are systematically introduced to representations and encouraged to use representations that make sense to them. As their learning progresses, students are given opportunities to make connections between different representations and the concepts and procedures they represent.” Examples include:

• Unit 1, Introducing Multiplication, Section B, Lesson 9, Activity 2, Student Work Time, students develop conceptual understanding as they represent situations involving equal groups in a way that makes sense to them. Student Facing states, “Represent each situation. a. There are 4 people wearing shoes. Each person is wearing 2 shoes. b. There are 2 boxes of markers. Each box has 10 markers. c. There are 3 basketball teams. Each team has 5 players.” (3.OA.1)

• Unit 2, Area and Multiplication, Section B, Lesson 7, Warm-up, Student Work Time and Activity Synthesis, students develop conceptual understanding of measurement units, larger square units can be useful in situations involving larger areas. Students see a picture of a girl on a playground holding a large square. In Student Work Time, Student Facing states, “What do you notice? What do you wonder?” Activity Synthesis states, “If needed, ‘What could you measure with this square?’ (You could measure the area of big areas, like the playground.) ‘Why might you want this square instead of square centimeters or square inches?’ (It takes fewer squares of this size to measure an area that is a lot larger like a playground or a room.)” (3.MD.6)

• Unit 8, Putting It All Together, Section A, Lesson 2, Warm-up, Student Work Time, students develop conceptual understanding as they compare fractions on a number line. An image of four different number lines with fractions is provided and Student Facing states, “Which one doesn’t belong?” (3.NF.2)

According to the Grade 3 Course Guide, materials were designed to include opportunities for students to independently demonstrate conceptual understanding, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “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. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:

• Unit 1, Introducing Multiplication, Section B, Lesson 11, Cool-down, students demonstrate conceptual understanding as they write expressions for equal groups. Student Facing states, “There were 6 envelopes. Each envelope had 2 notes in it. Write a multiplication expression to represent the situation. Explain or show your reasoning. Create a drawing or diagram if it’s helpful.” (3.OA.1)

• Unit 2, Area and Multiplication, Section B, Lesson 8, Cool-down, students demonstrate conceptual understanding as they reason about the area of a rectangle. Students are provided a drawing of a rectangle with tick marks rather than a completed grid. Student Facing states, “The tick marks on the sides of the rectangle are 1 foot apart. What is the area of the rectangle? Explain or show your reasoning.” (3.MD.7b)

• Unit 5, Fractions as Numbers, Section A, Lesson 3, Activity 2, Student Work Time, students demonstrate conceptual understanding of fractions as they match fractions to shaded diagrams. Student Facing states, “Your teacher will give you a set of cards for playing Fraction Match. Two cards are a match if one is a diagram and the other a number, but they have the same value. 1. To play Fraction Match: Arrange the cards face down in an array. Take turns choosing 2 cards. If the cards match, keep them and go again. If not, return them to where they were, face down. You can’t keep more than 2 matches on each turn. After all the matches have been found, the player with the most cards wins. 2. Use the cards your teacher gives you to create 4 new pairs of cards to add to the set. 3. Play another round of Fraction Match using all the cards.” (3.NF.1)

The materials reviewed for Open Up Resources K–5 Math Grade 3 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

According to the Grade 3 Course Guide, Design Principles, Balancing Rigor, “Warm-ups, practice problems, centers, and other built-in routines help students develop procedural fluency, which develops over time.” Examples include: 

• Unit 1, Introducing Multiplication, Section A, Lesson 4, Activity 2, Student Work Time, students develop procedural skill and fluency with data as they create a scaled picture graph. Student Work Time states, “‘Represent the data that you collected in your own scaled picture graph where each picture represents 2 students.’ 10 minutes: independent work time, Circulate as students work: Encourage them to include a title, category labels, and key. Pay attention to how students are grouping by 2. Support students with questions they may have (especially around representing odd number amounts).” Student Facing states, “Represent our survey data in a scaled picture graph where each picture represents 2 students.” (3.MD.B)

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section C, Lesson 16, Warm-up, Student Work Time, students develop fluency as they use strategies for finding the products of 4 and 6 as they relate to products of 5. Student Facing states, “Find the value of each expression mentally. 5\times7, 4\times7, 6\times7, 4\times8.” (3.OA.7) 

• Unit 7, Two-dimensional Shapes and Perimeter, Section B, Lesson 7, Warm-up, Student Work Time, students develop procedural skill and fluency as they use strategies they have learned to add multi-digit numbers. Student Facing states, “Decide whether each statement is true or false. Be prepared to explain your reasoning. 123+75+123+75=100+100+70+70+5+5+3+3, 123+75+123+75=(2\times123)+(2\times75), 123+75+123+75=208+208, 123+75+123+75=246+150.” (3.NBT.2)

According to the Grade 3 Course Guide, materials were designed to include opportunities for students to independently demonstrate procedural skill and fluency, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “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. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section B, Lesson 10, Cool-down, students demonstrate procedural skill and fluency as they use an algorithm to subtract within 1,000. Student Facing states, “Use an algorithm of your choice to find the value of 419-267.” (3.NBT.2) 

• Unit 4, Relating Multiplication to Division, Section B, Lesson 9, Activity 2, Student Work Time, students demonstrate fluency as they identify patterns in multiplication. Student Work Time states, “‘In the right column, work independently to write down at least two multiplication facts you can figure out because you know the given multiplication fact in the left column.’ 3–5 minutes: independent work time. ‘Now, share the facts that you found with your partner. Record any facts that your partner found that you didn’t find. Be sure to explain your reasoning.’” Student Facing states, “a. In each row, write down at least two multiplication facts you can figure out because you know the given multiplication fact in the left column. Be prepared to share your reasoning. If I know…  2\times4, then I also know 4\times2, 4\times4, 2\times8.” (3.OA.7) 

• Unit 8, Putting It All Together, Section D, Lesson 15, Activity 1, Student Work Time, students demonstrate procedural skill and fluency as they reason about subtraction and write a subtraction expression. Student Work Time states, “‘How would you find the value of each expression, without writing? For each expression, think of at least two ways. Then, share your thinking with your group.’ Reiterate to students that they are to consider how someone might reason about each difference, rather than only finding the value. 4 minutes: independent work time. 4 minutes: small-group discussion.” Student Facing states, “Here are three subtraction expressions. 600-400, 600-399, 500-399. 1. Think of at least two different ways to find the value of each difference mentally. 2. Write a fourth subtraction expression whose value can be found using one of the strategies you thought of.” (3.NBT.2)

The materials reviewed for Open Up Resources K–5 Math Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. 

According to the Grade 3 Course Guide, Design Principles, Balancing Rigor, “Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Multiple routine and non-routine applications of the mathematics are included throughout the grade level, and these single- and multi-step application problems are included within Activities or Cool-downs. 

Students have the opportunity to engage with applications of math both with teacher support and independently. According to the Grade 3 Course Guide, materials were designed to include opportunities for students to independently demonstrate application of grade-level mathematics, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “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. Students’ responses to the Cool-down can be used to make adjustments to further instruction.”

Examples of routine applications of the math include:

• Unit 1, Introducing Multiplication, Section B, Lesson 12, Activity 1, Launch and Student Work Time, students solve a real-world problem involving multiplication. Launch states, “Groups of 2. MLR5 Co-Craft Questions. Display only the problem stem, ‘Tyler has 3 boxes.’ without revealing the question. ‘Write a list of mathematical questions that could be asked about this situation.’ (What’s in the boxes? How many things are in the boxes? How many things does he have altogether?) 2 minutes: independent work time. 2–3 minutes: partner discussion. Invite several students to share one question with the class. Record responses. ‘What do these questions have in common? How are they different?’ Reveal the task (students open books), and invite additional connections.” In Student Work Time, Student Facing states, “Tyler has 3 boxes. He has 5 baseballs in each box. How many baseballs does he have altogether? Show your thinking using diagrams, symbols, or other representations.” (3.OA.3)

• Unit 3, Wrapping Up Addition and Subtraction within 1000, Section D, Lesson 19, Activity 2, Student Work Time, students solve a multi-step real-world problem and then write an equation to represent the problem. Student Work Time states, “‘Take some independent time to work on this problem. You can choose to solve the problem first or write the equation first.’ 5–7 minutes: independent work time, Monitor for different ways students: write an equation, represent the problem, such as by using a tape diagram, decide their answer makes sense, such as thinking about the situation or by rounding.” Student Facing states, “Kiran is setting up a game of mancala. He has a jar of 104 stones. From the jar, he takes 3 stones for each of the 6 pits on his side of the board. How many stones are in the jar now? a. Write an equation to represent the situation. Use a letter for the unknown quantity. b. Solve the problem. Explain or show your reasoning. c. Explain how you know your answer makes sense.” (3.OA.8)

• Unit 7, Two-dimensional Shapes and Perimeter, Section C, Lesson 10, Cool-down, students solve a real-world problem involving the perimeter of a rectangle. Student facing states, “Lin is building a fence around her rectangular garden. A diagram is shown. The area of the garden is 36 square feet. How many feet of fencing material will she need to enclose the whole garden?” (3.MD.8)

Examples of non-routine applications of the math include:

• Unit 4, Relating Multiplication to Division, Section C, Lesson 17, Activity 2, Student Work Time, students develop understanding of multiplication and its relation to division to solve real-world problems. Student Work Time states, “‘Work independently to solve these problems and write an equation with a letter for the unknown quantity to represent each situation. You can choose to solve the problem first or write the equation first.’ 5–7 minutes: independent work time’ Share your solutions and your equations with your partner. Also, tell your partner if you think their solutions and equations make sense or why not.’5–7 minutes: partner discussion.” Student facing states, “For each problem: 1. Write an equation to represent the situation. Use a letter for the unknown quantity. 2. Solve the problem. Explain or show your reasoning. a. Kiran is making paper rings each day to decorate for a party. From Monday to Thursday he was able to complete 156 rings. Friday, Kiran and 2 friends worked on making more rings. Each of them made 9 more rings. How many rings did they make over the week? b. Mai has 168 muffins. She put 104 of the muffins in a basket. She packed the rest of the muffins into 8 boxes with the same number of muffins. How many muffins were in each box? c. There are 184 cups on a table. Three tables with 8 people at each table come up to get drinks and each use a cup. How many cups are on the table now?” (3.OA.8)

• Unit 5, Fractions as Numbers, Section B, Lesson 6, Activity 1, Launch and Student Work Time, students solve a non-routine problem as they partition a number line that extends beyond one. Launch states, “Groups of 2, ‘Today we are going to partition number lines to locate unit fractions. Take a minute to look at how Clare, Andre, and Diego have partitioned their number lines into fourths.’ 1-2 minutes: quiet think time.” in Student Work Time, Student Facing states, “Three students are partitioning a number line into fourths. Their work is shown. Whose partitioning makes the most sense to you? Explain your reasoning.” Clare’s number line partitioned into halves;  Andre’s number line partitioned into fourths; and Diego’s number line partitioned into fifths are shown. (3.NF.2)

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section C, Lesson 15, Activity 1, Launch and Student Work Time, students solve a real-world problem by using concepts of time, weight, and volume. Launch states, “Groups of 2, ‘We’re going to solve some problems about a day at the fair. What are some things you could do during a day at the fair?’ (go on rides, walk around, eat fair food, look at some of the animals) 30 seconds: quiet think time. Share responses. Give each group tools for creating a visual display.” In Student Work Time, Student Facing states, “You spent a day at the fair. Solve four problems about your day and create a poster to show your reasoning and solutions. a. You arrived at the fair! Entry to the fair is $9 a person. You went there with 6 other people. How much did it cost your group to enter the fair? b. How did you start your day? (Choose one.) You arrived at the giant pumpkin weigh-off at 11:12 a.m. and left at 12:25 p.m. How long were you there? You spent 48 minutes at the carnival and left at 12:10 p.m. What time did you get to the carnival? c. What was next? (Choose one.) You visited a barn with 7 sheep. The sheep drink 91 liters of water a day, each sheep drinking about the same amount. How much does each sheep drink a day? You visited a life-size sculpture of a cow made of butter. The butter cow weighs 273 kilograms, which is 277 kilograms less that the actual cow. How much does the actual cow weigh? 4. Before you went home . . . You stopped for some grilled corn on the cob. On the grill, there were 54 ears of corn arranged in 9 equal rows. How many ears of corn were in each row?” (3.MD.1, 3.MD.2, 3.OA.3)

The materials reviewed for Open Up Resources K–5 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, or application include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section A, Lesson 4, Activity 2, Launch and Student Work Time, students develop procedural skill and fluency as they use the addition algorithm. Launch states, “Groups of 2, Give students access to base-ten blocks. ‘Now you are going to have a chance to try the algorithms that Lin and Han used in the last activity. Take a minute to think about which algorithm you want to use for each problem.’” In Student Work Time, Student Facing states, “Try using an algorithm to find the value of each sum. Show your thinking. Organize it so it can be followed by others. a. 475+231, b. 136+389, c. 670+257.” (3.NBT.2) 

• Unit 5, Fractions as Numbers, Section A, Lesson 3, Activity 1, Launch and Student Work Time, students extend their conceptual understanding to read and write fractions that represent images. Launch states, “Groups of 2, Display the table. ‘Let's look at the first table. The first three images are the squares we saw earlier. Let's name them again. (One-fourth, three-fourths, four-fourths) Let’s complete the second row of the table together. This is the square we just worked with in the Warm-up and the number that represents the total amount shaded is already in the table. How many of the parts are shaded? (Three) What is the size of each part? Write ‘three-fourths’ to record how we read this fraction.’” In Student Work Time, Student Facing states, “Each shape in each row of the table represents 1. Use the shaded parts to complete the missing information in the table. Be prepared to explain your reasoning.” A table is provided with the headings: number of shaded parts, size of each part, word name for the shaded parts, and number name for the shaded parts. (3.NF.1)

• Unit 7, Two-dimensional Shapes and Perimeter, Section B, Lesson 9, Cool-down, students apply their understanding of perimeter to solve a real-world problem. Student Facing states, “A rectangular swimming pool has a perimeter of 94 feet. If it is 32 feet on one side, what are the lengths of the other three sides? Explain or show your reasoning.” (3.MD.8)

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:

• Unit 1, Introducing Multiplication, Section C, Lesson 19, Cool-down, students use all three aspects of rigor, conceptual understanding, procedural skill and fluency, and application, as they use an equation to represent an array. Student Facing states, “Clare has 3 rows of baseball cards. Each row has 10 cards. How many cards does she have? a. Write an equation with a symbol for the unknown number to represent the situation. b. Find the number that makes the equation true. Explain or show your reasoning.” (3.OA.3)

• Unit 4, Relating Multiplication to Division, Section D, Lesson 19, Activity 2, Launch and Student Work Time, students develop conceptual understanding alongside procedural skill and fluency as they represent division within 100. Launch states, “Groups of 2-4, Give base-ten blocks to each group. Ask students to keep their materials closed. ‘Use base-ten blocks to find the value of 60\div5.’ 1–2 minutes: independent work time.” In Student Work Time, Student Facing states, “1. Jada and Han used base-ten blocks to represent 60\div5. Make sense of Jada’s and Han’s work. a. What did they do differently? b. Where do we see the value of 60\div5 in each person’s work? 2. How would you use base-ten blocks so you could represent these expressions and find their value? Be prepared to explain your reasoning. a. 64\div4: Would you make 4 groups or groups of 4? b. 72\div6: Would you make 6 groups or groups of 6? c. 75\div15: Would you make 15 groups or groups of 15?” (3.OA.2, 3.OA.7)

• Unit 7, Two-dimensional Shapes and Perimeter, Section B, Lesson 6, Activity 1, Launch and Student Work Time, students use procedural fluency and apply their understanding of perimeter of shapes to solve a non-routine real-world problem. Launch states, “Groups of 4, Give each group a copy of the blackline master and 25–50 paper clips. ‘Make a prediction: Which shape do you think will take the most paper clips to build?’ 30 seconds: quiet think time. Poll the class on whether they think shape A, B, C, or D would take the most paper clips to build.” Student Work Time states, “Work with your group to find out which shape takes the most paper clips to build. You may need to take turns with the paper clips.” In Student Work Time, Student Facing states, “Your teacher will give you four shapes on paper and some paper clips. Work with your group to find out which shape takes the most paper clips to build. Explain or show how you know. Record your findings here. Draw sketches if they are helpful.” (3.MD.8)

The materials reviewed for Open Up Resources K–5 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 they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

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 support of the teacher and independently throughout the units. Examples include:

• Unit 2, Area and Multiplication, Section B, Lesson 10, Activity 1, Student Work Time and Activity Narrative, students solve a real-world problem involving area. In Student Work Time, Student Facing states, “Noah is painting a wall in a community garden. The wall is shaped like a rectangle. A diagram of the wall is shown here. Paint is sold in 3 different sizes: A small container will cover 3 square meters. A medium container will cover 10 square meters. A large container will cover 40 square meters. What should Noah buy? Explain your reasoning.” Activity Narrative states, “The activity includes a rectangle where the side lengths are labeled. When students solve problems with multiple solutions and have to choose and justify a solution, they make sense of problems and persevere in solving them (MP1).” 

• Unit 6, Measuring Length, Time, Liquid, Volume, and Weight, Section D, Lesson 13, Cool-down, students make sense of problems involving weight and justify their reasoning. Preparation, Lesson Narrative states, “In this lesson, students solve problems involving weight in two Information Gap activities. They interpret descriptions of situations involving all four operations and in which one or more quantities are missing. Students determine the information that they need to answer the questions and then reason about the solutions.” Student facing states, “The winning pig weighed 48 kilograms when his owner decided to raise him to show at the fair. At the fair weigh-off, the pig weighed 124 kilograms. How much weight did the pig gain? Explain or show your reasoning.”

• Unit 7, Two-dimensional Shapes and Perimeter, Section B, Lesson 6, Warm-up, Launch, Student Work Time, and Activity Narrative, students make sense of perimeter concepts. Students are given an image of a shape and paper clips. Launch states, “Groups of 2, Display the image, ‘What do you notice? What do you wonder?’ 1 minute: quiet think time.” In Student Work Time, Student Facing states, “What do you notice? What do you wonder?” Activity Narrative states, “The purpose of this Warm-up is for students to visualize the idea of perimeter and elicit observations about distances around a shape. It also familiarizes students with the context and materials they will be working with in the next activity, where they will use paper clips to form the boundary of shapes and compare or quantify their lengths.”

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 support of the teacher and independently throughout the units. Examples include:

• Unit 1, Introducing Multiplication, Section A, Lesson 2, Activity 2, Student Work Time and Activity Narrative, students reason abstractly and quantitatively as they interpret data from a bar graph. Student Work Time states, “‘Now you’re going to use your bar graph to decide if statements are true or false.’ 1–2 minutes: independent work time.” In Student Work Time, Student Facing states, “1. Decide if each statement is true or false about how our class gets home. Explain your reasoning to your partner. a. More students walk than go home any other way. b. More students ride home on a bus than in a car. c. Fewer students walk home than ride their bikes. d. More students walk or ride their bikes than ride in a van. 2. Fill in the blanks as directed by your teacher, then answer each question. a. ‘How many more students ___  than ___?’ b. ‘How many more students ___  or ___ than ___?’” Activity Narrative states, “When students use expression, equations, or describe adding or subtracting to find how many more or less, they show they can decontextualize and recontextualize the data to make sense of and solve the problems (MP2). You will generate the questions students answer in this task from the class graph.”

• Unit 5, Fractions as Numbers, Section A, Lesson 4, Activity 2, students use diagrams to represent the fractional amount in a given situation. Activity Narrative states, “The purpose of this activity is for students to use diagrams to represent situations that involve non-unit fractions. The synthesis focuses on how students partition and shade the diagrams and how the end of the shaded portion could represent the location of an object. When students interpret the different situations in terms of the diagrams they reason abstractly and quantitatively (MP2).” Student Work Time states, “‘In the activity, each strip represents the length of a street where Pilolo is played. Work independently to represent each situation on a diagram.’ 3–5 minutes: independent work time. ‘With a partner, choose one of the situations and make a poster to show how you represented the situation with a fraction strip. You may want to include details such as notes, drawings, labels, and so on, to help others understand your thinking.’ Give students materials for creating a visual display. 5–7 minutes: partner work time.” In Student Work Time, Student Facing states, “Here are four situations about playing Pilolo and four diagrams. Each diagram represents the length of a street where the game is played. Represent each situation on a diagram. Be prepared to explain your reasoning. a. A student walks \frac{4}{8} the length of the street and hides a rock .b. A student walks \frac{2}}{3} the length of the street and hides a penny. c. A student walks \frac{3}{4} the length of the street and hides a stick. d. A student walks \frac{5}{6} the length of the street and hides a penny. e. This diagram represents the location of a hidden stick. About what fraction of the length of the street did the student walk to hide it? Be prepared to explain how you know.”

• Unit 6, Measuring Length, Time, Liquid, Volume, and Weight, Section A, Lesson 2, Warm-up, Activity Narrative, Launch, and Student Work Time, students practice estimation strategies with measurements. Activity Narrative states, “The purpose of this Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information. The Warm-up also draws students' attention to a length between a full inch and one-half of an inch, preparing students to work with such lengths later.” Launch states, “Groups of 2, Display the image. ‘What is an estimate that’s too high? Too low? About right?’ 1 minute: quiet, think time.” In Student Work Time, Student Facing states, “What is the length of the paper clip?” A paper clip is shown next to a ruler, and the length is between the 1 and 2 inch mark on the ruler.

The materials reviewed for Open Up Resources K–5 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. 

Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Activity Narratives and Lesson Activities’ Activity Narratives).

According to the Grade K Course Guide, Design Principles, Learning Mathematics By Doing Mathematics, “Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics or being told what needs to be done. Doing mathematics can be defined as learning mathematical concepts and procedures while engaging in the mathematical practices - making sense of problems, reasoning abstractly and quantitatively, making arguments and critiquing the reasoning of others, modeling with mathematics, making appropriate use of tools, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning. By engaging in the mathematical practices with their peers, students have the opportunity to see themselves as mathematical thinkers with worthwhile ideas and perspectives.”

Students construct viable arguments, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 2, Area and Multiplication, Section B, Lesson 10, Cool-down, students construct viable arguments as they find the area of a rectangle. Student Facing, “Kiran bought two pieces of fabric. The black fabric is 9 yards by 2 yards. The purple fabric is 4 yards by 5 yards. Which piece of fabric has the larger area? Explain or show your reasoning.”

• Unit 2, Area and Multiplication, Section C, Lesson 12, Activity 2, Activity Narrative, Launch, and Student Work Time, students find the area of a “figure” by decomposing the figure into rectangles and then critique the reasoning of others. Activity Narrative states, “Some students may partition diagonally to split the figure into what looks like 2 symmetrical parts, or cut the figure up into more than 2 parts. These are both acceptable ways of finding the area. Ask students who partition diagonally to find the area in the way they partitioned, but then encourage them to find a second way that has partitions on one of the grid lines. As students look through each others' work, they discuss how the representations are the same and different and can defend different points of view (MP3).”  Launch states, “Groups of 2. Display the image of the gridded figure. ‘What do you notice? What do you wonder?’ (Students may notice: It looks like 2 rectangles. It looks like a big rectangle with a chunk missing. There are squares. Students may wonder: What is this shape called? Could we find the area of the shape? How would we find the area?) 1 minute: quiet think time. Share responses. ‘This isn’t a shape that we have a name for like a square or triangle. Because of this, we’ll call it a “figure” as we work with it in this activity. This word will be helpful in describing other shapes that we don’t have a name for. Talk with your partner about different ways you could find the area of this figure.’ 1 minute: partner discussion.” In Student Work Time, Student Facing states, “What do you notice? What do you wonder? Find the area of this figure. Explain or show your reasoning. Organize it so it can be followed by others.”

• Unit 5, Fractions as Numbers, Section C, Lesson 11, Activity 1, Student Work Time and Activity Narrative, students construct a viable argument and critique the reasoning of others when they reason about fraction equivalence. In Student Work Time, Student Facing states, “1. The diagram represents 1.​​​​​​ a. What fraction does the shaded part of the diagram represent? b. Jada says it represents \frac{4}{8}. Tyler is not so sure. Do you agree with Jada? If so, explain or show how you would convince Tyler that Jada is correct. If not, explain or show your reasoning.” Activity Narrative states, “In the first problem, students construct a viable argument in order to convince Tyler that \frac{4}{8} of the rectangle is shaded (MP3).” 

Students critique the reasoning of others, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 1, Introducing Multiplication, Section A, Lesson 6, Activity 1, Student Work Time and Activity Narrative, students construct a viable argument and critique the reasoning of others as they create a scaled bar graph. In Student Work Time, Student Facing states, “Here is a collection of pattern blocks. Mai, Noah, and Priya want to make a bar graph to represent the number of triangles, squares, trapezoids, and hexagons in the collection. Mai says the scale of the bar graph should be 2. Noah says the scale of the bar graph should be 5. Priya says the scale of the bar graph should be 10. a. Who do you agree with? Explain your reasoning. b. Use the scale that you chose to create a scaled bar graph to represent the collection of pattern blocks.” Activity Narrative states, “They consider three students’ ideas, choose a scale of 2, 5, or 10, and create a scaled bar graph to represent the categorical data. Students must justify why they agree that a particular scale would be best. During the activity and whole-class discussion, students share their thinking and have opportunities to listen to and critique the reasoning of their peers (MP3).” 

• Unit 3, Wrapping Up Addition and Subtraction within 1,000, Section B, Lesson 9, Cool-down, students solve a subtraction problem using the algorithm and then critique the work of others. Preparation, Lesson Narrative states, “Previously, students learned to record subtraction using an algorithm in which the numbers are written in expanded form. They made connections between the structure and steps of the algorithm to those of base-ten diagrams that represent the same subtraction. In this lesson, students take a closer look at the algorithm and use it to find differences. They also examine a common error in subtracting numbers when decomposition of a place value unit is required. When students discuss shown work, they construct viable arguments and critique the reasoning of others (MP3).”  Student Facing states, (Students see the thinking of a student on the problem with regrouping.)  “Andre found the value of  739-255. His work is shown. Explain how he subtracted and the value he found for 739-255.”

• Unit 4, Relating Multiplication to Division, Section C, Lesson 15, Activity 2, Activity Narrative and Student Work Time, students construct a viable argument and critique the reasoning of others when they participate in a gallery walk and agree or disagree with other students’ work. Activity Narrative states, “The purpose of this activity is for students to see how other students solved one of the problems that involves a factor of a teen number. While students look at each other’s work, they will leave sticky notes describing why they think the answer does or does not make sense (MP3). The synthesis will look specifically at examples of how students used the area diagram to represent the problem.” Student Work Time states, “‘As you visit the posters with your partner, discuss what is the same and what is different about the thinking shown on each poster. Also, leave a sticky note describing why you think the solution does or does not make sense.’ 8 - 10 minutes: gallery walk. Monitor for different uses of the area diagram to highlight, specifically, a fully gridded area diagram with no labels and no decomposition, a gridded area diagram that was gridded, but also decomposed into parts or labeled along the sides or in the parts of the rectangle, a partitioned rectangle that was drawn with no grid, but labeled with side lengths or the area of the parts of the rectangle.”

The materials reviewed for Open Up Resources K–5 Math Grade 3 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose 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 they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Instructional Routines and Lesson Activities’ Instructional Routines).

MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, model situations with appropriate representations, and describe what they do with the model and how it relates to the problem. Students model with mathematics as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 4, Relating Multiplication to Division, Lesson 22, Section D, Activity 1, Student Work Time, students use multiplication and division to determine the arrangement of strawberry plants in a garden. Preparation, Lesson Narrative states, “Students model with mathematics (MP4) as they consider constraints, make assumptions and decisions about quantities, think about how to represent the relationships among quantities, and check their solutions in terms of the situation.” Student Work Time states, “2 minutes: independent work time. 10 minutes: partner work time. Monitor for students who: write multiplication or division expressions or equations, are able to represent the same situation with both multiplication and division.” In Student Work Time, Student Facing states, “For each situation, draw a diagram and write an equation or expression. 1. A strawberry patch has 7 rows with 8 strawberry plants in each row. a. How many strawberry plants are in the patch? b. To grow strawberries in the best way, the rows should be 4 feet apart. Each plant in the row should be 2 feet apart. How long and wide is the strawberry patch? c. You can harvest 12 strawberries per plant. How many strawberries will grow in each row? 2. With your partner, take turns explaining where you see the numbers in the expression or equation you wrote in your diagram.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section D, Lesson 16, Warm-up, Launch, Student Work Time, and Lesson Narrative, students make decisions on how to make a good carnival game. Students see a picture of a carnival game using coins and marbles. Launch states, “Groups of 2, Display the image. ‘What do you notice? What do you wonder?’ 1 minute: quiet think time” Student Work Time states, “‘Discuss your thinking with your partner.’ 1 minute: partner discussion, Share and record responses.”  Preparation, Lesson Narrative states, “When students make choices about quantities and rules, analyze constraints in situations, and adjust their work to meet constraints, they model with mathematics (MP4).”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section D, Lesson 13, Activity 1, Student Work Time and Instructional Routine, students apply what they have learned about perimeter and area to design a small park. Instructional Routine states, “The purpose of this Student Work Time is to provide students an opportunity to apply what they’ve learned about perimeter and area to design a small park. Since diagonal lines that connect the dots are not one length unit, students should use vertical and horizontal lines to design the park. When students make and describe their own choices for how they represent real-world objects, they model real-world problems with mathematics (MP4).” Student Work Time states, “‘Work independently to design your small park.’ 5 - 7 minutes: independent work time. ‘You can work with a partner or small group for the last few minutes or continue working on your own. Even if you choose to work alone, be available if your partner wants to think through something together.’ 3 - 5 minutes: partner, small group, or independent work time.”  In Student Work Time, Student facing states, “Your teacher will give you some dot paper for drawing. a. The distance from 1 dot to another horizontally or vertically represents 1 yard. Connect dots on the grid horizontally or vertically to design a small park that has 5 of these features: 1. basketball court  2. soccer goal  3. swings  4. a slide  5. an open area  6. picnic table  7. water play area  8. skate park  9. a feature of your choice  b. Describe the area and the perimeter of 3 features in the park.”

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the units to support their understanding of grade-level math. Examples include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section B, Lesson 7, Activity 1, students use appropriate tools strategically to subtract within 1,000. In Student Work Time, Student Facing states, “Find the value of each difference in any way that makes sense to you. Explain or show your reasoning. a. 428-213. b. 505-398. c. 394-127.”  Instructional Routine states, “Students may also use a variety of representations, which will be the focus of the Student Work Time synthesis. Students who choose to use base-ten blocks or number lines to represent their thinking use tools strategically (MP5).”

• Unit 4, Relating Multiplication to Division, Section C,Lesson 13, Cool-down, students use appropriate tools strategically when they multiply within 100. Student Facing states, “There are 6 bags of oranges and each bag has 11 oranges. How many oranges are in the bags? Show your thinking using objects, a drawing, or a diagram.” Students should also be encouraged to use strategies and representations from the previous section.” This outlines the goal of working with tools throughout this lesson.

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section A, Lesson 4, Activity 1, Student Work Time and Instructional Routine, students analyze a line plot as a tool for representing data. Students are given the heights of seedlings in inches on a line plot. In Student Work Time, Student Facing states, “a. Write 3 statements about the measurements represented in the line plot. b. What questions could be answered more easily with the line plot than the list? Write at least 2 questions.” Instructional Routine states, “When students recognize how organizing data helps to read the information and to answer questions, they learn that line plots are a powerful tool to present data (MP5).”

The materials reviewed for Open Up Resources K–5 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 they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

Students have many opportunities to attend to precision and the specialized language of math, in connection to grade-level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 2, Area and Multiplication, Section A, Lesson 4, Activity 1, Student Work Time and Activity Synthesis, students use specific language and precision to describe the rectangle they create. Activity Narrative states, “The purpose of this activity is for students to create and describe rectangles of a certain area. Students work in groups of 2. One partner creates a rectangle and describes it, and the other partner creates a matching rectangle based on the description. Then students compare how their rectangles are the same and different. Students should describe their rectangle to their partner without revealing the total number of squares they used, so that the focus is on understanding the rectangular structure. In the synthesis, students share language that helped them understand the rectangle their partner built. When students revise their language to be more precise in the descriptions of their rectangle, they attend to precision (MP6).” Student Work Time states, “‘The goal of this activity is to get both partners in a group to draw the same rectangle without looking at each other’s drawing. ‘If you are partner A, draw a rectangle and describe it to your partner. You can’t tell them how many squares you used to draw your rectangle. If you are partner B, draw the rectangle that you think your partner is describing and then compare the drawings. After you finish describing and drawing the first rectangle, switch roles and repeat.’ 10–12 minutes: partner work.”  In Student Work Time, Student Facing states, “a. Can you and your partner draw the same rectangle without looking at each other's drawing?  Partner A: Draw a rectangle on one of the grids provided. Describe it to your partner without telling them the total number of squares. Partner B: Draw the rectangle your partner describes to you. b. Place your two rectangles next to each other. Discuss: What is the same? What is different? c. Switch roles and repeat.”  Activity synthesis states, “‘What language did your partner use that was most helpful for you to draw the same rectangle they drew?’ (The number of squares in each row or column and the number of rows or columns.)”

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section B, Lesson 8, Cool-down, students use accuracy and precision when they use base-ten diagrams to make sense of a written subtraction algorithm. Student Facing states, “Explain how the diagram matches the algorithm.” Activity Narrative (for Activity 2) states, “As students work, encourage them to refine their descriptions of what is happening in both the diagrams and the algorithms using more precise language and mathematical terms (MP6).”

• Unit 5, Fractions as Numbers, Section B, Lesson 9, Activity 1, Student Work Time and Activity Synthesis, students attend to precision when using a number line to locate fractions. Student Work Time states, “‘Take a few minutes to locate 1 on these number lines. Then use any of the number lines to explain how you located 1.’ 5–7 minutes: independent work time.” In Student Work Time, Student Facing states, “2. Use any of the number lines to explain how you located 1.” Activity Narrative states, “In the second problem, they reinforce their knowledge that the denominator of a fraction tells us the number of equal parts in a whole and the size of a unit fraction, and that the numerator gives the number of those parts (MP6).” Activity Synthesis states, “‘Share your written reasoning for one of the number lines with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.’ 3 - 5 minutes: structured partner discussion. Repeat with 2 - 3 different partners. ‘Revise your initial draft based on the feedback you got from your partners.’ 2 - 3 minutes: independent work time. Invite students to share their revised explanations of how they located 1 on the number lines.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section A, Lesson 1, Activity 1, Activity Synthesis, students use the specialized language of mathematics as they discuss how to describe lengths using fractions of an inch. Activity Narrative states, “In the synthesis, discuss the need for fractions of an inch to describe lengths more precisely (MP6).” Activity Synthesis states, “Display the inch ruler and an object that wasn’t exactly a whole number of inches. ‘What is the length of this object? (Between 3 and 4 inches. More than 3 but less than 4. Three-and-a-half inches.) If needed, Could we say that the length of this object is (a whole number of) inches. (No, It's between 3 inches and 4 inches.) We need a way to make our measurements more precise. We'll think about this more in the next activity.’”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section A, Lesson 3, Cool-down, students attend to the specialized language of math as they describe shapes. Student Facing states, “a. Which quadrilateral is being described? Hint 1: It has 4 sides. Hint 2: All of its sides are the same length. Hint 3: It has no right angles. b. Which hints do you need to guess the quadrilateral? Explain your reasoning.” Students see four different quadrilaterals with different features. Activity Narrative (for Activity 2) states, “As students decide which questions to ask they think about important attributes such as side lengths and angles and have an opportunity to use language precisely (MP6, MP7).”

• Unit 8, Putting It All Together, Section A, Lesson 7, Warm-up, Activity Narrative, Launch, and Activity Synthesis, students attend to precision as they use a bar graph and see the importance of precise labels and titles. Activity Narrative states, “The purpose of this Warm-up is to elicit the idea that bar graphs need a title and a scale in order to be able to communicate information clearly (MP6), which will be useful when students draw a scaled bar graph in a later activity. During the synthesis, focus the discussion on the missing scale.”  Launch states, “Groups of 2. Display the graph. ‘What do you notice?  What do you wonder?’ 1 minute: quiet think time.” Activity Synthesis states, “Could each unit or each space between two lines on the graph represent 1 student? Why or why not? (No, because that would mean half of a student likes broccoli, cauliflower, and peas.) If each unit on the graph represents 2 students, how many students have broccoli as their favorite vegetable? (13) What if it represents 4 students? (26) How should you decide on a scale for your graph? (Think about how many people you surveyed and use a scale that will fit them on your graph. Use a scale that will make the bar graph easy to read.)”

The materials reviewed for Open Up Resources K–5 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 grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 1, Introducing Multiplication, Section C, Lesson 16, Warm-up, students look for and make use of structure while they notice the arrangement of a dozen eggs in relation to arrays. Activity Narrative states, “The purpose of this Warm-up is to elicit ideas students have about objects arranged in an array, which will be useful when students arrange equal groups into arrays in a later activity. While students may notice and wonder many things about this image, ideas around arrangement and equal groups are the important discussion points. When students notice the arrangement of the eggs they look for and make use of structure (MP7).” Launch states, “Groups of 2. Display the image. ‘What do you notice? What do you wonder?’” Student Facing states, “What do you notice? What do you wonder?” An egg carton with a dozen eggs is shown. Activity Synthesis states, “‘How does having the eggs in a carton help you see equal groups?’ (I can see how they could be split into equal groups. I can see 6 eggs in each row. I can see 6 groups of 2.) The eggs are arranged in an array. An array is an arrangement of objects in rows and columns. Each column must contain the same number of objects as the other columns, and each row must have the same number of objects as the other rows.”

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section A, Lesson 1, Activity 1, students look for and make use of structure as they represent numbers using base-ten blocks, base-ten diagrams, expanded form, numerals, and word form. Student Work Time states, “‘This set of cards includes numbers in different forms. Find the cards that match. Work with your partner to explain your matches.’ 8 minutes: partner work time” In Student Work Time, Student Facing states, “Your teacher will give you a set of cards that show numbers in different forms. Group the cards that represent the same number. Record your matches here. Be ready to explain your reasoning.” Lesson Narrative states, “As they make matches, students use their understanding of base-ten structure represented in many different ways (MP7).”

• Unit 8, Putting It All Together, Section A, Lesson 1, Cool-down, students use structure to determine if three representations all show the same fractional value. Preparation, Lesson Narrative states, “In previous lessons, students learned how to represent fractions with area diagrams, fraction strips, and number lines. In this lesson, students revisit each of these representations in an estimation context. Students have an opportunity to think about how to partition each representation to decide what fraction is shown (MP7). Additionally, if time allows and it seems of benefit to student understanding, there is an option after each activity to find the exact value of the fraction in the task statement.” Student Facing states, “Could the shaded part of the shape, the point on the number line, and the shaded part of the diagram all represent the same fraction?  Explain your reasoning.” Students see a diamond, a number line, and a diagram that do not all represent the same fraction.

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to use repeated reasoning in order to make generalizations and build a deeper understanding of grade-level math concepts as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 3, Wrapping Up Addition and Subtraction Within 1,000, Section C, Lesson 14, Activity 2, Student Work Time, students use repeated reasoning as they analyze the position of numbers relative to their immediate multiples of 10 and 100. Student Work Time states, “‘Work with your partner to complete these problems.’ 5 - 7 minutes: partner work time. Monitor for students who use the following strategies to highlight: Reason about the midpoint between a multiple of 10 or a multiple of 100 (5 or 50) to determine which multiple is closer, such as, ‘568 is closer to 570 because 565 would be the middle point between 560 and 570’; Use place value patterns to determine which multiple is closer, such as, ‘Since the 1 in 712 is less than 5, it tells me that the number is closest to 700’. Pause for a brief discussion before students complete the last problem. Select previously identified students to share the strategies they used to find the nearest multiple of 100 and the nearest multiple of 10. ‘Now take a few minutes to complete the last problem.’ 2 - 3 minutes: independent work time.” In Student Work Time, Student Facing states, “1a. Is 349 closer to 300 or 400? 1b. Is 349 closer to 340 or 350? 2a. Is 712 closer to 700 or 800? 2b. Is 712 closer to 710 or 720? 2a. Is 568 closer to 500 or 600? 2b. Is 568 closer to 560 or 570? 3a. Is 712 closer to 700 or 800? 3b. Is 712 closer to 710 or 720? 4. Without locating a given number on a number line, how did you decide: a. the nearest multiple of 100? b. the nearest multiple of 10?” Activity Narrative states, “When students notice and describe patterns in the relationship between the numbers and the nearest multiples of 10 or 100, they look for and express regularity in repeated reasoning (MP8).”

• Unit 5, Fractions as Numbers, Section A, Lesson 2, Cool-down, students use repeated reasoning as they partition shapes into equal parts. Student Facing states, “a. Label each part with the correct fraction. b. Partition and shade the rectangle to show \frac{1}{4}.” Activity 1 Narrative states, “When students make halves, fourths, and eighths they observe regularity in repeated reasoning as each piece is subdivided into 2 equal pieces. They observe the same relationship between thirds and sixths (MP8).” The Cool-down provides an opportunity to demonstrate this reasoning.

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section C, Lesson 10, Warm-up, Launch, Student Work Time, and Activity Synthesis, students use repeated reasoning as they choral count, using 15 minutes as the increment of time. Activity Narrative states, “The purpose of this Choral Count is to invite students to practice counting times by 15 minutes and notice patterns in the count. This will be helpful later in this section when students will solve problems involving addition and subtraction of time intervals. Students have an opportunity to notice regularity through repeated reasoning (MP8) as they count by 15 minutes over a span of 3 hours.” Launch states, “‘Count by 15 minutes, starting at 12:00.’ Record as students count. Record times in the count in a single column. Stop counting and recording at 3:00.” Student Work Time states, “‘What patterns do you see?’ 1–2 minutes: quiet think time. Record responses.” Activity Synthesis states, “‘How much time passed between 1:15 and 1:45? (30 minutes) 1:15 and 2:30?’ (75 minutes) Consider asking: ‘Who can restate the pattern in different words? Does anyone want to add an observation on why that pattern is happening here? Do you agree or disagree? Why?’”