2nd Grade - Gateway 2

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the Second Grade fluencies add and subtract within 20. 

The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.

The materials attend to the Grade 2 expected fluencies: 2.OA.2 fluently add and subtract within 20 using mental strategies. By the end of Grade 2, know from memory all sums of two one-digit numbers. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include:

• Module 2, Lesson 9, Time: Reinforcing on the hour and half-past the hour, Maintaining concepts and skills, students practice adding and subtracting within 20. 

• Module 12, Lesson 1, Division: Developing language (sharing), Maintaining concepts and skills, “This lesson provides projectable practice that is designed to foster fluency of basic facts. Project or read the facts to the students, allowing a few seconds between each fact that you show or read. Be sure to alternate this delivery from one lesson or module to the next. Roll over the image below to reveal the focus of the content.” Students are practicing fluency with 20.

• Maintaining Concepts and Skills lessons incorporate practice of previously learned skills from the prior grade level. For example, Maintaining Concepts and Skills in Module 3, Lesson 10,  Addition: Reinforcing the make-ten strategy, provides practice for adding within 20. 

• Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills, such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 6’s Interview 1 and 2 has students subtracting within 20. 

• “Fundamentals Games” contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Total Ten, students demonstrate fluency of adding within 20 (2.OA.2). 

• Some lessons provide opportunities for students to practice the procedural fluency of the concept being taught in the “Step Up” section of the student journal.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Teachers routinely engage students in single and multi-step application problems during the Step In Discussion at the beginning of lessons. Examples include:

• Module 1, Lesson 9, Addition: Reviewing Concepts, Student Journal, page 30, Step In Discussion, students represent and solve addition and subtraction non-routine problems. (2.OA.1) “What addition story could you say about this picture? Which number is the total in your story? How do you know? Which numbers are parts of the total? How do you know? What addition fact could you write to match your story?”

• Module 4, Lesson 10, Length: Working with feet and inches, Student Journal, page 146, Step In Discussion, students solve routine word problems involving calculations with standard measures of length. (2.MD.5) “How many inches equal one foot? How many inches equal two feet? How do you know? How many inches taller than one foot is this plant? How many more inches would the plant need to grow so it was two feet tall?” An image shows a plant measuring 15 inches.

• Module 10, Lesson 12, Subtraction: Reinforcing two- and three-digit numbers (decomposing tens and hundreds), Student Journal, page 390, Step In Discussion, students use equations to show subtraction with two and three digit numbers in non-routine real-world problems. (2.NBT.7) “These students figured out the number of days until they turned 8 years old. They recorded the number in the table. How many fewer days did Laura record than Ruby? What equations could you write to show your thinking? How could you figure out the difference with blocks? How could you find the difference on a number line?” A table shows Ruby 165 days, Nathan 132 days, Laura 117 days, and Carlos 285 days. 

Materials consistently provide opportunities for students to independently engage with routine and non-routine applications of mathematics. These are found across the grade level within Thinking Tasks, Problem Solving Activities, and Investigations. Examples include:

• Module 6, More Math, Thinking Tasks, Question 1, students compare values and use addition strategies in a non-routine real world problem. (2.OA.1) “Look at the prices of these balls. Baseball $31, Basketball $54, Golf ball $6, and Football $49. If you buy two different balls, which two balls would cost the least? Write an equation to show the total cost of the two balls.”

• Module 8, More Math, Investigation 2, students subtract two digit numbers from three digit numbers in non-routine problems. (2.NBT.7) “How many pairs of three-digit and two-digit numbers will make this subtraction equation true? 1__ __ - __5 = 92.” 

Module 11, More Math, Problem Solving Activity 3, students use make-a-table strategy to solve routine money problems. (2.MD.8) “How many different ways can you make 40￠ with quarters, dimes, and nickels? Complete the table to help you.” A table is shown with columns of 5 cents, 10 cents, and 25 cents.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.

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 modules. Examples include:

• Module 2, Lesson 5, Number: Comparing two-digit numbers on a number line, Step 3 Teaching the Lesson, students make sense of a problem and persevere in making sense of comparison problems and discussion pathways for solving them. “Arrange the place-value cards in separate piles facedown at the front of the classroom. Ask two students to each select a card from each pile to create two two-digit numbers. Ask the class to read the two numbers. Refer to the two numbers and ask, How can we compare these two numbers? Which number is greater? How do you know? Encourage students to share their suggestions such as, "We could show each number with blocks or fingers," or "We could compare the number of blocks on a pan balance." Some students may suggest comparing the digits in the tens then the ones place to find the greater number. If necessary, guide the discussion by asking questions such as, Why did you choose that tool? Is there another way you could compare the numbers? Can you explain the steps you could follow? (This discussion will support students in achieving MP1.)”

• Module 8, Lesson 5, Subtraction: Estimating to solve problems, Student Journal, page 295, Step Up Question 2a, students make sense of estimation problems to determine what they know and what they need to find out. “The movie runs for 96 minutes. Evan pauses the movie after 54 minutes to make some popcorn. About how many more minutes will the movie run? 30 minutes, 40 minutes, 50 minutes.” Teaching the lesson, the teacher helps students “make sense of the problem by asking students to restate the problem in their own words.”

• Module 9, Lesson 6, Addition: Two- and three-digit numbers (composing tens and hundreds), Student Journal, page 335, Step Ahead, students make sense of problems and persevere when they “analyze a real-world problem to identify what they know and what they need to find out, then persevere in finding a solution.” Students are given a picture of two different priced game consoles and three different priced games. “Jack bought a game console and one game. He had $200 and got some change. Circle the items he may have bought. There is more than one possible answer.” Step 4 Reflecting on the work, “For Step Ahead ask, What steps did you follow to solve this problem? Encourage students to explain their processes (MP1).”

• Module 11, Lesson 12, Money: Solving word problems, Step 3 Teaching the Lesson, students analyze word problems in groups in order to make sense of what they know, what they need to find out, and then persevere in solving them. “Organize students into small groups. Ensure each group has access to the resources. Project slide 2 as shown and read the problem aloud. Then discuss the points below (MP1): Alexis has a $1 bill, 2 pennies, and 3 dimes. How much money does she have? Module 11, Lesson 12, Money: Solving word problems, students make sense of problems as they “analyze word problems to determine what they know and what they need to find out, then persevere in solving them.” Teaching the lesson, students are given, “Alexis has a $1 bill, 2 pennies, and 3 dimes. How much money does she have? If students are struggling to figure out the answers, encourage perseverance (MP1) by asking questions such as: How could you describe the problem in your own words? What are you trying to figure out? What have you already tried? Is there a different tool you could use to figure out the answer?”

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 modules. Examples include:

• Module 3, Lesson 10, Addition: Reinforcing the make-ten strategy, Step 2 Starting the Lesson, students reason abstractly as they match a real world situation to an equation. “Organize students into pairs and distribute the ten-frames and counters. Project the equation 9 + 6 = ___ (slide 1). Ask, What real-word situation could this equation match? (MP2)”

• Module 5, Lesson 9, Subtraction: Reinforcing the think-addition strategy (doubles facts), Student Journal, page 182, Step Up, Question 1, students reason abstractly and quantitatively as they relate addition and subtraction facts with dots on dominoes. “Draw dots to help you complete the subtraction fact. Then complete the related addition fact.” Problem 1a, students are shown a domino with one half filled with 6 dots, and the other half is blank. “13 - 6 = ___, 6 + ___ = 13” Step 4 Reflecting on the work, “Discuss the students’ answers to Student Journal 5.9. For Questions 1 and 2, ask students to share the strategy they used to find out the missing number on the domino. Make sure they relate the equations to the domino picture (MP2).”

• Module 7, Lesson 2, Subtraction: Two-digit numbers (number line), Student Journal, page 247, Question 2a, students reason abstractly and quantitatively when they write equations to represent a word problem, relate the solution back to the problem to make sense of quantity in context, and think about real-world problems that could match each equation. Students are given a blank number line with points 40, 50, 60, and 70 labeled. “Complete each sentence. Draw jumps on the number line to show your thinking. 66 - 13 = ___.” Step 4 Reflecting on the work, “As time allows, have students think of real-world problems that could match these equations (MP2).”

• Module 8, Lesson 12, Time: Identifying and recording time using a.m. and p.m., Step 3 Teaching the Lesson, students contextualize a.m. and p.m. times by identifying activities that they do before and after noon. Students add sunrise and sunset times to a timeline with hourly increments. “Discuss what the students or their families do at different times of the day, for example, read a bedtime story, and have them identify the time using a.m. or p.m. and say whether it is nighttime or daytime (MP2).”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique  the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3. 

Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 1, Lesson 3, Number: Comparing and ordering two-digit numbers, Step 2 Starting the lesson, students construct viable arguments and critique the reasoning of others when they use place value skills to compare and order two-digit numbers. “Ask two students to come to the front and each take a handful of tens and ones blocks. Have them sort their blocks to determine the two-digit numbers they represent. Discuss the way in which the two students counted/sorted the blocks. For the first set of blocks, ask, How do you know (Lisa’s) blocks represent (16)? Have students form an argument that proves (Lisa’s) blocks represent (16) and share this with another student (MP2). Repeat for the second set of blocks. Then ask, Which number is greater? How do you know? When the greater number is identified, have another student use blocks to represent the number that is 10 greater. As a class, determine the order of the three numbers from least to greatest. Invite students to prove that the order of the three numbers is correct by representing the numbers with blocks (MP3). Ask, Do you agree these numbers are ordered from least to greatest? How do you know they are correct? Repeat the activity with three new numbers.”

• Module 3, More Math, Thinking Tasks, Question 2, students construct a viable argument and critique the reasoning of others as they represent and compare three-digit numbers. “Gloria scores 294 on her game app. Dwane scores 305 on the same game. Liam says Gloria’s score is greater because 9 is the greatest digit. Do you agree or disagree with Liam? Explain why.”

• Module 7, Lesson 12, 2D shapes: Drawing polygons, Student Journal, pages 276-277, Step Up, students critique the work of others and offer suggestions for improvement when drawing 2D shapes to match a given set of criteria. “Draw a shape to match each label. a. a triangle with exactly two sides the same length”. Step 4 Reflecting on the work, “Discuss the similarities and differences between the students’ drawings. Encourage critique by the students, asking them to explain why the shapes match (or do not match) the clues. For each non-example, ask them to suggest how it could be changed to make it match the clues. (MP3)”

• Module 8, Student Journal, page 319, Convince a friend, students construct viable arguments and critique the reasoning of others as they identify times using quarters of an hour. “Monique says she can write four times that are between 4 o’clock and half-past six and they all include the word quarter. Maka says he can write more times. Who is correct?” Students are given, “I think ___ is correct because…”

• Module 10, Lesson 9, Subtraction: Reinforcing two-digit numbers from three-digit numbers (decomposing tens and hundreds), Step 3 Teaching the lesson, students share their methods, justify their thinking, and critique the methods and reasoning of their peers. Students solve 435 - 52, “Then invite a student to write the difference in the diagram and demonstrate their method. Encourage others to critique the method and explanation. If needed, provide sentence stems such as the following to prompt the critique (MP3): I am confused by …, I think that makes sense, but …, I disagree with that method because …, I did it the same way because …”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within lesson notes.

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, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 3, Lesson 7, Number: Comparing to order 3-digit numbers, Step 4 Reflecting on the work, students model with math as they reason about digits and place value. “Discuss the students’ answers to Student Journal 3.7. Ask questions such as, Were there any scorecards for which you could decide the order just by looking at the digits in the hundreds place? Where did you need to look at the ones places to decide which number was greater? Can you think of another real-world situation where you would compare three-digit numbers? (MP4)”

• Module 4, Lesson 1, Subtraction: Reviewing concepts, Step 3 Teaching the lesson, students model with mathematics as they represent subtraction problems in a variety of ways and explain how the representations are connected. “Organize students into pairs and distribute the resources. Project the word problem (slide 1), read the problem aloud, and discuss the points below (MP1): What is the problem asking you to find out? How could you say the problem in your own words? How could you use the ten-frame to help solve the problem? What equation could you write to match the problem? Allow time for students to work together to solve the problem. Encourage them to represent the problem in a variety of ways, for example, drawing a picture, acting it out with the ten-frame and cubes, or writing an equation. (MP4)”

• Module 7, Lesson 2, Subtraction: Two-digit numbers (number line), Student Journal, page 246, Step Up, Questions 1a-b, students model with mathematics when they “model two-digit subtraction on number lines, and make connections between the jumps made and how they subtracted on the hundred chart in the previous lesson.” Students see two number lines with points 50, 60, and 70 labeled. “a. Draw jumps on this number line to show how you would figure out 68 - 12. b. Draw jumps to show another way you could figure out 68 - 12.” Step 4 Reflecting on the work, “Ask volunteers to demonstrate the two different ways they thought about the problem 68 - 12 (MP4). Ask others to describe the steps in each method. Write equations on the board to record the different methods.”

• Module 8, Student Journal, page 318, Mathematical modeling task, students model with mathematics when they use the math they know to solve problems connected to everyday situations. Students are given a picture of a cap $25, a necklace $15, a shirt $49, a pair of sunglasses $65, and a jacket $75. “Ruben has $109 left on a gift card he was given for his last birthday. He wants to buy some clothing but he does not want to spend all the money on his card. He would like to leave about $50 on the gift card. Which items of clothing could he buy?”

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 modules to support their understanding of grade level math. Examples include:

• Module 2, Lesson 12, Addition: Reinforcing strategies (count-on and doubles), Step 3 Teaching the lesson, students use appropriate tools strategically as they solve addition word problems. “Project the Step In discussion from Student Journal 2.12 and work through the questions with the whole class. Read the Step Up and Step Ahead instructions with the students. Refer to Question 2 and explain that counters, cubes, and number tracks can be used to help solve each problem. The students need to select the tool that they would like to use (MP5). Make sure they know what to do, then have them work independently to complete the tasks.”

• Module 7, Problem solving activities, Activity 1, Greatest difference, students choose appropriate strategies and tools to solve a word problem. Students see four number cards: 2, 5, 0, and 9. They are also given a blank number line and a hundreds chart. “Kevin chose these four number cards. He wants to write a subtraction equation that will give him the greatest possible difference. What equation should Kevin write? Use the number line or hundred chart to help your thinking. _ _ - _ _ = ___”

• Module 9, Thinking tasks, Questions 1 and 3, “students are encouraged to consider and select from the available tools to help them solve the problem” and then “solve the problem in a different way”. Question 1, students are given a chart, “Fun park meal deals, Family mega combo $45, Family combo $37, Family mini combo $26”. “Jie has $92. Entry tickets to the fun park will cost $53. Which meal combo can Jie buy for his family? Show your thinking.” Question 3, “Lillian uses a different strategy to solve Question 1. Show another way to solve the problem.”

• Module 10, Lesson 11, Subtraction: Reinforcing three-digit numbers (decomposing tens and hundreds), Student Journal, page 389, Step Up, Questions a-d, students choose an appropriate strategy as a tool to solve subtraction problems. Students see number lines on parts a and b, “a. 212 - 131 = ___, b. 184 - 127 = ___, c. 275 - 108 = ___, d. 232 - 116 = ___”. Step 3 Teaching the lesson, “Explain that students can choose the strategy (count-back or count-on) they use for each problem. (MP5)”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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. MP6 is explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 4, Lesson 8, Length: Measuring in inches, Step 2 Starting the lesson, students attend to the precision of math by measuring length with an inch ruler. “Review what the students know about measuring lengths with an inch ruler. Organize students into pairs and distribute the resources. Ask students to draw a line that measures exactly 6 inches long. The pairs exchange their work to confirm the length of the line (MP6). Repeat the activity by asking the students to draw lines of the following length: 3 inches, 8 inches, and 5 inches.”

• Module 7, Lesson 4, Subtraction: Counting back to subtract two-digit numbers bridging tens (number line), Step 3 Teaching the lesson, students attend to precision when they check the reasonableness of their answers when solving subtraction problems. “Read the Step Up and Step Ahead instructions with the students. Make sure they know what to do, then have them work independently to complete the tasks. Discuss reasonable answers and have students think about and suggest ways they could test their answers to make sure they are correct (MP6). For example, they could use a different method, different jumps, or use the relationship between addition and subtraction. For example, to check 65 - 26 = 39 they could add 39 + 1 + 25 to make sure it equals 65.”

• Module 9, Lesson 10, Length: Working with centimeters, Step 3 Teaching the lesson and Student Journal, page 347, students attend to precision when they measure lengths accurately. In Step 3, “Students should apply what they know about measuring with inch rulers to measuring with centimeter rulers. For example, the importance of aligning the first scale indicator (0) to the beginning length they want to measure (MP6).” Student Journal, Step Up, Question b, students are given a white strip, “Use a ruler to measure the distance along each white strip. Mark the length and color the strip to match. b. Measure 6 cm.”

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

• Module 3, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The bolded vocabulary below will be introduced and developed in this module. These words are also defined in the student glossary at the end of each Student Journal. A support page accompanies each module where students create their own definition for each of the newly introduced vocabulary terms. The unbolded vocabulary terms below were introduced and defined in previous lessons and grades. Addition, analog clock, digital clock, double, empty number line, equal, even number, expander, fact, greater than, greatest, half an hour, half-past, hour, hundreds, least, less, less than, longest, minute, more, near-double, nearest ten, number line, number name, number track, o'clock, odd number, on the hour, ones, position, shortest, temperature, tens, time, total.” Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.

• Module 5, Lesson 8, Subtraction: Reviewing the think-addition strategy (doubles facts), Student Journal, page 180, Words at Work, students attend to the specialized language of mathematics by explaining their strategy in words. “a) Write two different two-digit numbers that have more than 5 tens and fewer than 4 ones. b)Write an addition problem using the numbers. c)Write how you figure out the total.)”

• Module 11, Lesson 7, 3D objects: Identifying pyramids, Step 4 Reflecting on the work, students attend to the specialized language of mathematics as they use correct mathematical terms such as 3D object, corner, faces, triangle, stack, edge, and pyramid to identify and describe specific 3D objects and their attributes. “Organize students into pairs or small groups and have them discuss why pyramids are not used very often to make boxes for food. Listen to their discussions and remind students to use clear and precise language. Then invite students to share their thinking with the whole class. Establish that pyramids do not stack easily and things cannot be packed inside them easily either. (MP6)”

While there are examples of the intentional development of MP6, attend to precision, throughout materials, there is also evidence of imprecise language or content connections that are not grade-specific. Example include:

• Module 9, Lesson 1, Addition: Extending the count-on strategy to three-digit numbers, Step 3 Teaching the lesson, the term “turnaround” is used for the commutative property, “Project 20 + 867 = ___ (slide 8) and ask, How could you figure out the total? Discuss the students’ ideas and, if necessary, suggest using the turnaround (867 + 20) to make the calculation easier.” 

• Module 9, Lesson 2, Addition: Two- and three-digit numbers, Student Journal, page 325, Ongoing Practice, Question 2d, “Think of the turnarounds to help figure out the totals. d. 10 + 374 = ___"

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 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 throughout the year and they are often explicitly identified for teachers in several places:  Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.

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 throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Module 1, Lesson 2, Number: Writing two-digit numbers and number names, Step 2 Starting the lesson, students look for and make use of structure when using the known structure of a hundred chart to see patterns in two-digit numbers. “Open Flare Number Board online tool to reveal the hundred chart, as shown, and discuss the points below: Where is the number that is five more than 20? Where is the number that is one before 40? Where is the number that is five before 80? Encourage the students to describe what they know about each number. Guide students to refer to the known structure of the hundred chart to support their thinking. (MP7)”

• Module 5, Lesson 1, Addition: Two-digit numbers (hundred chart), Step 3 Teaching the lesson, students look for and make use of structure as they decompose a number to help with addition. “Project slide 3, as shown. Explain that one way of figuring out the total is to split one of the numbers into tens and ones and add each part to the other number (MP7). Have the students place a counter on 56. Discuss the points below: What number are you going to add to 56? (23.) How many tens does 23 have? (2.) 2 tens is 20. How can you move your counter to add 20? (Down two rows.) How many ones does 23 have? (3.) How can you move your counter to add 3 more? (Right three spaces.) Move your finger along the row to 79. Review the steps and write the equation 56 + 20 = 76 on the board. Then write 76 + 3 = 79 below. Then repeat for price tags showing $43 + $24 (slide 4), and then $62 + $37 (slide 5). Project the $56 and $23 price tags (slide 6) to repeat the activity. However, this time have the students add by counting on the ones first, then the tens (MP7). For example, 56 + 3 = 59; 59 + 20 = 79. Reinforce that the total in each method (tens first or ones first) is the same. Repeat the discussion for $43 + $24 (slide 4) and $62 + $37 (slide 5).”

• Module 8, Lesson 10, Time: Working with five-minute intervals, Step 4 Reflecting on the work, students look for and make use of structure when they “recall and apply previously learned concepts to make sense of the word half.” Students see an analog clock showing 3:30. The teacher asks, “How many different ways can we say this time? (Thirty minutes past 3, half- past three, three-thirty.) Why do we use the term half past? What does the half mean? Highlight responses that refer to halfway around the clock face, or relate half to the area model of fractions. Some students may also make connections between 30 minutes and half of 60 minutes. (MP7)”

• Module 9, Lesson 4, Addition: Composing three-digit numbers, Student Journal, page 329, Step Up, Question a, students look for and make use of structure when they “use the structure of our base-ten number system to represent the same number in a different way. For example, 1 hundred, 5 tens, and 14 ones is the same value as 1 hundred, 6 tens, and 4 ones.” Directions state, “Read the number of hundreds, tens, and ones. Write the number to match. Show your thinking. a. 2 hundreds, 1 ten, and 13 ones is the same value as ___.” Step 4 Reflecting on the work, students are given “a pile of base-10 blocks containing 1 hundred, 18 tens, and 12 ones”. Students group the blocks according to place value. The teacher asks, “What number is represented? What do we need to do to figure out the number? Is 1 hundred, 18 tens, and 12 ones the same value as 2 hundreds, 9 tens, and 2 ones? Why? (MP7)”

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 throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:

• Module 6, Lesson 10, Data: Introducing picture graphs, Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning by determining that skip counting by fives to count tallies, is more efficient than counting one by one. “Project the Step In discussion from Student Journal 6.10 and work through the questions with the whole class. Point out that pictures for this graph are arranged into rows, not columns. Read the Step Up and Step Ahead instructions with the students. Help the students vote on their favorite type of movie. These results can be recorded on the board with students transferring them into their Student Journal. Ask, What is a quick way of counting the tallies for each type of movie? Guide students to explain the shortcut method of counting by fives (MP8). The students can then work independently to complete the remaining tasks.”

• Module 7, Lesson 9, 2-D shapes: Identifying polygons, Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning when they “generalize about the number of vertices being the same as the number of sides for any polygon, then test their prediction by drawing different polygons.” Students draw a polygon on a sticky note. “They then attach their sticky note to the board to sort their polygons by the number of sides” and share their observations. Next, students “sort their polygons by the number of vertices (corners). Discuss the results. Students should note that their polygon was placed in the same group for each sort. Ask, Is it possible to draw a polygon that has more sides than vertices? (No.) Will the number of sides always match the number of vertices? (Yes.) Have students draw polygons on paper to test their predictions. (MP8)”

• Module 11, Lesson 11, Money: Working with dollars and cents, Student Journal, page 426, Step Up, Question 1b, students look for and express regularity in repeated reasoning when they “see patterns and make connections while working with coins and bills.” Students see a picture of an orange with a price tag of 30¢ each. “Write or draw two different ways to pay for each fruit using nickels, dimes, and quarters. Use exact amounts because no change will be given.” Step 4 Reflecting on the work, “For Question 1, have students draw their examples on the board and explain any patterns or connections they used, such as skip counting, doubling, or grouping. (MP8)”

• Module 12, Lesson 5, Common fractions: Showing the same fraction with wholes of different size, Step 4 Reflecting on the work, students look for and express regularity in repeated reasoning when they “make a generalize to describe their understanding about the same fractional amount of different and same sized wholes.” The teacher says, “Imagine a new student came to our class and they did not know anything about fractions of different sized wholes. How could you explain to that student what we have learned in this lesson? Organize students into pairs to brainstorm ideas, then invite them to present their generalizations to the class. For example, they could say, “If two whole shapes are the same in size, then the size of one-half of each whole will be the same. But if the two whole shapes are different in size, then the size of one-half of each whole will be different too. Encourage them to demonstrate their thinking with area models. (MP8)”