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)”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• ORIGO Stepping Stones 2.0 Comprehensive Mathematics, Teacher Edition, Program Overview, The Stepping Stone structure, provides a program that is interconnected to allow major, supporting, and additional clusters to be coherently developed. “One of the most unique things about ORIGO Stepping Stones is the approach to sequencing content and practice. Stepping Stones uses a spaced teaching and practice approach in which each content area is spaced apart, the key ideas and skills of these topics have been identified and placed in smaller blocks (modules) over time. In the actual lessons, work is included to help students fully comprehend what is taught alongside the other content development. Consequently, when students come to a new topic, it can be easily connected to previous work.”

• Module 1, Resources, Preparing for the module, Focus, provides an overview of content and expectations for the module. “In Grade 1, students worked with numbers up to 120. They used a variety of concrete resources and pictures to represent numbers. These resources — connecting cubes, finger pictures, and base-10 blocks — emphasized three key aspects of numbers: counting, place value, and relative position. This meant students could count in different ways; by ones, tens, twos, or fives. Place value was developed using finger pictures, connecting cubes grouped in tens and loose ones, and base-10 blocks showing tens and ones, and, later in the year, one hundred, some tens, and ones. The numeral expander was used with the place- value resources to help students record the numbers as they were represented. This module reviews all the work from Grade 1 that involved two-digit numbers. The lessons focus on using place-value models and the numeral expander to ensure students are confident with reading and writing two-digit numbers. Students compare and order two- digit numbers using the comparison symbols (< and >) to describe the relationship between the numbers. The number work in this module focuses on the place value of three-digit numbers, and counting by one or 100 within 1,000. Base-10 blocks and the numeral expander are used to help the students read and write number names and numerals for three-digit numbers. The digits in the tens place are all greater than one, which means the number names are easier to say. As students are working with the numeral expander, they are encouraged to say the name of the two-digit part of the number by looking at the tens and ones digits together. However, when reading three-digit numbers with teens it is difficult to read a number completely left to right; for example, 216 is read two hundred sixteen. It is better to read a number by looking at the digits in the tens and ones places in one eye movement and saying the number name. That is why the lessons in this module stress using the method of reading a number with hundreds, tens and ones before teen numbers are introduced in later discussions.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson, such as the Step In, Step Up, Step Ahead, Lesson Slides, Step 1 Preparing the Lesson, while other components, like the Step 2 Starting the lesson, Step 3 Teaching the lesson, and Step 4 Reflecting on the work, serve to ensure teachers have the support and knowledge they need to successfully implement the content.” Lesson notes can also highlight potential misconceptions to support teacher planning and practice. Examples include:

• Module 1, Lesson 6, Number: Reading and writing three-digit numbers, Step 2 Starting the lesson, teachers provide context with reading and writing three digit numbers. “Have the students stand in a circle and say, Today, we are going to count by hundreds from 150 in order around the circle. Have students count forward by 100, taking turns to say the numbers to 950, then have students count back from 950 to 150, continuing around the circle. As the students’ confidence increases, create a counting game by drawing a tally on the board each time a successful count forward to 950 and back to 150 occurs. This game can be used repeatedly throughout the week to improve counting fluency and foster enthusiasm for number-related activities.”

• Module 5, Lesson 5, Addition: Two-digit numbers bridging tens (number line), Step 3 Teaching the lesson provides teachers guidance about how to solve problems using place value to add two digit numbers. “Invite students to model their strategy on the board. Establish that it is easier to start with the greater number and then add on the lesser number. Talk about the different ways to break the lesser number (25) into parts to make it easier to add. For example, students might split the number by place value and think 48 + 20 + 5, while others may decompose the five and think 48 + 20 + 2 + 3. Discuss each of the strategies to highlight that each strategy aims to break one of the numbers into parts to make it easier to add. Organize students into pairs and distribute the resources. Ask them to use their number line to figure out the total cost of the items and to write an equation to match the steps they followed. Move around the room to observe their strategies and models. Ask questions such as, How did you break the numbers into parts to make it easier to add? What jumps will you draw to show your thinking? Can you think of a different way to figure out the total? Bring the students together to share their strategies and equations, and describe how they both show the quantities in the problem. Encourage respectful critique (SMP3) by asking, Do you agree with this strategy? How is it different from the strategy you used? How is it the same? If time allows, the price tags can be exchanged among the students, and the activity repeated. Project the Step In discussion from Student Journal 5.5 and work through the questions with the whole class. 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.”

• Module 9 Lesson 9, Length: Introducing centimeters, Lesson overview and focus,  Misconceptions, include guidance to address common misconceptions with measurements. “Measurement using centimeter cubes has the advantage of being firmly grounded in the use of everyday objects. The drawbacks are the potential for overlapping units and allowing gaps between units while measuring. Model correct measurement strategies, explicitly highlighting these possible errors early in the measuring lesson by intentionally leaving gaps or overlapping cubes and gauging students' responses. Later, when students measure the same object and get different answers, the ideal opportunity for more discussion can arise. Examine your class set of rulers to determine if they are appropriate. If possible, avoid rulers with millimeter markings at this grade level: centimeter-only rulers are commercially available or can be printed on card stock. If the class rulers have a space between the end of the object and the zero point, teach students to start at the zero point, not just at the end of the ruler.”

The materials reviewed for Origo Stepping Stones 2.0 Grade 2 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

Within Module Resources, Preparing for the module, there are sections entitled “Research into practice” and “Focus” that consistently link research to pedagogy. There are adult-level explanations including examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject. Professional articles support teachers with learning opportunities about topics such as ensuring mathematical success for all, early understanding of equality, and repeating patterns. There are also professional learning videos, called MathEd, embedded across the curriculum to support teachers in building their knowledge of key mathematical concepts. Examples include:

• Module 2, Preparing for the module, Focus, Number and operations in base ten, explains concepts connected to the introduction of the number line and the relative position of numbers. MathEd RTN3 Teaching number: Relative position, provides additional professional learning for teachers. “The number line is introduced in this module. This is a streamlined version of the number track that helps students work with relative position. At this stage, it is important to stress the idea that a number on a number line is a length; in other words, it is a distance from 0 (the origin or start). So the position of a number (for example, 39) is determined by its distance from 0. In Lesson 2, the placement of a number line just below a number track helps students see that the spaces on the track are the same as the distances between the individual marks on the number line. This also helps to show that 0 does not have any length. One of the first observations to make about the number line is that it is a good tool for comparing and ordering numbers, because greater numbers are farther away from 0. The number line is also handy for finding numbers that are nearby, and for rounding. As students become confident with the number line, they will see it is also useful for reinforcing place value. For example, encourage students to explain the thinking they would use to locate 39 on the number line, and to describe what part of the number they will consider first before making a "jump" from 0. Through discussion, students will see that they can make three jumps of ten, and then nine jumps of one, using the place-value idea. In time, students will use other strategies, but this is a good way to establish how a number line represents numbers. A variety of types of number lines are used in this module. In Lesson 6, students work with empty number lines, which only have marks showing one or two benchmark numbers. This type of number line will help students move away from counting strategies that they might want to use to help figure out answers.” MathEd, “For professional learning in relation to this content, select the following videos from the support resources online. RTN3 Teaching Number: Relative position.”

• Module 5, Preparing for the module, Research into practice, Subtraction, includes explanations and examples of common problem types for subtraction. To learn more includes further references where teachers can build knowledge. “There are three common problem types that can be represented through the subtraction operation, and each of these types of problems mirrors a story context: the separate type (take from), the part/part/total type (take apart), and the compare type. An example of the part/part/total problem type is the following: There are 22 children in Kylie's class. Some of the children take a bus to school and some walk to school. 10 of the children take the bus to school. How many children walk to school each day? A feature of the part/part/total problem type is that the situation can be represented as either a subtraction equation or as an addition equation. The example above can be represented by the following equations: 10 + ? = 22, 22 − 10 = ?, or even 22 − ? = 10. When the problem is thought of as an addition equation, students often count on from one part to the total in order to find the missing addend. When the problem is interpreted as a subtraction situation, students may count back from the total to the known addend to find the difference. It is an effective strategy grounded in the context and therefore accessible through a variety of representations, particularly with the number line and hundred chart.” To learn more, “Common Core Standards Writing Team. 2011. Progressions Documents for the Common Core Math Standards: Draft K–5 Progression on Counting and Cardinality and Operations and Algebraic Thinking. http://ime.math.arizona.edu/progressions/” 

• Module 6, Preparing for the module, Research in practice, Addition, supports teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, this work forms the foundation to extending the count-on strategy to three-digits numbers in Module 9 then sets the stage for the introduction of the standard addition algorithm in Grade 3 Module 7. In preparation for this work, provide many opportunities for students to practice place-value strategies that split the numbers into tens and ones before adding. For example, to solve 76 + 58, thinking 70 + 50 + 6 + 8 = 12 tens + 14 ones then regrouping 10 tens as 1 hundred and 10 ones as 1 ten to get the total 134. Read more in the Research into Practice section of Module 9 and Grade 3 Modules 2 and 7.”

• Module 9, Research into Practice, Addition, supports teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, this work forms the foundation to the introduction of the standard addition algorithm in Grade 3 Module 7, following a review of Grade 2 addition work in Module 2. In preparation for this work, use every opportunity for students to demonstrate and explain their addition thinking. For example, to solve 302 + 129, adding the places and thinking 4 hundreds + 2 tens + 11 ones = 400 + 30 + 1 after regrouping 10 ones as 1 ten. Read more in the Research into Practice section of Grade 3 Module 7.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. 

Correlation information is present for the mathematics standards addressed throughout the grade level/series and can be found in several places, including the curriculum front matter and program overview, module overview and resources, and within each lesson. Examples include:

• Front Matter, Grade 2 and the CCSS by Lesson includes a table with each grade level lesson (in columns) and aligned grade level standards (in rows). Teachers can search any lesson for the grade and identify the standard(s) that are addressed within.

• Front Matter, Grade 2 and the Common Core Standards, includes all Grade 2 standards and the modules and lessons each standard appears in. Teachers can search a standard for the grade and identify the lesson(s) where it appears within materials.

• Module 5, Module Overview Resources, Lesson Content and Learning Targets, outlines standards, learning targets and the lesson where they appear. This is present for all modules and allows teachers to identify targeted standards for any lesson.

• Module 4, Lesson 1, Subtraction: Reviewing concepts, the Core Standards are identified as 2.OA.A.1 and 2.NBT.B.5. The Prior Learning Standard is identified 1.OA.D.8. Lessons contain a consistent structure that includes Lesson Focus, Topic progression, Formative assessment opportunity, Misconceptions, Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, and Maintaining concepts and skills. This provides an additional place to reference standards, and language of the standard, within each lesson.

Each module includes a Mathematics Overview that includes content standards addressed within the module as well as a narrative outlining relevant prior and future content connections. Each lesson includes a Topic Progression that also includes relevant prior and future learning connections. Examples include:

• Module 2, Mathematics Overview, Operations and Algebraic Thinking, includes an overview of how the math of this module builds from previous work in math. “In Grade 1, students learned to use doubling as a strategy to help add numbers that are near each other, for example, 7 + 7 = 14, so 8 + 7 = 15. This strategy is reviewed and reinforced. The number facts in the count-on and use-doubles clusters of facts are merged and reinforced. Practice for all these facts is included in the maintaining concepts and skills activities, but it is always good to practice addition facts early in Grade 2, as time allows.”

• Module 9, Mathematics Overview, Coherence, includes an overview of how the content in 2nd grade connects to mathematics students will learn in third grade. “Lessons 9.1–9.8 focus on addition of up to two three-digit numbers using count-on, make-ten, and place-value strategies. This builds on prior work with addition of up to two two-digit numbers (2.6.1–2.6.9) and serves as a foundation for developing written methods and applying addition strategies to solve problems (3.2.1–3.2.5).”

• Module 11, Lesson 7, 3D objects: Identifying pyramids, Topic Progression, “Prior learning: In Lesson 2.11.6, students use the term polyhedron to describe 3D objects that have only flat surfaces. The ORIGO Big Book: Muddy, Muddy Mess is used to support students’ development of the concept. 2.G.A.1; Current focus: In this lesson, students identify pyramids by examining their features. 2.G.A.1; Future learning: In Lesson 2.11.8, students analyze 3D objects and record information about their faces, edges, and vertices. 2.G.A.1.” Each lesson provides a correlation to standards and a chart relating the target standard(s) to prior learning and future learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

Instructional approaches of the program are described within the Pedagogy section of the Program Overview at each grade. Examples include:

• Program Overview, Pedagogy, The Stepping Stones approach to teaching concepts includes the mission of the program as well as a description of the core beliefs. “Mathematics involves the use of symbols, and a major goal of a program is to prepare students to read, write, and interpret these symbols. ORIGO Stepping Stones introduces symbols gradually after students have had many meaningful experiences with models ranging from real objects, classroom materials and 2D pictures, as shown on the left side of the diagram below. Symbols are also abstract representations of verbal words, so students move through distinct language stages (see right side of diagram), which are described in further detail below. The emphasis of both material and language development summarizes ORIGO's unique, holistic approach to concept development. A description of each language stage is provided in the next section. This approach serves to build a deeper understanding of the concepts underlying abstract symbols. In this way, Stepping Stones better equips students with the confidence and ability to apply mathematics in new and unfamiliar situations.”

• Program Overview, Pedagogy, The Stepping Stones approach to teaching skills helps to outline how to teach a lesson. “In Stepping Stones, students master skills over time as they engage in four distinctly different types of activities. 1. Introduce. In the first stage, students are introduced to the skill using contextual situations, concrete materials, and pictorial representations to help them make sense of the mathematics. 2. Reinforce. In the second stage, the concept or skill is reinforced through activities or games. This stage provides students with the opportunity to understand the concepts and skills as it connects the concrete and pictorial models of the introductory stage to the abstract symbols of the practice stage. 3. Practice. When students are confident with the concept or skill, they move to the third stage where visual models are no longer used. This stage develops accuracy and speed of recall. Written and oral activities are used to practice the skill to develop fluency. 4. Extend. Finally, as the name suggests, students extend their understanding of the concept or skill in the last stage. For example, the use-tens thinking strategy for multiplication can be extended beyond the number fact range to include computation with greater whole numbers and eventually to decimal fractions.” 

• Program Overview, Pedagogy, The Stepping Stones structure outlines the learning experiences. “The scope and sequence of learning experiences carefully focuses on the major clusters in each grade to ensure students gain conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply this knowledge to solve problems inside and outside the mathematics classroom. Mathematics contains many concepts and skills that are closely interconnected. A strong curriculum will carefully build the structure, so that all of the major, supporting, and additional clusters are appropriately addressed and coherently developed. One of the most unique things about ORIGO Stepping Stones is the approach to sequencing content and practice. Stepping Stones uses a spaced teaching and practice approach in which each content area is spaced apart, the key ideas and skills of these topics have been identified and placed in smaller blocks (modules) over time. In the actual lessons, work is included to help students fully comprehend what is taught alongside the other content development. Consequently, when students come to a new topic, it can be easily connected to previous work. For example, within one module students may work on addition, time, and shapes, addressing some of the grade level content for each, and returning to each one later in the year. This allows students to make connections across content and helps students master content and skills with less practice, allowing more time for instruction.”

Research-based strategies within the program are cited and described regularly within each module, within the Research into practice section inside Preparing for the module. Examples of research- based strategies include:

• Module 2, Preparing for the module, Research into practice, “Number line: The number line can be a powerful tool for students to create a visual model of the sequence of numbers. Equally spaced tick marks partition a number line, and can show as little or as much density on the number line as desired. Density refers to the idea that no matter what two numbers are placed on a number line, there is always more that can be placed in between them. One noted problem with the number line is that the focus is often on the numbers labeling the increments, while the power and structure of the number line is focused on the distance between those marks. That distance between two points is a measurement: the distance from zero is a particularly good tool for comparing whole numbers on the number line, especially in later grades. Time: Time is an abstract concept — to measure time is to measure something that cannot be seen or touched. Clocks help us make sense of time. The benefit of using an analog dial to teach time is that when it is, say, 1:58, students can see that it is almost 2:00. A digital clock, however, requires a more in-depth knowledge for students to understand approximately what 1:58 is time-wise. To learn more: Bobis, Janette. 2007. “The Empty Number Line: A Useful Tool or Just Another Procedure?” Teaching Children Mathematics 13(8): 410-413. Van de Walle, John A., Karen S. Karp, and Jennifer M. Bay-Williams. 2010. Elementary and Middle School Mathematics: Teaching Developmentally. 7th ed. Boston: Pearson/Allyn and Bacon. References: Gunderson, Elizabeth A., Gerardo Ramirez, Sian L. Beilock, and Susan C. Levine. 2012. “The Relation between Spatial Skill and Early Number Knowledge: The Role of the Linear Number Line.” Developmental Psychology 48(5): 1229-41. Klein, A. S., M. Beishuizen, and A. Treffers. 1998. "The Empty Number Line in Dutch Second Grades: Realistic Versus Gradual Program Design." Journal for Research in Mathematics Education, 29(4): 443-464.”

• Module 8, Preparing for the module, Research into practice, “Subtraction: The subtraction strategies presented in Module 8 introduce composing and decomposing numbers into and out of groups of ten. This content moves away from the basic recall of facts (DOK Level 1) to emphasize the basic application of skills and concepts (DOK Level 2). It requires the conceptual understanding of regrouping by encouraging students to regroup 1 ten as 10 ones when needed. For this reason, base-10 blocks continue to be an important tool for building a strong understanding of the process of decomposing a group of ten to subtract. While the goals for Grade 2 include fluency in calculations within 100, calculations beyond 100 depend on a more secure understanding of decomposing and composing tens and ones, and so fluency is reserved for Grade 3. To learn more: Common Core Standards Writing Team. 2011. Progressions Documents for the Common Core Math Standards: Draft K–5 Progression on Counting and Cardinality and Operations and Algebraic Thinking http://ime.math.arizona.edu/progressions/, Fuson, Karen C. and Sybilla Beckman. 2013. “Standard Algorithms in the Common Core State Standards.” NCSM Journal of Mathematics Education Leadership 14 (2): 14–30., Reinke, Kay and Pat Lamphere-Jordan. 2002. “Working Cotton: Toward an Understanding of Time.” Teaching Children Mathematics 8 (8): 475–79. References: Fosnot, Catherine and Maarten Dolk. 2001. Young Mathematicians at Work: Constructing Number Sense: Addition, and Subtraction., Portsmouth, NH: Heinemann. Fuson, Karen C., Diana Wearne, James C. Hiebert, Hanlie G. Murray, Pieter G. Human, Alwyn I. Olivier, Thomas P. Carpenter, and Elizabeth Fennema. 1997. “Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction.” Journal for Research in Mathematics Education 28 (2): 130–62., Vakali, Mary. 1991. “Clock Time in Seven to Ten-Year-Old Children.” European Journal of Psychology of Education 6 (3): 325–36

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. In the Program Overview, Program components, Preparing for the module, “Resource overview - provides a comprehensive view of the materials used within the module to assist with planning and preparation.” Each module includes a Resource overview to outline supplies needed for each lesson within the module. Additionally, specific lessons include notes about supplies needed to support instructional activities, often within Step 1 Preparing the lesson. Examples include:

• Module 2, Preparing for the module, According to the Resource overview, teachers need, “base-10 blocks (tens and ones) for lesson 5, container for lessons 2 and 5, ORIGO Big Book: Jumping Jacks for lessons 2, 3, and 6, stick tack, Support 29 and Support 30 for lesson 2, Support 34 for Lesson 8, Support 35 for lesson 10, Support 37 for lesson 12, and The Number Case for lessons 2 and 5. Each pair of students needs counters and a cube labeled: 4, 5, 6, 7, 8, 9 in lesson 10. Each individual student needs base-10 one blocks and counters in lesson 1, cubes or counters, glue, scissors, Support 28 for lesson 1, Support 26 for lesson 12, the Student Journal for each lesson, Supports 32 and Support 33 for lesson 7.” 

• Module 2, Lesson 1, Number: Exploring position on a number track, Lesson notes, Step 1 Preparing the lesson, “Each student will need: 1 copy of Support 28, scissors, glue, base-10 blocks, counters, and Student Journal 2.1.” Step 3 Teaching the lesson, “Distribute the resources and direct the students to cut out the four strips.”

• Module 5, Preparing for the module, According to the Resource overview, teachers need, “cube labeled: 10, 10, 20, 20, 30, 30 in lesson 3, a cube labeled 10, 20, 30, 40, 50, 60 in lesson 6, non-permanent marker in lesson 2, and resources such as hundred charts, number lines, and ten frames from The Number Case, connecting cubes, counters and small objects such as toys and stones placed in a central position in the classroom for students to access as need in lessons 10 and 11. Each group of students needs a cube labeled: 30, 35, 42, 45, 51, 55 and a cube labeled: 55, 62, 65, 74, 75, 81 in lesson 7. Each pair of students needs counters in lesson 10, non-permanent marker and Support 55 in lesson 5, The Number Case in lessons 1, 4, 5, and 10, and transparent counters in lesson 1. Each individual student needs a 12 inch ruler in lesson 7, paper in lessons 7, 11, and 12, Support 48 in lesson 10, and the Student Journal in each lesson.”

• Module 8, Lesson 4, Subtraction: Reinforcing two-digit numbers (decomposing tens), Lesson notes, Step 1 Preparing the lesson “ You will need: 10 bundles of 10 straws in a container; Each student will need: Student Journal 8.4”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. In each Module Lesson, Differentiation notes, there is a document titled Extra help, Extra practice, and Extra challenge that provides accommodations for an activity of the lesson. For example, the components of Module 5, Lesson 8, Subtraction: Reviewing the think-addition strategy (doubles facts), include:

• Extra help, “Activity: Organize students into pairs and distribute the resources. Have the students cut out all the cards. They can then mix and match the cards.”

• Extra practice, “Activity: Organize students into pairs and distribute the resources. Have the students cut out all the cards. The dominoes are mixed and placed facedown in a central pile. Students take turns to select a domino, keeping it hidden from the other student, and calculate the total in their head. They then cover one end of the domino, show the other end to the other student, and say the total. The other student figures out how many dots are covered, and then they explain how they figured it out. The students alternate roles and repeat the activity several times.”

• Extra challenge, “Activity: Organize students into pairs and distribute the resources. Have the students cut out all the cards. The dominoes are mixed and placed facedown in a central pile. Students take turns to select a domino, keeping it hidden from the other student, and calculate the total in their head. They then say their total and the other student must say what the two parts of the domino show. If they are correct, the card remains upturned in a new pile. If they are incorrect, the card is returned facedown to the bottom of the pile. The students alternate roles and repeat the activity several times.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

While there are no instances where advanced students do more assignments than classmates, materials do provide multiple opportunities to investigate the grade-level content at a higher level of complexity. The Lesson Differentiation in each lesson includes a differentiation plan with an extra challenge. Each extra challenge is unique to an activity completed in class. Examples include:

• Module 2, Lesson 1, Number: Exploring position on a number track, Differentiation, Extra Challenge, “Distribute the resources. Have the students cut out all the number-track sections and tape them together to form a number track from 1 to 64. Organize students into pairs. They then take turns to say a missing number that the other student must identify on the track. They then both write the number on their own track.”

• Module 5, Lesson 5, Addition: Two-digit numbers bridging tens (number line), Differentiation, Extra Challenge, “Organize students into pairs and distribute the resources. Have the students cut out the purse cards. The cards are then scattered facedown on the floor. Students take turns to select a card, roll the cube, and calculate the total. Encourage the students to perform a mental calculation but allow them to use a number line to help, if necessary. They then place a counter on the matching total on the game board and return the purse card facedown. If an answer is unavailable, the student misses a turn. Play continues until one student has placed three adjacent counters in a horizontal or vertical line.”

• Module 10, Lesson 8, Two-digit numbers from three-digit numbers (decomposing tens and hundreds), Differentiation, Extra Challenge, “This activity builds upon the Extra Practice activity. Open Flare Number Line (b) and write these digits on the board: 6, 9, 4, 5, 3. Have the students arrange the digits to form a subtraction equation (a two-digit number being subtracted from a three-digit number) that they are unable to solve mentally. Students can then use the number line to figure out the difference, adjusting the range of the number line as needed. Repeat the activity for other subtraction equations.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Although strategies are not provided to differentiate for the levels of student language development, all materials are available in Spanish. Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the Mathematics Overview, English Language Learners, “The Stepping Stones program provides a language-rich curriculum where English Language Learners (ELL) can acquire mathematics in a natural second-language progression by listening, speaking, reading, and writing. Each lesson includes accommodations to be aware of when teaching the lesson to ensure scaffolding of content and misconceptions of language are addressed. Since there may be several stages of language development in your classroom, you will need to use your professional judgement to select which accommodations are best suited to each learner.” Examples include:

• Module 3, Lesson 7, Number: Comparing to order three-digit numbers, Lesson notes, Step 2 Starting the lesson, “ELL: Allow the students to watch the game for a few rounds to understand the directions. Then invite them to engage in the activity.” Step 3 Teaching the lesson, “ELL: Pair the students with fluent English-speaking students. During the activity, have students discuss the concepts in their pairs, as well as repeat the other student’s thinking. Allow students to discuss the words least, greatest, and first before moving on with the activity. Allow the students to work in their pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Pair the students with fluent English- speaking students to enhance language acquisition. Invite the students to explain their thinking to each other before speaking to the group.”

• Module 10, Lesson 8, Subtraction: Two-digit numbers from three-digit numbers (decomposing tens and hundreds), Lesson notes, Step 2 Starting the lesson, “ELL: Allow the students to process their answer, and encourage them to say the number in English. Project the number 107 (slide 1) and ask one volunteer, What number is shown? (107.) What number is 10 less than that number? (97.) What number is 20 less than the number shown? (87.) What number is 30 less than the number shown? (77.) Repeat with the remaining numbers (slides 2 to 30), as needed, so every student has a turn.” Step 3 Teaching the lesson, “ELL: Pair the students with fluent English-speaking students. Encourage them to discuss the concepts with their partner, as well as repeat the other student’s thinking. Allow the students to formulate an answer and discuss their thoughts with their partner before presenting them to the class. Allow the students to use hand gestures (such as thumbs up or down) to show they understand, or are confused by, the language being used. Allow pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Provide sentence stems such as, “The number in the boxes should be ___ because …”.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing  manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials consistently include suggestions and/or links, within the lesson notes, for virtual and physical manipulatives that support the understanding of grade level math concepts. Examples include: 

• Module 1, Lesson 4, Number: Exploring the properties of odd and even numbers, Step 3 Teaching the lesson, counters are identified as a tool to build an understanding of odd and even numbers. “Project the T-chart (slide 1) and have the students list the numbers that are odd and even. Then form the students into small groups and provide each group with twenty counters. Ask the students to share their counters into groups of two to identify the numbers between 10 and 20 that are odd or even. They should record their results on a sheet of paper.”

• Module 4, Lesson 4, Subtraction: Reinforcing the think-addition strategy (count-on facts), Step 3 Teaching the lesson, references dominoes and a support handout for working with subtraction facts. “Organize students into pairs and distribute the dominoes.”

• Module 9, Lesson 6, Addition: Two- and three-digit numbers (composing tens and hundreds), Step 2 Starting the lesson, references the online Flare tool for problems involving regrouping. “Open the Flare Place Value (a) online tool and review how to regroup when there is more than 9 in any single place. Ask a student to demonstrate how to regroup 14 ones to make 1 ten and 4 ones. Repeat for 3 hundreds, 17 tens, 5 ones; 4 hundreds, 2 tens, 18 ones; and 2 hundreds, 11 tens, 1 one.”