The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices across the year and they are often explicitly identified for teachers 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 1, Lesson 8, Multiplication: Using the turnaround idea with arrays, Step 2 Starting the Lesson and Step 3 Teaching the Lesson, students make sense of and persevere in using multiple representations of arrays to identify multiplication turnaround facts. “Organize students into pairs and distribute the resources. Ask, How can we show 24 cubes in equal groups? What can we write? (MP1) Encourage students to make observations on the different representations, the different structure of the groups/arrays, and the equations (being multiplication and/or addition).” Step 3, “Project the Step In discussion from Student Journal 1.8 and work through the questions with the whole class. Read the Step Up and Step Ahead instructions with the students. Explain that in Question 3 they must color the items to match the word problem, then write the two turnaround facts that give the same product (MP1).”

• Module 2, Lesson 5, Addition: Solving word problems, Step 3 Teaching the Lesson and Student Journal, page 57, students make sense of word problems involving addition of two and three-digit numbers and persevere in determining solution methods. “Project the word problem (slide 2) and read it out loud to the group. Discuss the points below (MP1): Noah and Daniela are collecting pennies for a local charity. Noah has collected 124 pennies and Daniela has collected 132. How many pennies have they collected?” The teacher asks “What is the problem asking you to do? What do you need to find out? How will you calculate the total number of pennies?  Will you choose a mental or written method to calculate the total? What numbers help you to decide?” Students are then guided to solve problems in Student Journal, page 57, independently before sharing answers during Step 4 Reflecting on the work. Question 2a, “Solve each problem. Show your thinking. 199 hotdogs were sold in the first half and 175 hotdogs in the second half. How many hotdogs were sold?”

• Module 4, Lesson 12, Common fractions: Relating models, Step 3 Teaching the Lesson, students analyze word problems, consider the different fraction models they could use to represent each problem, and persevere to find a solution. “Tell the students that they are now going to solve word problems that involve fractions and that it might be helpful to use a model to help them solve the problem. Project slide 1 as shown. Then discuss the points below (MP1): Each load of washing uses 14 of a cup of washing powder. Victor does 3 loads of washing. How many cups of washing powder does he use? Organize students into pairs and have them work together to solve the problem. Direct them to pages 156 and 157 of the Student Journal to show their thinking. If some students struggle in the process, ask questions such as What could you do differently? What other model could you try? What is a similar problem using whole numbers that you can solve? (MP1)”

• Module 7, More Math, Problem Solving Activity 4, Word Problems, students make sense and persevere in solving one and two-step word problems using various operations. “Project slide 1 and read the word problem with the students. Ask, What information do we need to solve this problem? What operations will we use? What will we do first? What will we do next? How could you show your thinking? Allow time for students to find a solution. Then invite students to share their solution (72) and explain their thinking. Slide 1: One box holds 9 muffins. Two boxes hold a total of 18 muffins. Three boxes hold a total of 27 muffins. How many muffins will be in 8 boxes?”

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 7, Multiplication: Solving word problems, Step 3 Teaching the Lesson and Student Journal, Step Up, page 100, students reason abstractly and quantitatively as they decontextualize word problems and represent them symbolically. Step 3, “Discuss the students’ answers to Student Journal 3.7. Invite students to write their equations for Question 1 on the board (MP2).” Student Journal, Question 1, “This recipe makes one large bowl of fruit gelatin. Write the answers. Fruit Gelatin: 1 packet of gelatin, 2 sliced peaches, 10 strawberries, 1 can of pineapple, 4 bananas.” Question 1a-d, “How many sliced peaches are needed to make four bowls of fruit gelatin? Hailey bought 20 strawberries. How many bowls of fruit gelatin could she make? How many cans of pineapple are needed to make four bowls of fruit gelatin? Andre has 16 bananas. How many bowls of fruit gelatin could he make?”

• Module 6, Lesson 9, Data: Working with many-to-one picture graphs, Step 3 Teaching the Lesson, students reason abstractly as they interpret a picture graph and connect information to the context of the problem. “Project the picture graph as shown. Explain that this picture graph shows the number of cans that were recycled by three different grade levels. If necessary, review the definition of recycle.” Students answer teacher questions. Then, “Have the students identify the number of cans that have been recycled by each grade. They can then write equations to figure out the differences between the numbers of cans that were recycled. Ask questions such as, How many more cans did Grade 3 recycle than Grade 1? What is the difference between the number of cans recycled by Grade 1 and Grade 2? How many cans were recycled in total? How do you know? (MP2)”

• Module 7, Lesson 1, Multiplication: Introducing the sixes facts, Step 3 Teaching the Lesson, students reason abstractly and quantivity about multiplication as they write equations to match arrays. “Project slide 1 and ask, What do you know about this array? What multiplication fact could we write to match? Interpret each array with the students. Encourage them to describe how a known multiplication fact (8 x 5 = 40) can be used to figure out an unknown multiplication fact (6 x 8 = 48). Say 5 rows of 8 is 40, 6 rows of 8 is 8 more, 6 rows of 8 is 48. Remind the students that the array shows another fact when it is rotated by a quarter turn. Ask a volunteer to write the matching equations 6 x 8 = 48 and 8 x 6 = 48  on the board. (MP2)”

• Module 10, Lesson 4, Area: Identifying dimensions of rectangles, Student Journal, Step Ahead, page 377, students reason abstractly and quantivity as they relate length to area in rectangles. “Use the grid to help solve this problem. A garden in a park is shaped like a rectangle. It has an area of 60 square units. The longer side of the garden is 15 units long. how long is the shorter side?” Step 4 Reflecting on the work, “Ask students to explain why all of the answers were the same. Have students discuss the possible dimensions of other parks that have an area of 60 square units where both dimensions are unknown. Finally, as time allows, discuss what the square units might be if the area is a park.(MP2)”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to 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 10, Multiplication: Introducing the tens facts, Step 3 Teaching the lesson, students justify their own thinking and critique the reasoning of others as they multiply tens. “Project the two groups of marbles (slide 5) and ask, How are the two collections of marbles the same? How are they different? (MP3) If needed, encourage students to think about the number of groups, the number in each group, and the product. Project the next two groups of marbles (slide 6) and repeat the discussion and questions with the two collections side-by-side. When students have established that the totals are the same in the two collections (four groups of ten is the same amount as ten groups of four), project slide 7 showing the summaries. Say, For the first collection you were able to count by tens to get the product. Does that work for the second collection of marbles? Is there another number you can skip count by to get the product? (Fours.) Emphasize that counting by ones, fours, or tens yields the same amount for either collection. If needed, ask volunteers to verify that it is true (MP3). Ask, Is there a way to figure out how many there are in total without having to skip count by tens? For example, is there a way to just know how many there will be in four groups of ten? Allow time for students to share their strategies on how they can remember without skip counting by tens (MP3).”

• Module 4, Lesson 8, Common fractions: Reviewing unit fractions, Step 3 Teaching the lesson, students justify examples and non-examples of unit fractions while critiquing the reasoning of others. “Discuss examples and non-examples created. If necessary, fold and mark one of the shapes so that it shows eight sections that are not equal in area (or length). Encourage a class debate about whether the sections are eighths or not. Make sure students justify their thinking and support their arguments with other examples. Prompt respectful critique by providing sentence stems such as (MP3): I agree/disagree with ___ because … That makes sense. I also think …  I understand why you think that, but …”

• Module 8, Student Journal, page 319, Convince a friend, students construct viable arguments and critique the reasoning of others as they determine equivalent fractions in real-word and mathematical problems. “Felipe cuts modeling clay into equal pieces for his art students. As he hands one piece to each of his 14 students he says, “Each person has one quarter of a block. Use it wisely, as there is not enough for everyone to have a second piece. Samantha figures out there must have been five blocks of clay to begin with. Do you agree or disagree with Samantha? Explain why. Share your thinking with another student to get feedback. Discuss how constructive feedback can help your learning.” 

• Module 10, Lesson 6, Area: Solving word problems, Students Journal, page 373, Step Ahead and Step 4 Reflecting on the work, students construct a viable argument and critique the reasoning of others when they solve word problems using units of measure and analyze solutions and answers of classmates. Step Ahead, “Write an area word problem to match this equation. Then write the area. A = 4 cm x 7 cm.” Step 4, “Invite students to share the word problems they wrote for Step Ahead. Remind other students to listen carefully and critique the problems (MP3). Prompt discussion with sentence stems such as: I can identify the numbers from the equation in … problem… I don’t think that problem matches because… We could change the problem by… The area is not correct because...” 

• Module 12, More Math, Thinking Tasks, Question 3, students construct viable arguments as they use geometric measurements to solve real world problems. “Students use black trim to put a border around the outside of the front of the display board. They have 40 feet of trim left over. Will they have enough trim for the back of the display board? If so, how much trim will be left? If not, how much more will they need? Explain and show your thinking.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 1, Student Journal, page 43, Mathematical modeling task, students model with math as they solve a word problem, explain their thinking, and then explain how others could use that thinking to solve similar problems. “To encourage recycling, Teresa promises 5 cents for every can or bottle the children in the neighborhood give to her. John lives down the street. He gives Teresa some bottles and collects a little over two dollars. Question a “Figure out the number of cans or bottles that could have been given to Teresa. Show your thinking.” Question b “Explain how the children in the neighborhood can apply the same thinking to figure out the amount they could collect for any number of cans or bottles.”

• Module 2, Lesson 3, Addition: Two- and three-digit numbers (with composing), Step 3 Teaching the lesson, students model addition strategies and explain their thinking about the strategy they chose. “Distribute a copy of the support page to each pair of students. Then project slide 4 as shown and discuss the points below: $38, $64 What is your estimate of the total cost of these two items? How did you form your estimate? How can you calculate the sum of the two items? What tool (base-10 blocks, number line, or written method) would you use? What steps would you follow? Have the students work in their pairs to calculate the sum. Although number lines and base-10 blocks are provided, stress that other strategies are also encouraged. It is important that students are given the freedom to choose a strategy/model that best reflects their thinking (MP5). Invite some students to show and explain their strategy (MP4).”

• Module 3, Lesson 9, Number: Comparing and ordering three-digit numbers, Step 3 Teaching the lesson, students model with math as they determine the order of three-digit numbers by placing them on a number line and by using the appropriate symbols to compare them. “Have two students mark the locations of the numbers on the number line (MP4). Highlight that when comparing two numbers on a number line, the number to the right will be greater than the number to the left. Then ask, What symbols can we use to show that a number is greater than or less than another number? Allow a student to write the symbols > and < on the board with the words greater than and less than labeled appropriately (MP4). Ask, ``Do any of you have a way to remember which symbol to use?”

• Module 7, Student Journal, page 280, Mathematical modeling task, students model a real- world problem involving calculations with perimeter. “Isaac and Naomi are building a sandbox with 7 sides like the one below. There is one post at each corner and there are 3 wooden planks between the posts on each side. Each wooden plank needs 2 bolts to fix it into place. Write a list to show how many wooden planks and how many bolts Isaac and Naomi need to 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 4, Lesson 3, Division: Introducing the tens facts, Step 3 Teaching the lesson, students use the appropriate strategy as a tool in order to solve problems in multiple ways, explain how methods are connected, and why solutions make sense. “Project the diagram shown above (slide 1) and say, Each set of three numbers belongs to a fact family. Why do you think there is a circle around one of the numbers in each set? (It represents the product.) Why does it represent the product? What do the other numbers represent? (Either the number of groups or the number in each group.) Organize students into pairs and distribute the resources. Have them work together to calculate and write the missing number in each group of three on the support page. Remind them that for each example, they can use strategies including acting it out with cubes or counters, drawing pictures, or using words to help find the solution (MP5).”

• Module 5, Lesson 9, Subtraction: Counting back to subtract two- and three-digit numbers (with decomposing), Step 3 Teaching the lesson, students choose strategies as tools in order to model subtraction of two and three-digit numbers. “Project the next equation (slide 3). Organize students into pairs to discuss how they would most likely solve the problem mentally or find a reasonable estimate. Encourage students to choose a strategy and/or tool to record or step through their thinking (MP5). Invite students to explain and demonstrate their preferred method, using Flare Place Value or simply drawing on the board for any discussion with base-10 blocks.”

• Module 10, Student Journal, page 356, Mathematical modeling task, students choose from tools or strategies they have learned to solve a multi-step real-world problem. “Paul is buying materials for a new building project. He notices 35 long wood screws are sold in each packet. He needs 300 wood screws in total and wonders if 8 packets are enough. How many packets of wood screws should Paul buy? Explain your thinking.” 

• Module 12, More math, Problem solving activity 1, students choose an appropriate strategy as a tool to solve a real-world problem. “Oliver is planning a birthday party and can order tables that can seat 4 or 6. 76 people are coming to the party and he wants all the tables to be filled. How many tables should Oliver order?” Directions to the teacher state, “Discuss points such as, Is there a way to organize the information to help you answer the question? Could you draw a picture to help? Could you use a table? What operation (addition, subtraction, multiplication, division) could you use? Can all the groups be equal in size? Is there more than one possible solution? Organize students in pairs to solve the problem. Observe whether they use a systematic approach to finding a solution. Afterwards, invite pairs of students to share the different solutions.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 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 1, Lesson 6, Number: Locating four-digit numbers on a number line, Step 3 Teaching the lesson, students attend to precision as they label 4-digit numbers on a numberline and check their work. “Project the Step In discussion from Student Journal 1.6 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. Remind students to use the number lines with precision and to take the time to check their answers before moving on (MP6).”

• Module 7, Lesson 4, Multiplication: Working with all facts, Student Journal, page 252, Step Up, students attend to precision as they find multiplication facts that are close to a given number. Question 1, ”Write four multiplication facts to match each of these. a. Facts with a product close to 39. b. Facts with a product close to 52. c. Facts with a product close to 46. d. Facts with a product close to 11.”

• Module 9, Thinking Tasks, Preparing for a School Assembly, Question 1, students attend to precision as they multiply to solve a real world problem. “Every year in the gym, the school hosts two choir assemblies where students perform for their families. Half the families come on the first night and half the families come on the second night. Each grade helps prepare for the choir performance. Grade 3 has two tasks: Set up the risers where students stand to sing. 6 students can fit on one riser. Set up the chairs for the families in the audience. 48 chairs fit in each section. Students will stand on the risers to sing. How many students will fit in each full row of risers? What is the greatest number of students who can stand on all the risers to perform all at once? Show your thinking.”  

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, array, closest, commutative property of addition, commutative property of multiplication, compare, distance, double, equation, fact, fraction, greater than, greater, greatest, hundreds, least, less than, longer, meter (m), multiplication, multiply, nearest, number line, one-fourth, one-half, one-third, order, place value, polyhedron, position, product, pyramid, rectangle, round (a number), rows of, shorter, split, tens.” 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 8, Lesson 8, Common fractions: Exploring equivalent fractions, Student Journal, page 304,  Words at Work, students use the specialized language of mathematics to write equivalent fractions and explain how they are equivalent. “Write two equivalent fractions. Write how you know the two fractions are equivalent.”

• Module 10, Lesson 2, Area: Calculating the area of rectangles (metric units), Step 2 Starting the lesson, students use the specialized language of mathematics as they reason about and explain area problems. “Review what the students know about the area by asking, What does area mean? Encourage students to share their understanding (MP6). Establish that area relates to the amount of space that an object covers.” Student Journal, Step Ahead, age 361, “a. Measure the area of this rectangle using these blocks and write the number of each. _ orange pattern blocks _ base-10 ones blocks. b. What do you notice? c. Why do you think this happened?”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices 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 3, Number: Representing four-digit numbers, Step 2 Starting the lesson, students look at and use base-10 blocks and expanders to apply their understanding of two- and three-digit numbers to four-digit numbers. “Open Flare Place Value showing the base-10 tens block and a base-10 ones block. Refer to the tens block and ask, How many ones would we need to show the same number? (Ten.) Why do we need exactly ten ones? Bring out that the total amount is the same (MP7). Say, One ten is the same amount as ten ones. Repeat the discussion for a tens block and a hundreds block. Show a thousands block and a ones block and ask, How many ones would you estimate are in the big block? (Note: Researchers have noted that many students, even many in Grade 6, will estimate that there are around six hundred ones represented in a thousands block. Many students see the thousands block as composed of six hundreds blocks, one for each face.) Demonstrate with blocks how a thousands block represents 10 hundreds blocks stacked on top of each other. Have students count by hundreds for each layer that is stacked. Say, Ten hundreds is the same amount as one thousand. Encourage students to think about a thousands cube as having ten layers of the hundreds blocks (MP7). Ask, How many tens blocks are in a thousands block? Allow time for students to figure out the amount then say, One hundred tens is the same amount as one thousand. Organize students into groups and distribute the resources. Have them work in groups to build a thousands block with tens blocks to demonstrate the relationship. (MP7)”

• Module 4, Lesson 6, Division: Introducing the twos and fours facts, Step 3 Teaching the lesson, students use the structure of multiplication to think about the relationship between multiplication and division. “Project slide 1 as shown. Clarify that 12 dots have been arranged into equal rows, and that some of the dots have been covered. Then discuss the points below: 12 dots, 2 equal rows, What do you know about this picture? What do you see? What do you need to figure out? (The number of dots in each row.)  How could we calculate the number of dots in each row? What equation could we write to help figure out the number in each row? Encourage students to use thinking such as “2 rows of ___ is 12,” “Double ___ is 12,” “12 divided equally into 2 rows is ___,” or “Half of 12 is ___.” (MP7) Write the multiplication equation with a missing factor, 2 × ___ = 12 and the related division equation 12 ÷ 2 = ___ on the board. Ask, Which equation is easier to solve? Invite individuals to share and justify their thinking (MP3). Complete the equations on the board. Repeat the activity for diagrams showing 16 dots, 2 equal rows (slide 2), and 10 dots, 5 in each row. (slide 3)”

• Module 7, Lesson 1, Multiplication: Introducing the sixes facts, Step 4 Reflecting on the work, students make use of structure as they connect strategies for sixes and nines multiplication facts. “Project slide 7. Ask students to describe the thinking they would use to figure out the products. Where possible, encourage them to suggest more than one strategy. Highlight the strategies that use the distributive property of multiplication. Ask, How is this strategy the same as (different from) the strategy we used for the nines multiplication facts? How is it different? Help students recognize the similarities between the structure and models used for the two strategies. (MP7)” Slide 7, “$6\times7$ = __  $6\times8$ = __ $6\times4$ = __ .”

• Module 9, Lesson 8, Common fractions: Comparing unit fractions (length model), Student Journal, page 340, Step Up, Question 1, students make use of structure as they recognize patterns in numbers. “a. Color one part in each row of this fraction chart. b. Circle the fraction that is greater in each pair. $\frac{1}{2}$ or $\frac{1}{4}$, $\frac{1}{8}$ or $\frac{1}{2}$, $\frac{1}{4}$ or $\frac{1}{8}$.” Step 4 Reflecting on the work, “Discuss the students’ answers to Student Journal 9.8. Refer to Step Up and ask, What is the same about all the fractions? (The numerator is always one.) Write the term unit fraction on the board and explain that unit fractions always have a numerator of one. Ask, What happens to the size of unit fractions when the denominators increase? Discuss the points below: As the denominator increases, the size of the unit fraction decreases. The denominator helps determine the size of the unit fraction and the numerator helps count how many unit fractions there are. For example, $\frac{3}{4}$means there are 3 (count) unit fractions of $\frac{1}{4}$(size). There is a pattern to the relationship between the number of parts and the size of the parts needed to fill the whole. (MP7) 2 one-halves make one whole, 3 one-thirds make one whole, 4 one-fourths make one whole.”

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 2, Lesson 1, Addition: Investigating patterns, Step 3 Teaching the lesson, students extend knowledge of number patterns to find unknowns in equations. “Project the next pan balance picture (slide 5) and ask, What will happen to the pan balance? How can we keep it level (even)? Encourage students to explain that one of the parts will need to be changed. Project the related equation 26 = 15 + ___ (slides 6 and 7) and have a volunteer write the unknown part (MP8). Repeat the discussion to change the total to 27 and then 28. (slides 8 to 10)”

• Module 7, More math, Investigation 3, Using written methods to add, students use repeated reasoning as they look for shortcuts to solve problems. “What are all the different written methods that could be used to calculate 537 + 374? How are the same methods (different)? What are the advantages (disadvantages) of the methods? Are there times when you would use one method over the other? Why?” 

• Module 8, Lesson 5, Common fractions: Counting beyond one whole, Student Journal, page 294, Step Up, Question 1, students use repeated reasoning as they represent fractions visually. “Each strip is one whole. Color parts to show each fraction. a. $\frac{1}{3}$ b. $\frac{2}{3}$ c. $\frac{3}{3}$ d. $\frac{4}{3}$ e. $\frac{5}{3}$ f. $\frac{6}{3}$ g. $\frac{7}{3}$.” Step 4 Reflecting on the work, “Some students may relate the length models to equal groups of two, four, and eight, and use multiplication to calculate the numbers in six wholes. For example, "Six wholes is six groups of two halves, or 12 halves." Others may use repeated addition or skip counting to figure it out. (MP8)”

• Module 12, Lesson 1, Division: Two-digit numbers, Student Journal, page 435, Step Up, Question 2a, students extend their fact families knowledge to writing equations. “Draw blocks in the large part to show the number being shared. Then draw blocks in the small parts to show the number in each share. Complete the equation. $48\div 2$.”  Step 4 Reflecting on the work states, “Refer to Question 2a. Remind students of the earlier lessons about fact families. Say, We know that $48\div 2 = 24$. What other related equations can we write? Invite volunteers to record the related equations ($48\div 2 = 24$, $24\times 2 = 48$, $2\times 24 = 48$) on the board. (MP8)”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 2, students explored the idea of adding equal groups. In this module, the multiplication symbol is introduced as a quick way to express an addition number sentence when all the addends are the same number. E.g. rather than writing 4 + 4 + 4 + 4 + 4, students explain that they could write 5 × 4. The array model for multiplication is also used to help students see that two multiplication equations can often be written for the single situation. E.g. the 5 by 4 array can be described as 5 × 4 = 20, and as 4 × 5 = 20. This relationship, known as the commutative property, helps students when they begin to learn multiplication number facts. In this module, the students begin to learn their first multiplication number facts. Without realizing it, they should already be familiar with many of the facts. The tens facts relate to what the students know about place value. E.g. 6 groups of 10 is 6 x 10, or 60. Using the commutative property, students realize that when the picture of 6 x 10 is represented as an array, it is the same as 10 x 6. These comprise the first set of 19 facts to be learned. The strategy to learn the fives facts is introduced here because it is closely connected to students’ knowledge of the tens facts.”

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: Locating four-digit numbers on a number line, Step 2 Starting the lesson, teachers provide context about equal parts on a number line. “Ask, What are some different ways we can represent one thousand? Encourage students to describe different methods that include individual objects (counters or people), grouped objects (money or a base-10 block or blocks), as place value (place-value chart), and relative position (the number line.)”

• Module 5, Lesson 2, Multiplication: Reinforcing the eights facts, Step 3 Teaching the lesson, provides teachers guidance about how to solve problems using the four operations. ““Organize students into pairs and distribute the cubes. Have students take turns to roll the cube and practice verbalizing the double-double-double strategy, for example, “Double (4) is (8), double (8) is (16), double (16) is (32). (8) times (4) is (32).”  After several turns each, distribute the support page. Have the students take turns to roll the cube and multiply the number rolled by eight. The student then shades an array to match and writes the two related multiplication facts. If a student rolls the same number, they should roll again. When the pairs have completed the support page, ask, What strategy did you use to calculate each product? Encourage discussion, as an alternative strategy may be more efficient in some instances. Project the Step In discussion from Student Journal 5.2 and work through the questions with the whole class. Emphasize how the turnaround fact 2 × 8 is easier than 8 × 2 because double 8 involves fewer steps than double double double 2. Read the Step Up and Step Ahead instructions with the students. Make sure they know what to do, reminding students to work with care and check their answers prior to moving on (SMP6). Then have them work independently to complete the tasks.”

• Module 9 Lesson 8, Common fractions: Comparing unit fractions (length model), Lesson overview and focus, Misconceptions, include guidance to address common misconceptions as students comprare fractions. “When comparing unit fractions, students often have the misconception that a greater denominator gives a greater value. Experiences such as folding strips of paper to create various fractions can reinforce the idea that if there are fewer pieces in the whole, each individual piece has a greater area.”

The materials reviewed for Origo Stepping Stones 2.0 Grade 3 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, Research in practice, Addition, supports teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, this work provides the foundation for the introduction of the standard algorithm for addition in Module 7 which extends to adding multidigit numbers and three addends in Grade 4 Module 2 focusing on fluency by the end of Grade 4. In preparation for this work, provide many opportunities for students to practice place-value strategies that involve adding the hundreds, tens, and ones separately. For example, to solve 443 + 175, thinking 400 + 100 = 500, 40 + 70 = 110, and 3 + 5 = 8, then 500 + 110 + 8 = 618. after regrouping 10 tens as 1 hundred. Read more in the Research into Practice section of Module 7 and of Grade 4 Module 2.”

• Module 5, Research into Practice, Multiplication, supports teachers with concepts for work beyond the grade. “Students will extend their multiplicative thinking to a third context, multiplicative comparison in Grade 4 Module 5. Read more about the ways multiplicative comparison develops in the Research into Practice section for Grade 4 Module 5.”

• Module 9, Preparing for the module, Research into practice, Subtraction, includes explanation and examples connected to subtraction. To learn more includes additional adult-level explanations for teachers. “Zero is a challenge in subtraction with regrouping. English number words do not always make the 0 evident (602 as six hundred two), and students must listen for omissions (nothing for the tens place) as well as for what is said (hundreds and ones places). Using a number line to represent subtraction as distance, or difference, between two numbers can be helpful. It may be easier to work through the challenges of 0 when considering a situation other than taking away.” To learn more, “Beckett, Paula F., Deb McIntosh, Leigh-Ann Byrd, and Sueann E. McKinney. 2011. “Action Research Improves Math Instruction.” Teaching Children Mathematics 17 (7): 398–401.”

• Module 10, Preparing for the module, Research into practice, Area, includes explanations and examples connected to area and spatial reasoning. To learn more includes additional adult-level explanations for teachers. “Students use area as they develop an understanding of multiplication. More formal study of area as measurement requires that students connect their numeric understanding of multiplication along with their spatial understanding of covering a flat surface with no gaps or overlaps. As students work with square units of various sizes, they extend their reasoning from fractions to the idea that it takes a greater quantity of smaller units to cover the same area. In other words, the area of a paper measured in square centimeters is a greater number than the same paper measured in square inches. They must also understand that area is additive; a shape can be partitioned into two or more non-overlapping parts and the area of the whole is the sum of the area of each part. This allows the area of unfriendly shapes to be calculated by partitioning the shape into smaller, more workable figures such as rectangles and squares.” To learn more, “Bay-Williams, Jennifer M. and Sherri L. Martinie. 2015. “Order of Operations: The Myth and the Math.” Teaching Children Mathematics 22 (1): 20–27. Karp, Karen S., Sarah B. Bush, and Barbara J. Dougherty. 2014. “13 Rules That Expire.” Teaching Children Mathematics 21 (1): 18–25.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 3 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 3 and the Common Core Standards, includes all Grade 3 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 8, 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 6, Lesson 9, Data: Working with many-to-one picture graphs, the Core Standard is identified as 3.MD.B.3. The Prior Learning Standard is identified 2.MD.D.10. 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 3, Mathematics Overview, Operations and Algebraic Thinking, includes an overview of how the math of this module builds from previous work in math. “In Grade 2, students explored the idea of adding equal groups. In this module, the multiplication symbol is introduced as a quick way to express an addition number sentence when all the addends are the same number. E.g. rather than writing 4 + 4 + 4 + 4 + 4, students explain that they could write 5 × 4. The array model for multiplication is also used to help students see that two multiplication equations can often be written for the single situation. E.g. the 5 by 4 array can be described as 5 × 4 = 20, and as 4 × 5 = 20. This relationship, known as the commutative property, helps students when they begin to learn multiplication number facts. In this module, the students begin to learn their first multiplication number facts. Without realizing it, they should already be familiar with many of the facts. The tens facts relate to what the students know about place value. E.g. 6 groups of 10 is 6 x 10, or 60. Using the commutative property, students realize that when the picture of 6 x 10 is represented as an array, it is the same as 10 x 6. These comprise the first set of 19 facts to be learned. The strategy to learn the fives facts is introduced here because it is closely connected to students’ knowledge of the tens facts.”

• Module 10, Mathematics Overview, Coherence, includes an overview of how the content in 3rd grade connects to mathematics students will learn in fourth grade. “Lessons 10.1–10.6 focus on area of rectangles, including units of measure, computation, and applications with word problems. This extends work from counting unit squares to find area (2.12.7–2.12.8) and prepares students both for further study of area (4.3.9–4.3.12) as well as for using the area model in multi-digit multiplication (4.6.1–4.6.5).”

• Module 8, Lesson 9, Common fractions: Identifying equivalent fractions on a number line, Topic Progression, “Prior learning: In Lesson 3.8.8, students use concrete materials and pictures to find different ways to describe the same fractional part of one whole. The whole is represented with area models of different shapes. 3.NF.A.3, 3.NF.A.3a, 3.NF.A.3b; Current focus: In this lesson, students place fractions on number lines and identify other fractions that are located on the same point on the number line. Some number lines are already partitioned and other number lines need to be partitioned by students. 3.NF.A.3, 3.NF.A.3a, 3.NF.A.3b, 3.NF.A.3c; Future learning: In Lesson 3.9.8, students use a length model to compare unit fractions. 3.NF.A.3, 3.NF.A.3d” 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 3 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, “Addition: In Grade 3, students are increasingly confident of their addition skills using manipulatives and visual models such as base-10 blocks and number lines. They learn that the strategies they know can generalize to multi-digit numbers because of the structure of the base-ten number system. Students are adding by combining quantities within a single place-value column and then regrouping to find the total. Written methods such as partial sums lay a solid foundation for mastery of the standard algorithm which will come in Grade 4. Time: Elapsed time is a very difficult concept for elementary students, in part because there are multiple strategies for finding a solution. Do we jump ahead one hour and then count back? Count ahead to the next hour and then continue? Open time lines are powerful tools for helping students think about elapsed time because they can be flexible in the jumps they make to determine the amount of time passing between beginning and ending times. 2D shapes: Students’ understanding of geometry does not become more sophisticated simply with the passage of time, but instead is gained through specific instructional experiences. Understanding quadrilaterals, particularly the relationships among squares, rectangles, and rhombuses, requires students to think about attributes not in terms of which ones a shape has, but in terms of which ones are required for a given label. Students must be confident of their ability to identify the attributes of shapes before they are able to see the relationships among shapes in a given family. To learn more: Dixon, Juli K. 2008. “Tracking Time: Representing Elapsed Time on an Open Timeline.” Teaching Children Mathematics 15(1): 18-24. Howse, Tashana D. and Mark E Howse 2014. “Linking the van Hiele Theory to Instruction.” Teaching Children Mathematics 21(5): 304-313. References: Burger, William F. and J Michael Shaughnessy. 1986. “Characterizing the van Hiele Levels of Development in Geometry.” Journal of Research in Mathematics Education 17(1): 31-48. Fuson, Karen and Sybilla Beckmann. 2012. “Standard Algorithms in the Common Core State Standards.” NCSM Journal of Mathematics Leadership 14-30. Monroe, Eula Ewing, Michelle P. Orme, and Lynnette B. Erickson. 2002. "Working Cotton: Toward an Understanding of Time." Teaching Children Mathematics 8(8): 475-79.”

• Module 10, Preparing for the module, Research into practice, “Area: Students use area as they develop an understanding of multiplication. More formal study of area as measurement requires that students connect their numeric understanding of multiplication along with their spatial understanding of covering a flat surface with no gaps or overlaps. As students work with square units of various sizes, they extend their reasoning from fractions to the idea that it takes a greater quantity of smaller units to cover the same area. In other words, the area of a paper measured in square centimeters is a greater number than the same paper measured in square inches. They must also understand that area is additive; a shape can be partitioned into two or more non-overlapping parts and the area of the whole is the sum of the area of each part. This allows the area of unfriendly shapes to be calculated by partitioning the shape into smaller, more workable figures such as rectangles and squares. Multiplication: As students consolidate their multiplication skills, they start to integrate their own understanding of multiplication (including basic facts, area models, properties, and place value) into a larger picture of the operation. Students use place-value thinking to understand multiplication by ten, although teachers must be careful to avoid the add a zero generalization as this will not work with decimals (2.5 × 10 ≠ 2.50). The doubling-and-halving strategy is extended to a wider range of numbers, building confidence in this as a strong strategy. Students also begin to extend the area model to partial products, and develop basic understanding of the distributive property when they think about 4 × 12 as (4 × 10) + (4 × 2). This is the foundation for understanding why the multiplication algorithm works. Algebra: As students reason the process of solving multistep problems, they develop conceptual understanding of the order of operations. They realize that the sequence of steps in solving a problem depends on the situation, and that the order in which they make calculations follows from this logic. This conceptual foundation for the order of operations is critical to a deep understanding of the order of operations as a mathematical principle. Ensure students can reason the steps to solve a problem and identify common patterns before teaching the rules. To learn more: Bay-Williams, Jennifer M. and Sherri L. Martinie. 2015. “Order of Operations: The Myth and the Math.” Teaching Children Mathematics 22 (1): 20–27. Karp, Karen S., Sarah B. Bush, and Barbara J. Dougherty. 2014. “13 Rules That Expire.” Teaching Children Mathematics 21 (1): 18–25. References: Lampert, Magdalene. 1986. “Knowing, Doing, and Teaching Multiplication.” Cognition and Instruction 3 (4): 305–42. Lynne M. Outhred and Michael C. Mitchelmore. 2000. “Young Children’s Intuitive Understanding of Rectangular Area Measurement.” Journal of Research in Mathematics Education 31(2): 144-167.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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, “objects of different and equivalent masses, pan balance and a set of cubes each having the same mass in lesson 1. Each group of students need circles of strings in lesson 12, cube labeled: 1, 2, 3, 4, 5, 6, cube labeled: 10, 20, 30, 40, 50, 60 in lesson 1, a ruler in lessons 11 and 12, and Support 52 in lessons 10, 11, and 12. Each pair of students needs base-10 blocks (hundreds, tens, and ones) in lesson 3 and a ruler in lesson 10. Each individual student needs small cubes or counters and Support 46 in lesson 1, scissors and glue and Support 53 in lesson 12, square tiles in lesson 10, and the Student Journal in each lesson.” 

• Module 2, Lesson 10, 2D shapes: Exploring Rectangles, Lesson notes, Step 1 Preparing the lesson, “Each group of students will need: 1 set of shape cards from Support 52 (Note: Retain for use in Lessons 2.11 and 2.12). Each student will need: square tiles (if needed and Student Journal 2.10.” Step 2 Starting the lesson, “Organize students into groups and distribute the shape cards. Ask students to look through the shape cards and separate those shapes that are rectangles from the rest of the shapes.”

• Module 5, Preparing for the module, According to the Resource overview, teachers need, “connecting cubes in lessons 4 and 5, paper plates in lesson 5 and Support 74 in lesson 6. Each pair of students needs base-10 blocks (if needed) in lesson 8, connecting cubes in lesson 5, transparent counters, and a cube labeled: 3, 4, 5, 6, 7, 8 in lesson 3, cube labeled: 4, 5, 6, 7, 8, 9 and Support 72 in lesson 2, paper in lessons 8 and 10, plastic drinking cubs in lesson 5, and Support 73 in lesson 3. Each individual student needs paper in lessons 4, 6, and 12, Support 77 in lessons 8, 9, 10, and 11, and the Student Journal in each lesson.”

• Module 7, Lesson 9, Addition: Working with the standard algorithm (composing hundreds), Lesson notes, Step 1 Preparing the lesson, “You will need: base-10 blocks (hundreds, tens, and ones); Each student will need: Student Journal 7.9.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 6, Multiplication: Reinforcing the ones and zeros facts, include:

• Extra help, “Activity: Organize students into groups and distribute the cards. Mix the cards and lay them facedown in a pile. Ask each student to choose a card and represent the expression as a picture. This can be repeated as time allows.”

• Extra practice, “Activity: Organize students into pairs and distribute the game boards. Ask each student to write a single-digit number (including 1 and 0 at least once) inside each square, record each product in the corresponding circle then erase the four factors. Pairs exchange their game boards, then write the missing factors to complete the diagram.”

• Extra challenge, “Activity: Organize students into pairs. Mix the cards and distribute them to each student, facedown in two piles. Have students then take turns to turn over their top card, faceup, into a central pile. Students say the answer to the problem as they turn their card. If two cards are turned that show the same answer, students slap the pile and then add the accumulated cards to the bottom of their pile. The student who has more cards at the end of the game wins.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 6, Time: Reading and writing to the minute, Differentiation, Extra Challenge, “Organize students into pairs and distribute the resources. Have the students cut the support page in half so that they each have six clocks and labels. Each student then draws hands on their clocks to show six different times. They exchange clocks and complete the relevant labels directly below. Afterward, have the students cut apart each clock and its label. They can then mix-and-match the clocks and labels.”

• Module 5, Lesson 11, Counting on to subtract two- and three-digit numbers (with composing), Differentiation, Extra Challenge, “Organize students into pairs to play the online Fundamentals game, Make a Difference. As students play the game they can describe whether they used a count-back or count-on strategy for each calculation.”

• Module 10, Lesson 10, Algebra: Investigating order with multiple operations, Differentiation, Extra Challenge, “Organize students into groups and distribute the resources. Have students mix the number cards and place them facedown in a pile. Students take turns to turn over four cards and write the numbers in the order in which they were turned over from left to right in the first equation on their sheet. They then use their knowledge of the order of operations to calculate the answers. This is repeated as time allows or until five equations are solved. Further challenge students to write the multiplication and addition symbols (or use subtraction, depending on the abilities and confidence of the students) in any order they like for the final two equations. If time allows, have students then exchange sheets with another member of the group and write a word problem to match the first equation on the reverse of the sheet.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 4, Lesson 6, Division: Introducing the twos and fours facts, Lesson notes, Step 2 Starting 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. Provide time for the student to process the questions, formulate an answer, and then speak about their thoughts to another student before presenting their ideas to the class.” Step 3 Teaching the lesson, “ELL:Allow the students to use hand gestures (such as thumbs up or down) to show their agreement or disagreement with another student's methods of solving the equation. Allow the students to work in their pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Provide sentence stems, such as, "It helps me because ..." or "The fact families are ..."”

• Module 11, Lesson 10, Capacity: Reviewing cups, pints, and quarts, Lesson notes, Step 2 Starting the lesson, “ELL: Allow students to discuss cups, pints, and quarts before continuing the activity. Ensure they know the difference between the word cup as in the measurement for capacity, and cup as something to drink from; also the difference between the words quart as in the measurement for capacity, and court as in a basketball court. When saying the word quart, remember to clearly enunciate the qu sound. Encourage the students to say the word with you a few times. Provide examples of cups, pints, and quarts in pictorial and/or real-world form. Encourage the students to talk about a time they have seen or used a cup, pint, or quart.” Step 3 Teaching the lesson, “ELL: Encourage the students to explain what they are learning to check that they understand the concept. 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 pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Allow the students to use hand gestures (such as a thumbs up or down) to show they agree, or disagree, with another student’s answers.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 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 2, Lesson 2, Addition: Two-digit numbers (with composing), Step 3 Teaching the lesson, references base-10 blocks, a number line and an online tool as strategies to add two digit numbers. “Organize students into pairs and distribute the resources. Have them work together to solve the problem. Place the resources (number lines, base-10 blocks) at the front of the classroom. Inform students that the resources are there to help their thinking but are not compulsory. Bring the students together to share their strategies. Students who used base-10 blocks should use the Flare Place Value online tool to model their strategy.”

• Module 6, Lesson 1, Multiplication: Introducing the nines facts, Step 2 Starting the lesson, identifies the online Flare tool to support work with the tens facts. “Open the Flare Number Board online tool and ask, Where are the numbers we say when we count in steps of ten? Invite volunteers to randomly select the numbers, saying the numbers before they are revealed.”

• Module 10, Lesson 1, Area: Calculating the area of rectangles (customary units), Step 3 Teaching the lesson, references blocks, rulers, and a support handout to support practice with measuring customary units. “Distribute the resources. Have students use their ruler to measure the length of one side of the block. Demonstrate how the markings on the ruler are labeled to show how many inches fill the length of the ruler.”