## ORIGO Stepping Stones 2.0

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### Overall Summary

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials partially meet expectations for rigor and meet expectations for practice-content connections.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that they assess grade-level content and, if applicable, content from earlier grades.

Each Grade Level consists of 12 modules. Each module contains three types of summative assessments. Check-ups assess concepts taught in the module, and students select answers or provide a written response. Performance Tasks assess concepts taught in the module with deeper understanding. In Interviews, teachers ask questions in a one-on-one setting, and students demonstrate understanding of a module concept or fluency for the grade. In addition, Quarterly Tests are administered at the end of Modules 3, 6, 9, and 12.

Examples of assessment items aligned to Grade 3 standards include:

• Module 1, Check-Up 1, Problem 2, “Solve each problem. Write an equation to show your thinking. a. Luke has a sheet of stickers that has 10 rows of 5 stickers. How many stickers does he have in total? b. Mom cut 5 lengths of ribbon. Each piece was 4 inches long. What was the total length of the ribbon? c. Dad bought 8 balloons. They cost 10 cents each. How much did Dad pay for the balloons?” (3.OA.3)

• Module 6, Quarterly Test B, Problem 22, “A student figured the difference between 325 and 257 using the count-on strategy. Choose the equation that best matches. A. 325 - 257 = 57, B. 325 - 257 = 68, C. 325 - 257 = 65, D. 325 - 257 = 168.” (3.NBT.2)

• Module 9, Performance Task, Problem 1, “On the number line the distance from 0 to 1 is one whole. a. Label \frac{4}{6} and \frac{11}{8} on the number line. b. Write a fraction that is greater than \frac{4}{6} but has a denominator of 8. c. Write a fraction that is less than \frac{4}{6} but has a denominator of 6.” (3.NF.3).

There are some assessment items that align to standards above Grade 3; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include:

• Module 3, Interview, students double numbers by finding the product of 2\times 30, 43\times 2, 2\times 35, 2\times 45, and 17\times 2. (4.NBT.5).

• Module 3, Check-Up 2, uses numbers over 1,000 for rounding to the nearest ten or hundred. In item 1.a., students round the following numbers to the nearest hundred: 391; 4,386; 7,019; 1,089. In item 1.b, students round the following number to the nearest ten: 674; 899; 3,562; 1,499.

• Module 3, Performance Task, students write the nearest ten, nearest hundred, and nearest thousand depending on where the arrow points on a number line with values between 7,500 to 7,600. Module 3 uses numbers over 1,000 for rounding to the nearest ten or hundred.

• Module 3, Quarterly Test A, Problem 19, students round 5,346 to the nearest ten. Test B item 19 students round 1,452 to the nearest ten. Module 3 uses numbers over 1,000 for rounding to the nearest ten or hundred.

• Module 10, Interview, students find the area of a room that is 13\times 7. Students would need to be provided graph paper so they could draw out the room and count squares (4.NBT.5).

• Module 11, Check-Up 2, Problem 2, students figure change and identify coins and values of money. This does not relate to the standard of fluently adding and subtracting within 1,000 because decimals are required (5.NBT.7).

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in 3rd grade by including different types of student problems in each lesson. There is a Student Journal with problems in three sections: Step In, Step Up, and Step Ahead. Maintaining Concepts are in even numbered lessons and include additional practice opportunities, including Computation Practice, Ongoing Practice, Preparing for Module _, Think and Solve, and Words at Work. Each Module includes three Investigations and, within grade 3, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 1, Lesson 12 and Module 2, Lesson 4 engage students in extensive work with 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) as students use place value reasoning to solve problems. Lesson 12, Multiplication: Reinforcing the tens and five facts, Student Journal, Maintaining Concepts and Skills, Page 41, Question 1, “Cross out blocks to help you write the number of hundreds, tens, and ones that are left. Then write the difference. 465 - 130= ___. There are ___ hundreds. There are ___ tens. There are ___ ones.” Lesson 4, Addition: Developing written methods, Student Journal, Maintaining Concepts and Skills, Page 55, Question 2, “Write the number of hundreds, tens, and ones. Then write an equation to show the total. You can use blocks to help. 267 + 25. There are ___ hundreds. There are ___ tens. There are ___ ones. ___+___+___=___.”  Student Journals in Lessons 2, 4, 6, 8, 10, and 12 of each module, include two pages called Maintaining Concepts and Skills that provide all students additional practice in order to engage in extensive work with grade-level problems.

• Module 5 engage students in extensive work with 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations). In More Math, Problem Solving Activities, Activity 2, students reason about the relationship between quantities in a word problem. The teacher projects the question “At the zoo, one display has several spiders and a nearby display has legless lizards. Jayden counts 56 legs and 13 bodies in total in the displays. How many spiders and lizards are there?” Students work in partners to use eights and zeroes strategies to solve the word problem. Students discuss strategies with partners and then the class shares strategies as a whole.

• Module 9, Lesson 9, Common fractions: Comparing unit fractions (number line), engages students with extensive work with 3.NF.3d (Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, <, and justify the conclusions, e.g., by using a visual fraction model). In Student Journal, Step Up, page 344, Question 1, students use number lines to compare and order common fractions. “On each number line, the distance from 0 to 1 is one whole. a. Write the correct fraction above each mark on the number line. b. Split the distance from 0 to 1 into eighths and write the correct fraction below each mark. c. Write the correct fraction above each mark on the number line. d. Split the distance from 0 to 1 into sixths and write the correct fraction below each mark.”

The instructional materials provide opportunities for all students to engage with the full intent of 3rd grade standards through a consistent lesson structure, including sections called Step In, Step Up and Step Ahead. Step In includes a connection to prior knowledge, multiple entry points to new learning, and guided instruction support. Step Up engages all students in practice that connects to the objective of each lesson. Step Ahead can be used as an enrichment activity. Examples of meeting the full intent include:

• Module 4, Lesson 10, Common fractions: Representing unit fractions on a number line, engages students in the full intent of 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram), 3.NF.2a (Represent a fraction \frac{1}{b} on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size \frac{1}{b} and that the endpoint of the part based at 0 locates the number \frac{1}{b} on the number line), and 3.NF.2b (Represent a fraction \frac{a}{b} on a number line diagram by marking off a lengths \frac{1}{b} from 0. Recognize that the resulting interval has size \frac{a}{b} and that its endpoint locates the number \frac{a}{b} on the number line.) In the Student Journal, Step Up, page 147, Question 2, students label three number lines with one-fourth, one-sixth, and one-eighth. “The distance between 0 and 1 is one whole. Split each number line into more equal parts. Then draw an arrow to show the fraction.”

• Module 6, Lessons 8 and 9, engage students in the full intent of 3.MD.3 (Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.) In Lesson 9, Data: Working with many-to-one picture graphs, Student Journal, Step Up, page 220, Question 1, “This table shows the pizza sales for 5 days. Complete the graph at the top of page 221 to show the results.”  Students draw circles in the bar graph to represent the data from the table. Each circle represents 10 pizzas. Question 2a “Look at the graph above. On what day were the most pizzas sold?” Question 2b “How many pizzas were sold before Thursday?” Question 2c “How many more pizzas were sold on Friday than Wednesday?” Question 2d “How many pizzas were sold in 5 days?” Question 2e “How many more pizzas were sold on Thursday and Friday than on Monday and Tuesday?“

• Module 11, Lesson 6, Number: Reinforcing rounding with five-digit numbers, engages students with the full intent of 3.NBT.1 (Use place value understanding and properties of operations to perform multi-digit arithmetic). In the Student Journal, Step Up, page 411, Question 3, students round multi-digit numbers to the nearest ten or hundred using place value understanding. “Round each number to the nearest ten and hundred. 14,312, 51,678, 29,087, 26,305.” Step Ahead, page 411, “Carmen rounds a number to the nearest ten. Her answer is 26,000. She then rounds the same number to the nearest hundred. Her answer is 26,000. She then rounds the same number to the nearest thousand. Her answer is 26,000. Write five possible numbers Carmen could have rounded.”

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

##### Indicator {{'1c' | indicatorName}}

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days are included.

• The approximate number of modules devoted to major work of the grade (including supporting work connected to the major work) is 10 out of 12, which is approximately 83%.

• The approximate number of days devoted to major work of the grade (including supporting work connected to the major work, but not More Math) is 105 out of 156, which is approximately 67%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 94 out of 144, which is approximately 65%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 65% of the instructional materials focus on major work of the grade.

##### Indicator {{'1d' | indicatorName}}

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers on a document titled, “Grade __ Module __ Lesson Contents and Learning Targets” for each module. Examples of connections include:

• Module 2, Lesson 9, Time: Measuring intervals in minutes, Student Journal, Step Up, page 69, connects supporting work of 3.MD.B (Represent and interpret data) to the major work 3.MD.A (Solve problems involving measurement and estimation). Students solve problems about time intervals using a number line. Question 2b, “Draw jumps on the number line to solve each problem. A frozen pizza is put in the oven at 1:35 p.m. The pizza is taken out of the oven 40 minutes later. At what time was the pizza taken out?”

• Module 4, Lesson 8, Common fractions: Reviewing unit fractions, Student Journal, Step Up, page 141, connects the supporting work of 3.G.2 (Partition shapes into parts with equal areas) to the major work of 3.NF.1 (Understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts.) Students partition shapes into parts and determine the fraction. Question 3, “Each shape below is one whole. Color one part of each shape. Record the number of parts and then complete the fraction words. a. __ part of __ equal parts. ___ is shaded. b. __ part of __ equal parts. ___ is shaded c. __ part of __ equal parts. ___ is shaded.”

• Module 5, Lesson 12, Subtraction: Solving word problems, Student Journal, page 190, Step Up, connects supporting work 3.NBT.A (Use place value understanding and properties of operations to perform multi-digit arithmetic) and major work 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Students solve multi-digit, multi-step word problems. Question 2b “Solve each problem. Show your thinking. A spool holds 192 feet of rope. 54 feet was first cut off, then another 75 feet. How much rope is left on the spool?”

• Module 6, Lesson 10, Data: Working with bar graphs, Student Journal, Step Up, pages 222-223, connects supporting work of 3.MD.B (Represent and interpret data) to the major work of 3.OA.D (Solve problems involving the four operations, and identify and explain patterns in arithmetic). Students read tables, create graphs, and then solve word problems. Question 1, “This table shows the mass of some American animals. Complete the bar graph at the top of page 223 to show the results. Raccoon, 32, Beaver, 55, Wolf, 89, Coyote, 50.” Question 2a “Which two animals are of similar mass?” Question 2b “Which three animals have a total mass of about 150 pounds?” Question 2c “What is the difference in mass between the wolf and raccoon?” Question 2d “What is the difference in mass between the beaver and wolf?” Question 2e “What is the total mass of the beaver, wolf, and coyote?”

• Module 6, Lesson 12, Data: Working with line plots (fractions), Student Journal, Step Up, pages 228-229, connects supporting work of 3.MD.B (Represent and interpret data) to the major work of 3.NF.A (Develop understanding of fractions as numbers). Students measure the length of pieces of spaghetti to the nearest \frac{1}{4} inch then plot the lengths on a line plot and answer questions about the data. Question 1, “Your teacher will give your group some pieces of dry spaghetti. Use your inch ruler to measure the length of 20 pieces. Round each length to the nearest fourth of an inch. Use tallies to record the lengths on this chart.” Question 2, “Look at the tally chart in Question 1 on page 228. Draw an x on the line plot below to show each length.”

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Materials are coherent and consistent with the Standards. Examples of connections include:

• In Module 1, Lesson 8, Multiplication: Using the turnaround idea with arrays, Teaching the lesson, lesson notes, students interpret products of whole numbers, 3.OA.1, and apply properties of operations as strategies to multiply and divide, 3.OA.B, by using arrays to show the properties of operations.

• Module 6, Lesson 4, Multiplication: Solving word problems, Student Journal, p. 204, Step Up, Problem 1c, connects represent and solve problems involving multiplication and division 3.OA.A to solve problems involving the four operations 3.OA.D. Students are given a chart of County Fair Admission with prices: Child $4 each, Adult$9 each, Senior $5 each, and Weekend Pass$12 each. Solve each problem. Show your thinking. “If you buy two weekend passes, how much change will you receive from $30?” • In Module 4, students represent and solve problems involving multiplication and division, 3.OA, and develop understanding of fractions as numbers, 3.NF.A. • In Module 6 student represent and solve problems involving multiplication and division,3.OA, and solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects, 3.MD.A, by using graphs to solve word problems involving multiplication and division. ##### Indicator {{'1f' | indicatorName}} Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Materials relate grade-level concepts from 3rd Grade explicitly to prior knowledge from earlier grades. These references are consistently included within the Topic Progression portion of Lesson Notes and within each Module Mathematics Focus. At times, they are also noted within the Coherence section of the Mathematics Overview in each Module. Examples include: • Module 1, Lesson 7, Multiplication: Introducing the symbol, Lesson Notes connect 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) to work from grade 2 (2.OA.4). “In Lesson 2.11.5, students build arrays and describe them using rows of __. The lesson relates the set and area models of multiplication as students join the connecting cubes in each row to show groups. In this lesson (1.7), students use cubes to model multiplication problems and describe the representations using a variety of language.” • Module 5, Mathematics, Focus, Numbers and Operations in Base Ten, relates 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method). “This module reviews and extends strategies to add two-digit numbers, and is interwoven with work involving Operations and Algebraic Thinking described above. Students review composing with two-digit and three-digit numbers to add.” • Module 11, Lesson 7, Money: Adding amounts in cents (bridging dollars), Lesson Notes connect 3.NBT.2 (Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction) to the work from grade 2 (2.MD.8). “In Lesson 2.11.12, students solve word problems involving money. In this lesson (11.7), students use coins to add prices involving cents that total more than one dollar.” Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Topic progression portion of Lesson Notes and within the Coherence section of the Mathematics Overview in each Module. Examples include: • Module 2, Lesson 12, 2D shapes: Exploring relationships between shapes, Lesson Notes connect 3.G.1 (Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories) to work of grade 5 (5.G.3, 5.G.4). “In this lesson, students examine shapes whose properties allow them to belong to more than one shape family. Venn diagrams are used to sort shapes. In Lesson 5.5.10, students examine a defining feature of parallelograms.” • Module 7, Mathematics Overview, Coherence, “This work extends the learning from previous study of addition (3.2.1–3.2.5) and prepares students to fully understand and use the standard algorithm for addition (4.2.1– 4.2.7).” • Module 10, Lesson 6, Area: Solving word problems, Lesson Notes connect 3.OA.8 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) to the work of grade 4 (4.NBT.5, 4.MD.3). “In this lesson, students build square units of area with materials and then solve word problems involving the same units of measure. In Lesson 4.3.9, students calculate area by covering rectangles with square-inch tiles and using the dimensions of the rectangles to determine the total number of square units of area. Students use this practice to develop a rule for calculating the area of rectangles.” ##### Indicator {{'1g' | indicatorName}} In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 foster coherence between grades and can be completed within a regular school year with little to no modification. There are a total of 180 instructional days within the materials. • There are 12 modules and each module contains 12 lessons for a total of 144 lessons. • There are 36 days dedicated to assessments and More Math. According to the publisher, “The Stepping Stones program is set up to teach 1 lesson per day and to complete a module in approximately 2\frac{1}{2} weeks. Each lesson has been written around a 60 minute time frame but may be anywhere from 30-75 minutes depending upon teacher choice and classroom interaction.” ###### Overview of Gateway 2 ### Rigor & the Mathematical Practices The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). ##### Gateway 2 Meets Expectations #### Criterion 2.1: Rigor and Balance Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 partially meet expectations for rigor. The materials give attention throughout the year to procedural skill and fluency and spend sufficient time working with engaging applications of mathematics. The materials partially develop conceptual understanding of key mathematical concepts and partially balance the three aspects of rigor. ##### Indicator {{'2a' | indicatorName}} Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include some problems and questions that develop conceptual understanding throughout the grade level. Students have limited opportunities to engage with concepts from a number of perspectives, or to independently demonstrate conceptual understanding throughout the grade. Cluster 3.OA.A includes representing and solving problems involving multiplication and division. In Modules 6, 7, and 8, there are some opportunities for students to work with multiplication and division through the use of visual representations and different strategies. Examples include: • Module 6, Lesson 3, Multiplication: Exploring patterns with the nines facts, Step 2 Starting the lesson, “Ask, If we start at three and count in steps of three, what numbers between 0 and 60 will we say? How do you know? Write the numbers, as shown, on the board as the students count. After writing the two rows of numbers, discuss the points below: What do you notice? What do you think the last number in the next row will be? What numbers would we say between 100 and 120? Students make predictions and discuss patterns they see.” In the Step In portion of the lesson students fill in a hundreds chart with multiples of 9 and examine jumps of 9 on a number line. In the “Step Up” portion of the lesson, students relate subtraction facts with nines multiplication facts such as 10 - 1 = 1 x 9; 20 - 2 = 2 x 9; 30 - 3 = 3 x 9, etc (3.OA.1). • Module 4, Lesson 2, Division: Connecting multiplication and division, Step 3 Teaching the lesson, Open Flare Mats and Manipulatives (b) to reveal the grouping and sharing mat as shown. Then discuss the points below: What do you see in this picture? (The number of groups and the number in each group.) What is unknown? (The total.) How can we calculate the total? (Multiply.) What equation can we write to show what happened? (3 × 4 = 12.) Move the counters to the large space to confirm the total as shown. Write the equation 3 × 4 = 12 on the board, and remind students that when multiplying, the total is called the product. Then refer back to the picture to discuss the points below: What do you know about this picture? (The total and the number of groups.) What is unknown? (The number in each group.) How can we calculate the number in each group? (Divide.) What equation can we write to show what happened? (12 ÷ 3 = 4.) Move the counters equally into the small spaces to confirm the number in each group. Repeat the discussion using a mat with 4 groups and 3 counters in each group. Write the equations 4 × 3 = 12 and 12 ÷ 4 = 3 on the board. Indicate the four equations on the board and review (or introduce) the term fact families. Say, All of these equations form a fact family because they are related. Why do you think they are related? Guide the students to explain that all of the equations represent the same total (product) of 12 and that the number of groups and the number in each group is either 3 or 4.” During “Step In”, the teacher guides students through writing multiplication and division facts that are related to a given array. When students begin to practice independently in the “Step Up” portion of the lesson, they are provided the opportunity to use arrays to write related multiplication and division facts. (3.OA.2) • Module 6, Lesson 5, Division: Introducing the eights facts, Step 3 Teaching the lesson, “Project slide 3 as shown. Explain that each bag must have the same number of marbles. Then discuss the points below.What do you need to find out? What equation could we write?” (3.OA.2) • Module 7, Lesson 1, Multiplication: Introducing the sixes facts, Step 3 Teaching the lesson, Interpret each array with the students. Encourage them to describe how a known fact (5 × 8 = 40) can be used to figure out an unknown fact (6 × 8 = 48). Say, 5 rows of 8 is 40, 6 rows of 8 is 8 more. 6 rows of 8 is 48. Remind students that the array shows another fact when rotated a quarter turn. Ask a volunteer to write the matching facts 6 × 8 = 48 and 8 × 6 = 48 on the board. (MP2) Repeat this discussion with slides 3 to 6. Make sure students share their thinking and identify two multiplication facts to match each array showing a sixes fact. Organize students into pairs and distribute the resources. Demonstrate how to cut out and fold an array to create a build-up strategy card, as shown. Allocate a sixes fact to each pair and have them create the matching card (MP4). Then have students use the build-up strategy for their card to model the sixes facts it shows (MP7) and record the equations to match. Pairs can exchange cards as time allows.” (3.OA.1) • Module 8, Lessons 1-4 address conceptual understanding by focusing on division facts using arrays. Students are given an array with some of the array covered but the total amount of dots given, total rows of dots. Students then represent the array as a division equation and write multiplication problems related to the division problem (3.OA.2). The instructional materials present few opportunities for students to independently demonstrate conceptual understanding throughout the grade-level. In most independent activities students are directed how to solve problems. Examples include: • Module 1, Lesson 11, Multiplication, Introducing the 5’s Facts, Student Journal, page 36, Step Up, “Complete the tens fact. Circle half of the array and then complete the two fives facts to match.” Arrays are provided for students and students record the associated multiplication fact (3.OA.1). • In Module 1, Lesson 8, Multiplication: Using the turnaround idea with arrays, Activity 1, students determine the mystery number, 2,564, through a series of questions that do not require students to demonstrate conceptual understanding (3.OA.1). • In Module 6, Lesson 5, Division: Introducing the eights facts, Step 3 Teaching the lesson, “Project the Step In discussion from Student Journal 6.5 and work through the questions with the whole class. Ask, What strategy did you learn when you were multiplying by twos, fours, and eights? (Repeated doubling.) Use the diagrams to connect halving to division by two, four, and eight. Ask, How many times should you halve something to divide by 2? (Once.) Divide by 4? (Twice.) Divide by 8? (3 times.) Read the Step Up and Step Ahead instructions with the students. Remind students that they can use tools from the resource center to model the halving strategy in Question 1. Make sure they know what to do, then have them work independently to complete the tasks.” Students are told how to calculate the problem and are not given the opportunity to demonstrate their understanding. (3.OA.2) ##### Indicator {{'2b' | indicatorName}} Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the Grade 3 expected fluencies, single-digit products and quotients (products from memory by end of Grade 3) and add/subtract within 1000. The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills. The materials attend to the Grade 3 expected fluencies: 3.OA.7 fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. For example, In Module 3, Lesson 1 students build fluency through completing Maintaining Concepts and Skills. In Maintaining Concepts and Skills, students identify addition, subtraction and multiplication facts primarily of fives and tens. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include: • Maintaining Concepts and Skills lessons incorporate practice of previously learned skills from the prior grade level. For example, Maintaining Concepts and Skills in Module 1, Lesson 2, Number: Identifying three-digit numbers on a number line, provides practice for adding and subtracting within 20 (2.NBT.2). • Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills , such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 4’s Interview 1 has students demonstrate fluency of 2’s multiplication facts and Interview 2 has students demonstrate fluency of 4’s multiplication facts. • “Fundamentals Games” contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Double Bucket, students demonstrate fluency of 2’s multiplication facts and on Interview 2 students demonstrate fluency of 4’s multiplication facts (3.OA.7). • Some lessons provide opportunities for students to practice the procedural fluency of the concept being taught in the “Step Up” section of the student journal. • Activities provide practice for skills learned earlier in the grade such as, Module 9, Lesson 6, Subtraction: Exploring subtraction involving zero, where students practice multiplication facts (3.OA.7). ##### Indicator {{'2c' | indicatorName}} Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step word problems presented in contexts in which mathematics is applied. There are routine problems, and students also have opportunities to engage with non-routine application problems. Thinking Tasks found at the end of Modules 3, 6, 9, and 12, provide students with problem-solving opportunities that are complex and non-routine with multiple entry points. Examples of routine application problems include: • Module 1, Lesson 7, Multiplication: Introducing the symbol, Student Journal, Step Up, page 25, Problem 2d, addresses standard 3.OA.3, “Henry cut 5 lengths of rope. Each piece was 4 meters long. What was the total length of rope?" • Module 4, Lesson 6, Division: Introducing the twos and fours facts, Student Journal, Step Up, page 135, Problem 3b, addresses standard 3.OA.3, “32 chicken nuggets are shared equally among 8 friends. How many nuggets are in each share?” • Maintaining Concepts and Skills includes some application problems and addresses standard 3.OA.8, for example Module 3, Lesson 8, Number: Working with place value, Student Journal, Maintaining concepts and skills, Ongoing Practice, page 105, Problem 2a, “Samuel’s mom bought 3 tickets for the roller coaster. Tickets are$4 each. What was the total cost?”

• Module 6, Lesson 4, Multiplication: Solving word problems, Student Journal, Maintaining concepts and skills, Words at Work, page 206, addresses standard 3.OA.8, “Michelle’s grandmother gave her $40 to spend at the county fair. Michelle had 6 rides on the Mega Drop and 4 rides on the Rollercoaster. Rides on the Mega Drop cost$5 each and rides on the Rollercoaster cost $8 each. She also bought lunch for$12. At the end of the day, she has $2 left. How much of her own money did she take to the fair?” • Module 1, Lesson 11, Multiplication: Introducing the five facts, Problem Solving Activity 3, addresses standard 3.OA.3, “Stella has been collecting baseball cards. Every week she doubles the number of baseball cards she has. Stella has 120 cards. How many cards did she have three weeks ago? How many cards will Stella have next week?” • Module 8, Lesson 12, Mass/capacity: Solving word problems, Problem Solving Activity 4 has eight story problems and addresses standard 3.OA.3, “A farmer planted fruit trees in rows of 9. He planted 81 trees in total. How many rows did he plant?” Examples of non-routine application problems with connections to real-world contexts include: • Module 2, Lesson 7, Time: Relating past and to the hour, Investigation 2, students brainstorm a list of real-life situations where it would be necessary to read and write time to the nearest minute. In the extension, students brainstorm situations where it would be necessary to write time to the nearest second (3.MD.1). • Module 3, Lesson 12, Number: Rounding three- and four-digit numbers, Thinking Task, Question 2 asks, “A class of Grade 3 students is raising money for a field trip. They decide to run a car wash as a fundraiser. Customers can decide between three different types of car washes (A chart with car wash prices is provided). At the end of the carwash, the Premium Wash option raised$90. The Quick Wash option raised the same amount. How many cars were washed with the Quick Wash option?”

• Module 6, Lesson 12, Angles: Estimating and Calculating, Thinking Task, Question 1 states, “This year, the PTA raised $300 to plant a school garden. The PTA president announces that this year they raised$124 more dollars than last year. How much money did they raise last year.”

• Module 9, Lesson 12: Common fractions: Solving comparison word problems, Thinking Task, Question 1 provides a diagram of where students and families will sit during a choir performance in the gym. Problems include, “How many students will fit in each full row of the risers? What is the greatest number of students who can stand on all the risers to perform all at once?”

• Module 12, Perimeter/area: Solving word problems,  Thinking Task, “Mrs Chopra’s Grade 3 class has been asked to hang their drawings on a folding display board, the board has four rectangular panels, each panel is 3 feet x 6 feet, drawings can be posted on the front and the back of each panel, all the drawings were made on rectangular paper in three different sizes.” A table of drawing sizes is provided with the following information: 32 small 1 x 1, 16 medium 1 x 2, 8 large 2 x 2. Problem 1: “What is the area of each panel?” Students must use the information from the table to answer the question. Question 2 states, “Write an expression that shows how to find the total area for the front and the back panels of the display board."

##### Indicator {{'2d' | indicatorName}}

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

There is some evidence that the curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials have an emphasis on fluency, procedures, and algorithms.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• Module 2, Lesson 4, Addition: Developing written methods, (3.NBT.2), students use the traditional algorithm to solve addition problems. Scaffolding is given by providing the place value chart and the addends placed in the chart for the students to only find the sum.

• Module 10, Lesson 12,  Algebra: Writing equations to match two-step word problems, (3.OA.8), students match equations to two step word problems provided.

• Module 8, Lesson 9, Common fractions: Identifying equivalent fractions on a number line (3.MD.7), students use the area model to multiply whole numbers.

Examples of students having opportunities to engage in problems that use two or more aspects of rigor include:

• Module 3, Lesson 7,  Multiplication: Solving word problems, (3.OA.D), students solve problems involving the four operations, and identify and explain patterns in arithmetic.

• Module 10, Lesson 11,  Algebra: Solving problems involving multiple operations, (3.OA.8), students write a single equation that could be used to solve a word problem, and come up with two step equations that solve the problem.

• Module 3, Thinking Task, students are provided a chart with car wash prices. Question 4 asks, “A Premium Wash takes 30 minutes to complete. A Deluxe Wash takes 15 minutes, and a Quick Wash takes only 10 minutes. Which of these options would the class of Grade 3 students want their customers to choose? Remember, the class wants to raise as much money as possible. Explain which option you think is best.”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Indicator {{'2e' | indicatorName}}

Materials support 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.

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)”

##### Indicator {{'2f' | indicatorName}}

Materials support 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.

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.”

##### Indicator {{'2g' | indicatorName}}

Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

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.”

##### Indicator {{'2h' | indicatorName}}

Materials attend to 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.

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?”

##### Indicator {{'2i' | indicatorName}}

Materials support 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 the grade-level content standards, as expected by the mathematical practice standards.

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)”

### Usability

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain 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; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

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Materials provide 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.

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.”

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Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

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.”

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Materials include standards correlation information that explains the role of the standards in the context of the overall series.

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.

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Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provides strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

ORIGO ONE includes 1-minute videos, in English and Spanish that can be shared with stakeholders. They outline big ideas for important math concepts within each grade. Each module also has a corresponding Newsletter, available in English and Spanish, that provides a variety of supports for families, including the core focus for each module, ideas for practice at home, key glossary terms, and helpful videos. Newsletter examples include:

• Module 1, Resources, Preparing for the module, Newsletter, Core Focus, “Number: Writing four-digit numerals and number name, Number: Locating three- and four-digit numbers on a number line, Multiplication: Introducing the multiplication symbol and fives and tens facts. Number- When base-10 place value is understood for numbers in the hundreds, students know just about everything necessary to work with three- and four-digit numbers. In this module, students extend their understanding of one-, two-, and three-digit numbers to four-digit numbers using tools like place-value charts. Multiplication is a significant focus in Grade 3. In Grade 2, multiplication was introduced by arranging objects in an array. Now students learn to visualize a collection of equal-sized groups. Though multiplication concepts were presented in Grade 2, the actual symbol for multiplication is introduced in this module, as well as formal multiplication equations.”

• Module 3, Resources, Preparing for the module, Newsletter, Glossary, “Partially covered arrays show the total and either the number of groups or the number in each group to represent division using images already familiar to students from their study of multiplication. The area model of fractions shows fractions as parts of a two-dimensional area. The number line model is a more sophisticated length model. Number lines specifically require that students interpret fractions as numbers.” Module 3, Newsletter, Helpful videos, “View these short one-minute videos to see these ideas in action. go.origo.app/j5q8k. go.origo.app/ff ttu.”

• Module 6, Resources, Preparing for the module, Newsletter, Ideas for Home, “Practice the tens and nines facts together. Encourage your child to explain how knowing the tens fact makes the nines fact easier to solve. “I know that 5 × 10 is 50, and 50 − 5 is 45, so 9 × 5 is 45.” Create arrays with pennies to illustrate 10 × ___ and then cover one row to illustrate 9 × ___ . Encourage a self-check with nines fact pattern. Say, “When the digits of the total are added together, do they equal 9?” In 51, 5 + 1 equals 6, so 51 can’t be a multiple of 9.”

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Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

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 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.”

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Materials provide a comprehensive list of supplies needed to support instructional activities.

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.”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 partially meet expectations for Assessment. The materials identify the standards, but do not identify the mathematical practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

While Check-ups, Quarterly tests, Performance tasks, and Interviews consistently and accurately identify grade level content standards within each Module assessment overview, mathematical practices are not identified. Examples from formal assessments include:

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provide opportunities for teachers to use a variety of grouping strategies.

Suggested grouping strategies are consistently present within lesson notes and include guidance for whole group, small group, pairs, or individual activities. Examples include:

• Module 1, Lesson 1, Number: Writing three-digit numerals and number names, Step 1 Preparing the lesson, “Each group of three students will need: 1 set of base-10 picture cards from The Number Case (remove the thousands cards), access to base-10 blocks (hundreds, tens, and ones), 1 three-digit numeral expander from The Number Case, 1 non-permanent marker, 1 copy of Support 43 (Note: Print on card stock and cut out ahead of time.), scissors. Each student will need: Student Journal 1.1.” Step 2 Starting the lesson, “Organize students into groups of three and distribute the resources.” Step 3 Teaching the lesson, “Project the Step In discussion from Student Journal 1.1 and work through the questions with the whole class.”

• Module 5, Lesson 9, Subtraction: Counting back to subtract two- and three-digit numbers (with decomposing), Step 3 Teaching the lesson, “Organize students into pairs to discuss how they would most likely solve the problem mentally or find a reasonable estimate. Have the students work individually to solve the remaining equations (slides 4 to 6). Repeat the previous discussion points for each slide. Project the Step In discussion from Student Journal 5.9 and work through the questions with the whole class.”

• Module 12, Lesson 2, Division: Two-digit numbers (with regrouping), Step 3 Teaching the lesson, “Organize students into pairs and distribute the resources. Project the Step In discussion from Student Journal 12.2 and work through the questions with the whole class.“

##### Indicator {{'3q' | indicatorName}}

Materials provide 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.

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.”

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the student journal represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Names include multi-cultural references such as Hernando, Jose, Terek, and Riku and problem settings vary from rural, to urban, and international locations. Each module provides Cross-curricula links or Enrichment activities that provide students with opportunities to explore various demographics, roles, and/or mathematical contexts.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

While there are supports in place to help students who read, write, and/or speak in a language other than English, there is no evidence of intentionally promoting home language and knowledge. Home language is not specifically identified as an asset to engage students in the content nor is it purposefully connected within mathematical contexts.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0, Grade 3 provide some guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Spanish materials are consistently accessible for a variety of stakeholders, including ORIGO ONE Videos, the Student Journals, the glossary, and the Newsletters for families.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provide some supports for different reading levels to ensure accessibility for students.

Each module provides support specific to vocabulary development, called ‘Building vocabulary’. Each Building vocabulary activity provides: “Vocabulary term, Write it in your own words, and Show what it means”. While the Lesson overview, Misconceptions, and Steps within each lesson may include suggestions to scaffold vocabulary or concepts to support access to the mathematics, these do not directly address accessibility for different student reading levels. Examples of vocabulary supports include:

• Module 1, Lesson 7, Multiplication: Introducing the symbol, Lesson overview and focus, Misconceptions, “When first learning the multiplication symbol, some students may confuse it with the symbol for addition, reading or writing one when they mean the other. Encourage students to describe what is happening in the problem — “I’m joining groups” (addition) or “I’m making copies of something” (multiplication) — and then check that they have the correct symbol for the action.”

• Module 6, Lesson 4, Multiplication: Solving word problems, Lesson overview and focus, Misconceptions, “Some students will struggle with two-step word problems. Encourage them to act out the situation with counters or other manipulatives to understand the sequence of actions and steps necessary to calculate the solution to the problem. Some students will struggle to sort out what information is important in a problem where there are many facts, and possibly extra facts, available. Encourage students to record the information they need on their paper so they can focus on the right information at the right time.”

• Module 8, Lesson 10, Common Fractions: Exploring the Multiplicative Nature (number line model), Lesson Notes, Misconceptions, “If students struggle to label capacity on a vertical number line, turn the page so they can see it is the same number line, just oriented differently. A thermometer is another analogy which supports some students.”

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. Examples include:

• While all components of the materials can be accessed digitally, some are only accessible digitally, such as The Number Case, Interactive Student Journal, Fundamentals Games and Flare Online Tools.

• ORIGO ONE videos describe the big math ideas across grade level lessons in one minute clips. There is a link for each video that makes them easy to share with various stakeholders.

• Every lesson includes an interactive Student Journal, with access to virtual manipulatives and text and draw tools, that allow students to show work virtually. It includes the Step In, Step Up, Step Ahead, and Maintaining Concepts and Skills activities, some of which are auto-scored, others are teacher graded.

• The digital materials do not allow for customizing or editing existing lessons for local use, but teachers can upload assignments or lessons from the platform.

• Digital Student Assessments allow for Progress Monitoring. Teachers can enter performance data and then monitor student progress for individual students and/or the class.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

While teacher implementation guidance is included for Fundamentals games and Flare online tools, there is no platform where teachers and students collaborate with each other. There is an opportunity for teachers to send feedback to students through graded assignments.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provide a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within modules and lessons that supports student understanding of the mathematics. Examples include:

• Each lesson follows a common format with the following components: Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, Maintaining Concepts and Skills, Lesson focus, Topic progression, Observations and discussions, Journals and portfolios, and Misconceptions. The layout for each lesson is user-friendly as each component is included in order from top to bottom on the page.

• The font size, amount and placement of directions, and print within student materials is appropriate.

• The digital format is easy to navigate and engaging. There is ample space in the Student Journal and Assessments for students to capture calculations and write answers.

• The ORIGO ONE videos are engaging and designed to create light bulb moments for key math ideas. They are one minute in length so students can engage without being distracted from the math concept being presented.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Program Overview includes a description of embedded tools, how they should be incorporated, and when they can be accessed to enhance student understanding. Examples include:

• Program Overview, Additional practice tools, “This icon shows when Fundamentals games are required.” Lessons provide this icon to show when and where games are utilized within lesson notes.

• Program Overview, Additional practice tools, “This icon shows when Flare tools are required.” Lessons provide this icon to show when and where these tools are utilized within lesson notes.

## Report Overview

### Summary of Alignment & Usability for ORIGO Stepping Stones 2.0 | Math

#### Math K-2

The materials reviewed for Origo Stepping Stones 2.0 Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 1 and 2 meet expectations for Usability, Gateway 3, and the materials reviewed for Origo Stepping Stones 2.0 Kindergarten partially meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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