3rd Grade - Gateway 3

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

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

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

• Module 1, Resources, Preparing for the module, Focus, provides an overview of content and expectations for the module. “In Grade 2, students explored the idea of adding equal groups. In this module, the multiplication symbol is introduced as a quick way to express an addition number sentence when all the addends are the same number. E.g. rather than writing 4 + 4 + 4 + 4 + 4, students explain that they could write 5 × 4. The array model for multiplication is also used to help students see that two multiplication equations can often be written for the single situation. E.g. the 5 by 4 array can be described as 5 × 4 = 20, and as 4 × 5 = 20. This relationship, known as the commutative property, helps students when they begin to learn multiplication number facts. In this module, the students begin to learn their first multiplication number facts. Without realizing it, they should already be familiar with many of the facts. The tens facts relate to what the students know about place value. E.g. 6 groups of 10 is 6 x 10, or 60. Using the commutative property, students realize that when the picture of 6 x 10 is represented as an array, it is the same as 10 x 6. These comprise the first set of 19 facts to be learned. The strategy to learn the fives facts is introduced here because it is closely connected to students’ knowledge of the tens facts.”

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

• Module 1, Lesson 6, Number: Locating four-digit numbers on a number line, Step 2 Starting the lesson, teachers provide context about equal parts on a number line. “Ask, What are some different ways we can represent one thousand? Encourage students to describe different methods that include individual objects (counters or people), grouped objects (money or a base-10 block or blocks), as place value (place-value chart), and relative position (the number line.)”

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

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

The materials reviewed for Origo Stepping Stones 2.0 Grade 3 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

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

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

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

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. 

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

• Front Matter, Grade 3 and the CCSS by Lesson includes a table with each grade level lesson (in columns) and aligned grade level standards (in rows). Teachers can search any lesson for the grade and identify the standard(s) that are addressed within.

• Front Matter, Grade 3 and the Common Core Standards, includes all Grade 3 standards and the modules and lessons each standard appears in. Teachers can search a standard for the grade and identify the lesson(s) where it appears within materials.

• Module 8, Module Overview Resources, Lesson Content and Learning Targets, outlines standards, learning targets and the lesson where they appear. This is present for all modules and allows teachers to identify targeted standards for any lesson.

• Module 6, Lesson 9, Data: Working with many-to-one picture graphs, the Core Standard is identified as 3.MD.B.3. The Prior Learning Standard is identified 2.MD.D.10. Lessons contain a consistent structure that includes Lesson Focus, Topic progression, Formative assessment opportunity, Misconceptions, Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, and Maintaining concepts and skills. This provides an additional place to reference standards, and language of the standard, within each lesson.

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

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

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

• Module 8, Lesson 9, Common fractions: Identifying equivalent fractions on a number line, Topic Progression, “Prior learning: In Lesson 3.8.8, students use concrete materials and pictures to find different ways to describe the same fractional part of one whole. The whole is represented with area models of different shapes. 3.NF.A.3, 3.NF.A.3a, 3.NF.A.3b; Current focus: In this lesson, students place fractions on number lines and identify other fractions that are located on the same point on the number line. Some number lines are already partitioned and other number lines need to be partitioned by students. 3.NF.A.3, 3.NF.A.3a, 3.NF.A.3b, 3.NF.A.3c; Future learning: In Lesson 3.9.8, students use a length model to compare unit fractions. 3.NF.A.3, 3.NF.A.3d” Each lesson provides a correlation to standards and a chart relating the target standard(s) to prior learning and future learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

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

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

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

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

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

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. In the Program Overview, Program components, Preparing for the module, “Resource overview - provides a comprehensive view of the materials used within the module to assist with planning and preparation.” Each module includes a Resource overview to outline supplies needed for each lesson within the module. Additionally, specific lessons include notes about supplies needed to support instructional activities, often within Step 1 Preparing the lesson. Examples include:

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

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

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative Assessments include Pre-test, Observations and discussions, and Journals and Portfolios. Summative Assessments include Check-ups, Interviews, Performance tasks, and Quarterly tests. All assessments regularly demonstrate the full intent of grade level content and practice standards through a variety of item types: multiple choice, short answer, and constructed response. Examples include:

• Module 1, Performance task, develops the full intent of standard 3.OA.1, interpret products of whole numbers, e.g., interpret 5 \times 7 as the total number of objects in 5 groups of 7 objects each. Question 1, “a. Circle one number in each box. Box 1(3,6,7) Box 2(4,5). b. Write the numbers in the spaces below. ___ rows of ___ apples. c. Draw a picture to match. d. Complete this equation to match your picture. ___ \times ___ = ___. e. Complete a different equation to match your picture. ___ \times ___ = ___. Question 2, “Draw rows of apples to show 5 \times 4 = 20.” 

• Module 6, Quarterly test B questions support the full intent of MP2, reason abstractly and quantitatively, as students make sense of quantities and their relationships as they read a picture graph. Question 28, “Look at the picture graph. It shows that 33 apple muffins, 30 cinnamon muffins, 42 banana muffins, and 60 blueberry muffins were sold. Based on this information, choose the number of muffins that each (picture of a muffin) represents. A. 5, B. 6, C. 10, D. 2.” 

• Module 9, Quarterly test questions support the full intent of MP4, model with mathematics, as students use the commutative and distributive properties of multiplication. For example, Question 7, “Write two multiplication facts to describe the array. ___ \times ___ = ___. ___ \times ___ = ___.” 

• Module 11, Interview 1 and Check-up 1, develop the full intent of 3.NBT,1, use place value understanding to round whole numbers to the nearest 10 or 100. Interview 1, “Steps: Write the following numbers on a sheet of paper one at a time, asking the student to round each one in turn to the nearest 10. Ask the student to explain their thinking for each number. 43,276, 80,523, 62,803. Write the following numbers on a sheet of paper one at a time, asking the student to round each one in turn to the nearest 100. Ask the student to explain their thinking for each number. 37,841, 50,173, 26,982. Draw a ✔ beside the learning the student has successfully demonstrated.” Check-up 1, Question 1, “Round each number to the nearest ten. a. 52,589, b. 31,012, c. 48,989. Question 2. Round each number to the nearest hundred. a. 45,639, b. 89,853, c. 56,020.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. In each Module Lesson, Differentiation notes, there is a document titled Extra help, Extra practice, and Extra challenge that provides accommodations for an activity of the lesson. For example, the components of Module 5, Lesson 6, Multiplication: Reinforcing the ones and zeros facts, include:

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

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

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

• Module 2, Lesson 6, Time: Reading and writing to the minute, Differentiation, Extra Challenge, “Organize students into pairs and distribute the resources. Have the students cut the support page in half so that they each have six clocks and labels. Each student then draws hands on their clocks to show six different times. They exchange clocks and complete the relevant labels directly below. Afterward, have the students cut apart each clock and its label. They can then mix-and-match the clocks and labels.”

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

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

• Module 4, Lesson 6, Division: Introducing the twos and fours facts, Lesson notes, Step 2 Starting the lesson, “ELL: Pair the students with fluent English-speaking students. During the activity, have students discuss the concepts in their pairs, as well as repeat the other student's thinking. Provide time for the student to process the questions, formulate an answer, and then speak about their thoughts to another student before presenting their ideas to the class.” Step 3 Teaching the lesson, “ELL:Allow the students to use hand gestures (such as thumbs up or down) to show their agreement or disagreement with another student's methods of solving the equation. Allow the students to work in their pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Provide sentence stems, such as, "It helps me because ..." or "The fact families are ..."”

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 3 meet expectations for providing  manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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

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

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

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