2nd Grade - Gateway 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 2 meet expectations for providing 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 3, Check-up 2 and Performance task, develop the full intent of standard 2.NBT.4, compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Check-up 2, Question 1, “Write < or > to complete each of these. a. 485 ___ 619, b. 520 ___ 531, c. 349 ___ 342.” Performance task, Question 2, “Look at these numbers below. Write two more numbers so that all five numbers are in order. 387, ___, 423, ___, 502.”

• Module 6, Quarterly test questions support the full intent of MP7, look for and make use of structure, as students use fact family strategies to solve a complex problem. Question 9, “Choose the missing fact from this fact family. 14 - 5 = 9, 14 - 9 = 5, 9 + 5 = 14. A. 9 - 5 = 14, B. 5 + 9 = 14, C. 9 + 14 = 23.”

• Module 9, Quarterly test A questions support the full intent of MP5, use appropriate tools strategically, as students choose a subtraction strategy to solve a word problem. Question 2, “Solve the problem. Show your thinking. There are 67 people at a zoo. 10 people leave on the first bus and 12 people leave on the second bus. How many people are left at the zoo?” 

• Module 11, Interview 1 and Check-up 2, develop the full intent of 2.MD.8, solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Interview 1, “Resources: play money: one $1, 6 quarters, 12 dimes, 25 nickels, and 30 pennies. Steps: Provide the student with the dollar bill and coins. Ask, How many cents are there in one penny? Repeat for the other coins and the dollar bill. Ask the student to use the coins to demonstrate their answer to the following questions. Ask, How many nickels have the same value as one dime? How many nickels have the same value as one quarter? How many dimes have the same value as one dollar? How many quarters have the same value as one dollar? Ask the student to show a combination of coins that equals 78 cents. Draw a ✔ beside the learning the student has successfully demonstrated.” Check-up 2, Question 2, “Figure out and write how much each person has. a. Katherine has two quarters, three dimes, and a penny. b. Samuel has two dimes, five pennies and a nickel. c. Sara has three nickels, two dimes, and two quarters.”

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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