1st Grade - Gateway 3

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 2, Resources, Preparing for the module, Focus, provides an overview of content and expectations for the module. “The first lesson of this module uses the example of bears on/off a school bus to review the idea of addition. The students write equations to show how they would calculate the unknown amount. Lessons 2 to 7 develops the use of the count-on strategy to add. This strategy is initially used to help students learn many of the addition number facts. To ensure students become fluent with addition, it is important for them to realize that they can count on from the number of one collection to figure out the total, rather than counting every item in both collections. For numbers less than ten, students are encouraged to sight recognize (subitize), and use important benchmarks such as five fingers to help them count on. In Lesson 3, domino cards are used to formally introduce the count-on strategy. Pennies are used in Lesson 4 to reinforce the count-on strategy. The students cannot see the starting number, so they must visualize the strategy. Students use the strategy to solve word problems. The number track is also used as a model to help count on for numbers to 20. The count-on strategy helps students add when one of the addends is small. This module introduces the commutative property (or turnaround idea), another method that helps with any pair of addends. Lessons 6 and 7 use connecting cubes, dominos, or clothespins to demonstrate the commutative property, and then turn the picture around to show that both representations have the same total (for example, 7 + 2 = ___ has the same total as 2 + 7 =___.) The focus of Lessons 8 and 9 is doubling one-digit numbers. Students will analyze real-life situations to find and then create examples that show doubles. It is important that students begin to learn doubles at this stage as this knowledge is the basis for more addition facts in Module 5. After a thinking strategy has been introduced and reinforced, it is essential to practice the number facts that can easily be solved using the strategy. The maintaining concepts and skills in this and later modules provide valuable practice, but it is a good idea to also provide additional practice when time allows.”

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: Representing teen numbers, Step 2 Starting the lesson, teachers provide context with representing teen numbers. “Project slide 1 as shown below and ask, How many dots are there? How do you know? If students counted, have them explain their counting. Through the discussion, encourage students to use their subitizing skills instead of individually counting the dots. Repeat for the remaining domino dot and scattered dot arrangements for one to six (slides 2 to 12).”

• Module 5, Lesson 2, Addition: Reinforcing the double-plus-1 strategy, Step 3 Teaching the lesson provides teachers guidance on how to work with addition and subtraction equations. “Organize students into groups of three and distribute the dominoes. Then ask, Who has a domino that shows a double? How do you know? What addition fact could you write for that double? Invite students to write the facts across the board for all the doubles dominoes from 1 + 1 = ___ to 9 + 9 = ___. Highlight that examples such as 1 + 1 = 2 and 2 + 2 = 4 are both doubles facts and count-on facts. Ask, Who has a domino that shows a double-plus-1 fact? What is the total for your domino? Which fact on the board could help you figure out the total? Allow time for the groups to talk about their domino. Then have volunteers write their double-plus- 1 fact and its turnaround below the related double on the board. Project the Flare Number Track online tool and say, Choose a number between one and ten. When you double your number, what total do you get? As the students identify their doubles, draw a check above each number on the track. Ask, When you double and add one to your number, what total do you get? How do you know? As the students identify the totals, draw a check below each number. Refer to the checked numbers and ask, What do you notice? Encourage a variety of observations. For example, the doubles totals can be found with jumps of two, and every double-plus 1 total falls between two doubles totals. Project the Step In discussion from Student Journal 5.2 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 8, Addition: Two-digit numbers, Lesson overview and focus, Misconceptions, include guidance to address common misconceptions with place value understanding in addition problems. “One common misconception for students in this module revolves around continued development of place-value understandings. For example, when adding 39 + 3 students may write 312. An effective strategy is to return to the base-10 blocks or hundred chart that are the models presented in this module. Encourage students to model the addition and keep the focus on counting-on using the hundred chart, and on composing a group of ten with the base-10 blocks. Remember that Grade 1 students should not rely on a written standard algorithm, but rather figure out the total using physical models and place-value strategies.”

The materials reviewed for Origo Stepping Stones 2.0 Grade 1 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 1, Preparing for the module, Research in practice, Teen numbers, supports teachers with context for work beyond the grade. “As the Mathematics Focus suggests, this module provides a strong foundation for addition (Modules 2, 5, 8, and 9) and for subtraction (Modules 4, 6, 7, 11, and 12) throughout Grade 1. It also prepares students for extending the representation and comparison of number to within 120 (Modules 3, 5, and 7). In preparation for representing and comparing numbers within 1,000 in Grade 2 (Modules 1–3), develop students’ number sense by encouraging them to use many different representations of numbers and to explain how they are the same and how they are different. Read more about making connections in the Research into Practice section of Grade 1 Modules 5 and 7.”

• Module 3, Research into Practice, Length Measurement, supports teachers with context for work beyond the grade. “In preparation for work with standard units of length (both customary and metric) in Grade 2, students are beginning to understand transitivity and the importance of a standard tool for both measurement and comparison. Read more about the ways transitivity develops in the Research into Practice section for Grade 2 Module 4.”

• Module 5, Preparing for the module, Research into practice, includes explanations and examples of addition strategies. To learn more includes further references where teachers can build knowledge. “Addition, Research shows that basic fact mastery is grounded in firm number sense, including a student's ability to recognize patterns among numbers and decompose them into usable pieces. Number sense should emerge in a predictable order. Students may at first use a counting-on strategy to find a sum. For example, 6 + 4 may be figured as 6 (shows six fingers) 7, 8, 9, 10 (raising one more finger for each number) “It's 10!” Instruction should then emphasize patterns within the facts that can be easily recalled and expanded upon. For example, doubles and doubles plus one (and doubles plus two) are strategies that typically grow out of pattern recognition activities. The lessons in Module 5 give students opportunities to connect their growing knowledge of doubles-based facts to different representations of number they have used in the past: dominoes, number tracks, and base-10 blocks.” To learn more, “Baroody, Arthur J. 2006. “Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them.” Teaching Children Mathematics 13 (1): 22–31.”

• Module 9, Preparing for the module, Research into practice, includes explanations and examples of addition concepts. “The goal for addition in Grade 1 is to use place-value structure and properties of addition to add two-digit numbers. This standard comes from extensive research that shows that students who build meaning for numbers and the value of the numbers in a place-value system are more successful over the long term than those who rely solely on a rote procedure for adding. Students make sense of the place-value system as they acquire extensive experience counting and creating groups of ten. The process of flexibly perceiving a group of ten objects as both a set of ten individual objects as well as a single group of one ten is called unitizing, and it is a critical skill for learning to compose and decompose numbers in the process of adding. In Module 3, students explored units of one and ten, composing groups of ten using their fingers, the expander, and base-10 blocks. Also important to learning to add is decomposing place values in order to add and subtract numbers. Considered a critical learning phase, learning to add multiples of ten easily and flexibly is an important precursor skill to adding two-digit numbers. By spending much of Grade 1 breaking apart and recomposing groups of tens and ones to add, students build the capacity to establish a standard algorithm for adding at a later stage. For now, building flexibility with place-value strategies is the goal.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 1 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 1 and the Common Core Standards, includes all Grade 1 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 2, 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 (take apart), the Core Standards are identified as 1.OA.C.6, 1.OA.D.8 and 1.NBT.A.1. The Prior Learning Standards are identified K.OA.A.1 and K.OA.A.2,. 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 1, Mathematics Overview, Numbers and Operations in Base Ten, includes an overview of how the math of this module builds from previous work in math. “In the Kindergarten year of Stepping Stones, students worked with key concepts and skills to develop confidence with numbers to 20. For numbers to ten, they matched number names and numerals to collections of objects, and vice versa; matched number names to numerals, and vice versa; wrote numerals to match a collection and/or number names; and were encouraged to sight recognize (subitize) collections up to nine. For numbers 11 to 20, students represented teen numbers as a group of ten and some ones; used coins to represent teen numbers with pennies or one dime and pennies; and matched numerals and number names to collections, and vice versa. This module reviews and builds on the above concepts and skills. It introduces new models for students to use to represent numbers and numerals, and then extends the applications of numbers to writing teen numbers, and comparing and ordering numbers to 20. They use ten-frames to help make their decisions. The ten-frame and the number track are used to extend the language to making a specific comparison, e.g. ___ is 2 less than 9. In Kindergarten, students used counters, number tracks, and their fingers to represent numbers to 20. In this module, a new resource, sets of cards showing outstretched fingers, is used to make it easier to work with the finger picture of numbers. This means students can quickly show the number 14 by selecting a card with ten fingers and a card with four fingers. This is a speedy way to build a place-value picture for teen numbers. The cards provide a meaningful picture of place value, and are used in other modules when students work with two-digit numbers up to 100.”

• Module 9, Mathematics Overview, Coherence, includes an overview of how the content in 1st grade connects to mathematics students will learn in second grade. “Lessons 9.1–9.12 focus on addition of one-digit and two-digit numbers, then two two-digit numbers using the count-on strategy and place-value strategies. This extends prior work with the count-on addition strategy (1.2.1–1.2.6) and serves as a foundation for addition with two-digit numbers using a number line (2.5.1–2.5.7).”

• Grade 1, Module 7, Lesson 8, Subtraction: Reinforcing the think-addition strategy (near- doubles facts), Topic Progression, “Prior learning: In Lesson 1.7.7, students use the think- addition subtraction strategy to solve problems involving near-Doubles. 1.OA.B.4, 1.OA.C.6, 1.OA.D.8; Current focus: In this lesson, students practice the think-addition subtraction strategy to solve problems involving near-doubles. 1.OA.B.4, 1.OA.C.6, 1.OA.D.8; Future learning: In Lesson 1.7.9, students practice all strategies to solve word problems. 1.OA.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 1 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, “Counting on: Counting objects efficiently and accurately is a primary goal in Kindergarten, but in Grade 1 students begin to discover strategies for joining quantities of objects. There are many kinds of addition reasoning strategies that students can be expected to utilize. One research group distinguished between perceptual counting, figural counting, and the initial number sequence stages of addition to describe this change. Students who are perceptual counters are able to count a set of joined objects only in the presence of physical materials, and they will most likely need to start from 1 to count the joined set. When figural counting students are shown two sets of joined objects, which are then hidden, they can still imagine the objects and count efficiently, even if they start at 1. Students who are beginning the initial steps of the number sequence stage recognize a numerical composite, a quantity that they can be maintained in a whole chunk. For example, shown 8 blocks and 3 blocks, the student is able to recognize and hold 8 blocks as a numerical composite and count on three more to eleven, with or without fingers accompanying their count: “8. 9, 10, 11!” This strategy is called counting on. There is ample evidence that students who demonstrate proficiency counting on may still turn to the counting all strategy at times, long after it is expected, but this is a normal occurrence. Telling time: Using a clock to tell time is not a superficial task. Unlike length, time itself is not tangible and is therefore more challenging to measure. A student can lay a block next to an object and compare lengths. However, nothing can be laid next to time for comparison. Marking the passage of hours increases awareness both of the clock and of time itself. To learn more: Eisenhardt, Sara, Molly H. Fisher, Jonathan Thomas, Edna O. Schack, Janet Tassell, and Margaret Yoder. 2014. “Is it counting, or is it adding?” Teaching Children Mathematics 20(8): 498-507. Reinke, Kay, and Pat Lamphere-Jordan. 2002. “Working Cotton: Toward an Understanding of Time.” Teaching Children Mathematics 8(8): 475-79. 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: Long, Kathy, and Constance Kamii. 2001. “The Measurement of Time: Children’s Construction of Transitivity, Unit Iteration, and Conservation of Speed.” School Science and Mathematics 101 (3): 125–32. Tzur, Ron, and Matthew Allen Lambert. 2011. “Intermediate participatory stages as zone of proximal development correlate in constructing counting-on: A plausible conceptual source for children’s transitory ‘regress’ to counting-all.” Journal for Research in Mathematics Education 42 (5): 418–50. Wright, Robert J., Jim Martland, and Ann K. Stafford. 2006. Early numeracy: Assessment for teaching and intervention. London: Sage.”

• Module 9, Preparing for the module, Research into practice, “Addition: The goal for addition in Grade 1 is to use place-value structure and properties of addition to add two-digit numbers. This standard comes from extensive research that shows that students who build meaning for numbers and the value of the numbers in a place-value system are more successful over the long term than those who rely solely on a rote procedure for adding. Students make sense of the place-value system as they acquire extensive experience counting and creating groups of ten. The process of flexibly perceiving a group of ten objects as both a set of ten individual objects as well as a single group of one ten is called unitizing, and it is a critical skill for learning to compose and decompose numbers in the process of adding. In Module 3, students explored units of one and ten, composing groups of ten using their fingers, the expander, and base-10 blocks. Also important to learning to add is decomposing place values in order to add and subtract numbers. Considered a critical learning phase, learning to add multiples of ten easily and flexibly is an important precursor skill to adding two-digit numbers. By spending much of Grade 1 breaking apart and recomposing groups of tens and ones to add, students build the capacity to establish a standard algorithm for adding at a later stage. For now, building flexibility with place-value strategies is the goal. To learn more: National Governors Association Center for Best Practices, and Council of Chief State School Officers. 2010. Common Core State Standards Mathematics. Washington, D.C.: National Governors Association Center for Best Practices, Council of Chief State School. 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: Baroody, Arthur J. 2006. “Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them.” Teaching Children Mathematics 13 (1): 22–31. Clements, Douglas H. and Julie Sarama. 2009. Learning and Teaching Early Math: The Learning Trajectories Approach. 1st ed. Studies in Mathematical Thinking and Learning. New York: Routledge. Richardson, Kathy. 2012. How Children Learn Number Concepts: A Guide to the Critical Learning Phases. Bellingham, Washington: Math Perspectives Teacher Development Center.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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, Lesson 6, Addition: Using the commutative property, Lesson notes, Step 1 Preparing the lesson, “You will need: 2 pieces of tagboard, each 8 inches by 10 inches, clothespins; Each student will need: Student Journal 2.6 ”

• Module 3, Preparing for the module, According to the Resource overview, teachers need, “pan balance, paper clip and strips of paper for lesson 9, permanent marker, small resealable plastic bags in lesson 6, soccer ball or similar in lesson 4, string in lessons 9 and 10, Support 37 in lesson 12, The Number Case in lessons 3, 4, 5, and 6. Each group of students needs counters and base-10 blocks (tens and ones), non-permanent marker, play dimes and pennies, The Number Case in lesson 2, lengths of string, scissors in lesson 9, and a tub of connecting cubes in lesson 11. Each pair of students needs base-10 blocks (tens and ones) and The Number Case in lesson 8, and play dimes and pennies in lesson 7. Each individual student needs connecting cubes in lesson 11, glue and strips of paper in lesson 9, paper in lesson 3, scissors and adhesive tape and Support 37 in lesson 12, string in lesson 10, and the Student Journal for each lesson.”

• Module 3, Lesson 9, Length: Making direct comparisons, Lesson notes, Step 1 Preparing the lesson, “You will need: string, measuring cup, pan balance, paper clip, craft stick, strips of paper. Each group of three students will need: length of string (approximately 1 yard) and scissors. Each student will need: 12 strips of paper (approximately \frac{1}{2} inch by 8 inches), glue, and Student Journal 3.9.” Step 2 Starting the lesson, “Display the string, measuring cup, pan balance, paper clip, and craft stick and say, Today we are going to measure some distances. Which of these measure tools do you think we can use?”

• Module 7, Preparing for the module, According to the Resource overview, teachers need, “base-10 blocks (hundreds, tens, and ones) in lesson 6, non-permanent marker in lesson 5, ORIGO Big Book: The Cat Nap in lesson 10, resources such as connecting cubes, counters, containers, base-10 blocks, and drinking straws in lesson 1, Support 63 in lesson 8, Support 64 in lesson 9, Support 67 in lesson 12, and The Number Case in lessons 1, 3, 4, 5, 7, 8, and 9. Each group of students needs base-10 blocks (hundreds, tens, and ones) in lessons 2, 3, 4, and 6, non-permanent markers in lessons 2, 3, and 6, paper in lesson 6, and The Number Case in lessons 2, 3, and 6. Each individual student needs the Student Journal in each lesson.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 2, Check-up 2 and Module 4, Performance task, develops the full intent of 1.OA.8, determine the unknown whole number in an addition or subtraction equation relating three whole numbers. Check-up 2, Question 2, “Complete the equation to match each domino. You can draw more dots on the domino to help. a. 5 + ___ = 8, b. ___ + 2 = 8.” Module 4, Performance task, “a. Write two numbers to complete this equation. 7 - ___ = ___ . b. Draw a picture of some people on the bus and some people off the bus to match your equation.”

• Module 6, Quarterly test questions support the full intent of MP7, look for and make use of structure, as students use fact strategies to solve a complex problem. For example, Question 3, “Choose the pair of facts that match the picture. 8 dots in total. A. 8 - 8 = 0, 8 + 0 = 8, B. 6 - 2 = 8, 6 + 2 = 8, C. 8 - 4 = 4, 4 + 4 = 8.”

• Module 9, Quarterly test A questions support the full intent of MP6, attend to precision, as students read and calculate a total from a tally chart. Question 15, “Look at the tally chart. How many first graders picked yellow as their favorite color? A. 12, B. 7, C. 13” A tally chart titled, “First Grade Students Favorite Color” shows tallies for Blue, Red, Green, and Yellow. 

• Module 11, Interview 2 and Check-up 2, develops the full intent of 3.G.1, distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Interview 2, “Resources: 1 copy of Support 11, Building blocks like those shown on Support 11. Steps: Give the student the blocks. Have them choose one block and describe the surfaces of that block. Display a rectangular-based prism and ask the student to join some of the blocks together to make a longer version of that prism. Display a triangular-based prism and ask the student to join some of the blocks together to make a larger version of that prism. Show the student the support page and ask them to recreate the object using the blocks. Draw a ✔ beside the learning the student has successfully demonstrated.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 5, Addition: Comparing all strategies, include:

• Extra help, “Activity: Organize students into groups and distribute the dominoes. The dominoes are placed facedown and mixed around. The students take turns to select a domino and identify whether it represents a count-on fact or a use-doubles fact (or neither). Make sure they explain how they decided.”

• Extra practice, “Activity: Organize students into pairs and distribute the cubes. The students take turns to roll both cubes, add the numbers, and write the matching addition equation. If the equation involves using the double-plus-1 or double-plus-2 strategy, the student scores a point. The first student to score five points wins.”

• Extra challenge, “Activity: Organize students into groups and distribute the cards. Direct the students to draw two columns on a piece of paper, and label them count on and use doubles. The cards are mixed and placed facedown in a central pile. The students take turns to select a card and identify the addition strategy they could use to have that number as the total. They then write a matching equation in the appropriate column. For example, if a student selects a card for 9, they could write 7 + 2 = 9 or 8 + 1 = 9 in the count on column or 5 + 4 = 9 or 4 + 5 = 9 in the use doubles column. The activity continues until there are five different equations in each column.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 7, Addition: Extending the count-on strategy (within 20), Differentiation, Extra Challenge, “Organize students into pairs and distribute the resources. One student writes a count-on-1 or count-on-2 equation involving a teen number. The other student then writes the turnaround equation to match. Roles are alternated and the activity continues until all the cards are used. The students then use the cards to play matching games such as Memory.”

• Module 5, Lesson 11, Number: Recording comparisons (with symbols), Differentiation, Extra Challenge, “Organize students into small groups and distribute the resources. Students take turns to roll both cubes. They then write the numbers they roll in any of the empty boxes on their support page to make true balance scenarios. The activity is repeated until one student successfully completes four balance scenarios.”

• Module 11, Lesson 10, Money: Determining the value of a collection of coins, Differentiation, Extra Challenge, “Organize students into groups and distribute the resources. Have the students identify pennies, nickels, dimes, and quarters and give their value in cents. Then have them work together to create five bags of coins that have a total value of 75 cents. Each bag should show a different combination of coins.”

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 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 1, Lesson 7, Number: Making groups to show greater or less (up to 20), Lesson notes, Step 2 Starting the lesson, “ELL: Provide students with a number track up to 20 to scaffold the before, between, and after understanding of number.” Step 3 Teaching the lesson, “ELL: Pre-teach the phrases one more and one less to the students by providing them with a number track and three different colored counters. Say, I would like for you to point to the number seven. Place the (red) counter on the number seven. What is the number after seven? (8.) Eight is one more than seven. Ask the students to place their (green) counter on the number eight and count the number of spaces between one and eight. Emphasize how eight is one more space on the number track than seven. Ask, What number comes before seven? (6.) Six is one less than seven. Ask the student to place their (blue) counter on the number six and count the number of spaces between one and six. Emphasize how six is one less space on the number track than seven. Repeat with other examples, if necessary. Encourage the students to use non-verbal cues (such as thumbs down) if they are confused by the concept or the language they hear. Pair the students with fluent English-speaking students. During the activity, have the students discuss the concepts in their pairs, as well as repeat the other student’s thinking. Allow the pairs to work together to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Provide the students with counters to help them justify their thoughts during the reflection.”

• Module 5, Lesson 10, Number: Introducing comparison symbols, Lesson notes, Step 3 Teaching the lesson, “ELL: Give students a visual aid, such as an index card with the symbols and picture for them to reference. Create an anchor chart showing the comparison symbols for students to reference. Provide adequate time for students to process the questions, formulate their answer, and share their thoughts with the other student before presenting their ideas to the class. During the activity, have them discuss the concepts in their pairs, as well as repeat the other student’s thinking. Have the pairs work together to read the Student Journal.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 1 meets 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 3, Number: Matching representations (up to ten), Step 3 Teaching the lesson, identifies DecaCards and a support handout as strategies for students to match number names and their representations. “Organize students into pairs and distribute the resources. Then say a number from zero to ten, such as four. Direct one student in each pair to find the matching DecaCard and the other student to write the matching number name on the paper.”

• Module 6, Lesson 2, Subtraction: Exploring the unknown-addend idea, Step 3 Teaching the lesson, describes the use of wire coat hangers, clothespins and a handout to show subtraction problems with missing addends. “Organize students into four small groups and give each group a hanger and some clothespins. Encourage them to create different unknown-addend equations and show their thinking on the hanger.”

• Module 10, Lesson 5, Subtraction: Writing fact families, Step 2 Starting the lesson, references an online Fundamentals game to review creating addition equations. “Organize students into two groups and open the online Fundamentals game, Add ’em Up. Explain that the class is going to play a game. Groups take turns to roll the cubes and for each roll, they create an addition equation where the total appears on the board.”