Kindergarten - Gateway 3

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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. “There are three aspects that help students develop a full understanding of numbers. These are the concrete or pictorial representation, the spoken number name, and the symbol that is written for each number. For the symbol, this could include a written word or a numeral. In this module, each lesson includes activities where the students work with two of the three aspects. For example, students identify the number name or numeral for a collection of objects shown with concrete materials or with pictures, or they might reverse the process. The examples are limited to any of the three aspects for the numbers one (1) to five (5). Other one-digit numbers and the number ten (10) are explored in the same way in Module 2. An important objective of these lessons is to ensure students can confidently identify the number associated with a collection. The number is the cardinality of that collection and answers the question, How many ...? Many younger students can count the number in a collection, but do not understand that the last number they say is a property that relates to the entire collection. For example, when shown a group of three flowers and asked to say how many flowers are in the picture, they might count, One, two, three without realizing that the last number name they have said applies to the entire collection. During the lessons it is important to reinforce the idea that the last number said applies to the entire collection. In later modules, students will be encouraged to identify the number in the collection without any counting.”

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 3, Number: Creating groups of pictures to match numerals (1 to 5), Step 2 Starting the lesson, teachers provide context with representing teen numbers. “Invite three students to come to the front and stand in line. Say, Let’s all count the students: one, two, three. Point to each student as everyone counts. Repeat the counting, starting from a different student (order-irrelevance principle). Ask the three students to rearrange themselves, then ask the other students, Does the number change if the students move to a different space? Encourage students to explain their answer. Repeat the activity with a new group of students coming to the front.”

• Module 5, Lesson 3, Equality: Identifying two parts that balance a total, Step 3 Teaching the lesson, provides teachers guidance on how to work with addition and subtraction equations. “Open the Flare Pan Balance online tool and ask, How can we make this picture balance? Establish that the same number of shapes must be placed on the other pan. Ask, Can you think of two groups of shapes that would balance the picture? Drag circles onto the pan balance, then color the circles to match each suggestion, for example, four blue and two green, or one blue and five green. Organize students into groups and distribute the resources. Explain that they will work together in their groups to identify two groups that balance four. Encourage the students to use the range of resources to represent the problem, for example, breaking up cube trains, using their fingers, drawing pictures, and acting it out on the pan balance (SMP5). Afterward, invite groups to share their ideas and to explain the steps they followed to find the solutions. Ask questions such as, How does your picture show the same as your fingers? How do you know your answer is correct? Repeat the activity to identify two groups that balance seven. If students experience difficulty in starting the activity, encourage perseverance by asking questions such as: What do you already know? What do you have to find out? Can you explain that another way? What tool have you tried? How did you do that? What different tools can you use? Read the instructions at the top of Student Journal 5.3 (orange elephant) with the students. Make sure they know what to do, then have them work independently to complete the task.”

• Module 9, Lesson 3, Number: Working with position (up to 20), Lesson overview and focus,  Misconceptions, include guidance to address common misconceptions about one more or one fewer using ten-frames. “When students find one more or one fewer using a ten-frame, certain combinations may be challenging. For example, showing one more than 10 requires the student to make a mark outside of a full ten-frame. On the other hand, to find one greater or one less on a number track is comparatively easy. However, these two representations pose different challenges. The ten-frame representation may be difficult for students who are not yet independently counting within a ten-frame structure. In this case drawing the individual dots and keeping track of the count might make this task challenging for some students. In this case, offer blank ten-frames to help structure their counting. When naming one less and one greater on the number track, students may find the correct number accurately enough using a number track, but not be able to do the same with a set of counters. In this case, working with the abstract numbers may not be enough. Assess student thinking as they work: ask them to demonstrate one more and one fewer using counters as well as one less and one greater on the number track.”

The materials reviewed for Origo Stepping Stones 2.0 Kindergarten 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, Focus, Counting and Cardinality, includes important context for the key mathematical ideas in the module and the linked MathEd video, JTN1 Teaching number: Counting principles, adds context for key concepts. “There are three aspects that help students develop a full understanding of numbers. These are the concrete or pictorial representation, the spoken number name, and the symbol that is written for each number. For the symbol, this could include a written word or a numeral. In this module, each lesson includes activities where the students work with two of the three aspects. For example, students identify the number name or numeral for a collection of objects shown with concrete materials or with pictures, or they might reverse the process. The examples are limited to any of the three aspects for the numbers one (1) to five (5). Other one-digit numbers and the number ten (10) are explored in the same way in Module 2. An important objective of these lessons is to ensure students can confidently identify the number associated with a collection. The number is the cardinality of that collection and answers the question, How many …? Many younger students can count the number in a collection, but do not understand that the last number they say is a property that relates to the entire collection. For example, when shown a group of three flowers and asked to say how many flowers are in the picture, they might count, One, two, three without realizing that the last number name they have said applies to the entire collection. During the lessons it is important to reinforce the idea that the last number said applies to the entire collection. In later modules, students will be encouraged to identify the number in the collection without any counting.” MathEd, “For professional learning in relation to this content, select the following video from the support resources online. JTNI Teaching number: Counting principles”

• Module 3, Research into Practice, Comparing Numbers, supports teachers with context for work beyond the grade. “In preparation for work with the comparison of numbers within 100 in Grade 1 Module 5, encourage students to use comparison language at every opportunity and to explain their thinking about comparison. For example, when students compare numbers such as 7 and 4, represented with groups of 2 dot cards, they should describe the comparison by saying, “7 is greater than 4” or “4 is less than 7” and could explain how they know by placing the cards face to face to show there are 3 more dots on the 7 card. Read more about comparing numbers in the Research into Practice section for Grade 1 Module 5.

• Module 4, Preparing for the module, Research in practice, Connecting representations of numbers, supports teachers with context for work beyond the grade. “Written words are just one more way of representing numbers as is using the structure of a five-frame and a ten-frame. This work sets the stage for representing number within 20 (Module 7) and supports the writing of equations to represent addition and subtraction situations (Modules 6, 8, and 11). In preparation for representing numbers within 100 in Grade 1 Module 3, encourage students to make and describe connections between different representations of a number. For example, if students represent the number 7 with their fingers, have them represent the same number on a five-frame and a ten-frame, then explain how all the representations are the same and how they are different. Read more about the importance of making connections in the Research into Practice section for Grade K Module 7.”

• Module 5, Preparing for the module, Research into practice, includes examples and explanations of equality and To learn more includes an article reference where a teacher can build additional knowledge of equality concepts. “Students often view the equals symbol (=) as a signal to do something. In other words, they view it as an operator, and our language often reflects this because we say, “Two and three make five,” where make indicates that something active is happening and the equals symbol makes it happen. But the correct meaning of an equals symbol is that it shows the relationship between two expressions. This understanding gives students the fundamental knowledge to complete, for example, this equation: 4 + 5 = ___ + 3. Students who consider the equals symbol an operator will complete the blank with 9. However, students with a relational understanding will complete the blank with 6 because they know that the answer must result in the right side of the equation equaling the left side. Students in this grade are not yet adding with symbols, nor are they working with two addends on each side, but it is still important that the language they hear and the work they do reflect the equals symbol as a balancer, describing an equivalent relationship between expressions on both sides of the symbol.” To learn more, “Leavy, Aisling, Mairéad Hourigan, and Áine McMahon. 2013. “Early Understanding of Equality.” Teaching Children Mathematics 20, no. 4: 246 - 252.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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 K 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 K and the Common Core Standards, includes all Kindergarten 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 7, 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 3, Lesson 4, Length: Making comparisons, the Core Standards are identified as K.MD.A.1 and K.MD.A.2. The Prior Learning Standards are identified as early years. 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 the 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, Counting, includes an overview of how the math of this module builds from previous work in math. “Students in the early stages of counting may not yet demonstrate one-to-one correspondence. To encourage them to match one number to one object, guide them to line up objects in a row and actively move each object as it is counted. Alternatively, offer a fixed number of objects already organized for counting. For example, beads on a length of yarn or straw.”

• Module 9, Mathematics Overview, Coherence, includes an overview of how the content in Kindergarten connects to mathematics students will learn in first grade. “Lessons 9.5–9.6 focus on identifying and using 3D objects, and sorting 3D objects and 2D shapes. This extends the previous work with 3D objects (K.7.5–K.7.6) and supports the future work with identifying, sorting, analyzing, and creating 2D shapes (1.4.8–1.4.12) and 3D objects (1.10.10–1.10.12).”

• Module 2, Lesson 3, Number: Writing numerals 1 to 6, Topic Progression, “Prior learning: In Lesson K.2.2, students match numerals and domino dot arrangements from 1 to 9. K.CC.A.3, K.CC.B.4, K.CC.B.4b, K.CC.B.5; Current focus: In this lesson, students write the numerals 1 to 6. Numerals 1, 4, and 6 are taught together as they involve downward hand movements, while numerals 5, 2, and 3 require hand movements to the left and right. K.CC.A.1, K.CC.A.2, K.CC.A.3; Future learning: In Lesson K.2.4, students write the numerals 7, 8, and 9 using a movement from left to right. They write the numeral 0, and then combine the numerals 1 and 0 to write 10. K.CC.A.1, K.CC.A.2, K.CC.A.3” 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 Kindergarten 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, “Matching quantity to numeral: Mathematical quantities can be expressed through the use of multiple representations. These representations include physical objects, pictures, symbols (such as numerals), words, and by their use in everyday situations. When students count objects, hear the number name, and then see the numeral and number name, this continues to reinforce their correlations between these representations. After repeated similar experiences, students will become fluent with the form, sound, and quantity associated with each numeral. Conclusive research shows that numerals, as abstract representations of quantity, should always be paired with concrete or pictorial representations of the quantity represented. Writing numerals: Depending on exposure to numerals and number words, preschoolers will often learn to recognize numerals quite early, however writing numerals is a much more complex skill. Students must coordinate left-right orientation, exercise motor control, in addition to forming and following a mental image of the shape of the numeral. Research varies on an exact order for learning to form numerals, however many studies suggest that numerals be grouped according to some feature of the numeral. For example, the numerals 1 and 4 both begin with a downward stroke and could therefore be logically presented together. It is not unusual for students to incorrectly reverse numerals – 6 and 9 being the most common error – however this may have no relation to students’ understanding of the value of these numerals. To learn more: Copley, Juanita V. 2010. The Young Child and Mathematics, 2nd ed. Washington DC: National Association for the Education of Young Children. Leinwand, Steven, Daniel J. Brahier, and DeAnn Huinker. 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: National Council of Teachers of Mathematics. References: Arnas, Yaşare Aktaş, Ayperi Dikici Siğirtmaç, and Ebru Deretarla Gül. 2004. "A study of 60- to 89-mo.-old children’s skill at writing numerals.” Perceptual and Motor Skills 98 (2): 656–60. National Research Council. 2009. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. https://www.nap.edu/catalog/12519/mathematics-learning-in-early-childhood-paths-towardexcellence-and-equity.”

• Module 9, Preparing for the module, Research into practice, “Number position: Throughout early childhood, students build strong connections between many different representations of a number. First, they acquire a stable counting sequence (they can reliably say the sequence of counting numbers) and then they begin to associate the numbers in that sequence with the values they represent, and finally they count sets. One of the first steps to mastering addition is recognizing the quantity that is one less than a given number, and not just the numeral that represents the quantity. For example, given a set of 8 counters, if the teacher adds one counter to the pile, the student recognizes that there must be 9 counters, without actually recounting them. Evidence shows that students are able to reliably demonstrate one more than a quantity before they are able to show one fewer. Sorting shapes: In a previous module, students started identifying the attributes of some three-dimensional objects and sorting them. Since young learners identify objects holistically, still learning to identify specific attributes, geometry lessons should always start with students making verbal descriptions of attributes in their own words. 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/ 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: National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, D.C.: Authors. (p.88) 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 Kindergarten 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, “empty box or container for lessons 2 and 3, connecting cubes in lesson 2, hand puppet in lesson 4, large cube labeled: 6, 7, 8, 9, 10 in lesson 1, large tagboard or carpet squares in lesson 5, ORIGO Big Book: Hip Hop Hippos in lessons 5 and 6, The Number Case in lessons 1, 2, and 5, and toy animals in lesson 3. Each individual student needs a large number track, ORIGO Big Book: Hip Hop Hippos in lesson 5, and The Number Case in lesson 6.” 

• Module 2, Lesson 5, Number: Introducing the number track, Whole group lesson, Step 1 Preparing the lesson, “You will need: ORIGO Big Book: Hip Hop Hippos, 10 large tagboard or carpet squares labeled with numerals 1 to 10, numeral card for 1 to 10 from The Number Case (optional). Each student will need: Student Journal 2.6.” Step 3 Teaching the lesson, “Display the Cover Hip Hop Hippos. Have students place the large numeral cards in order to make a number track.”

• Module 6, Preparing for the module, According to the Resource overview, teachers need, “animal counters (or similar), clear jars or containers, clear resealable plastic bags, foam cubes or counters, play pennies, purse (alternatively, uses pieces of material to represent a purse), sheets of green paper, Support 6, workstation A-D in lesson 5, connecting cubes, counters in lesson 4, ORIGO Big Book: Just a Few More in lessons 3 and 5, ORIGO Big Book: Mice, Mice, Everywhere in lesson 1, resources such as ten-frames and number tracks from The Number Case, connecting cubes, counters, pennies, and other small objects such as stones, or toys located in a central position in the classroom for students to access as need in lessons 4 and 6. Each pair of students needs a resealable plastic bag and play pennies (or print copies of Support 5) in lesson 3. Each individual student needs connecting cubes in lesson 1, Support 6 in lesson 5, Support 7 in lesson 6 and the Student Journal in each lesson.”

• Module 7, Lesson 2, Number: Matching representations for 19, 18, and 15, Whole group lesson, Step 1 Preparing the lesson, “You will need: 1 soccer ball (or similar) Each student will need: vegetables cut into different shapes for stamping, (optional) different color paint, each in a shallow dish (optional), Student Journal 7.2”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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, 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, Quarterly test questions support the full intent of MP4, model with mathematics, as students use concrete materials and pictures to compare numbers up to 10. For example, Question 5, “Draw a picture to show a quantity that is more.” An image shows a box with five flowers. 

• Module 6, Check-up 2 and Module 10, Interview 2, students engage with the full intent of K.OA.5, fluently add and subtract within 5. Check-up 2, “Question 1, Write an equation to match each picture. a. 3 bees + 2 bees = ___ bees. b. 4 lady bugs + 1 lady bug = ___ lady bugs, c. 2 bees + 1 bee = ___ bees. Question 2, Write an equation to show the total number of dots on each domino. a. 1 and 3 dots. ___ + ___ = ___. b. 2 dots and 2 dots. ___ + ___ = ___.” Interview 2, “Steps: Say the expression listed below one at a time in a random order. You may wish to contextualize the facts by using simple stories, such as, Three apples take one apple. How many do I have? Allow about 10 seconds for the student to say the difference. Draw a ✔ beside the learning the student has successfully demonstrated. 5 - 0, 4 - 0, 3 - 0, 2 - 0, 1 - 0, 0 - 0, 5 -1, 4 - 1, 3 - 1, 2 - 1, 1 - 1, 5 - 2, 4 - 2, 3 - 2, 2 - 2, 5 - 3, 4 - 3, 3 - 3, 5 - 4, 4 - 4, 5 - 5.” 

• Module 9, Check-up 2 and Quarterly test B, develop the full intent of K.G.3, identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Check-up 2, Question 1, “Circle the two pictures that have been sorted into the wrong group. 3D objects, 2D shapes. Quarterly test B, Question 9, “Choose the 3D object. A. Heart, B. Polygon, C. Rectangular Prism.”

• Module 12, Quarterly test questions support the full intent of MP7, look for and make use of structure, as students decompose numbers. For example, Question 4, “Choose the picture that shows 3 + 3 = 6. A. 3 blocks shaded and 3 blocks not shaded, B. 1 block shaded and 5 blocks not shaded, C. 2 blocks shaded and 4 blocks not shaded.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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, Position: Using spatial language, include:

• Extra help, “Activity: For each scene in the book, point to the different animals and ask, Where is this (grub)? Then point to the other (grub) and ask, Where is this (grub)? Encourage students to use the appropriate position language.”

• Extra practice, “Activity: Organize students into pairs and distribute the resources. One student selects a card and uses a small toy and cube to represent the spatial position on the card. The student tells the other student how to place their toy and cube. Help the student use spatial language, if needed. The students alternate roles and repeat the activity until all the cards are used.”

• Extra challenge, “Activity: Have the students draw a scene from the book and locate some animals in different positions. Help them write the position word near the animals.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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 1, Lesson 5, Data: Sorting into two categories, Differentiation, Extra Challenge, “Have the students find and cut out pictures from magazines for different categories to make a collection of pictures for sorting. Say, We are going to create charts to show our sorting. Have students suggest categories for headings, such as houses, food, toys and games, or animals. Write a heading on each sheet of paper. Work with the students to paste the sorted pictures on the charts.”

• Module 5, Lesson 4, Equality: Developing the language of equality, Differentiation, Extra Challenge, “Place seven blue cubes on one pan of the balance. Students then place red and green cubes on the other pan to figure out the different combinations to balance the pans. Encourage students to record each combination on a sheet of paper, for example, 4 and 3 = 7, 1 and 6 = 7, and 2 and 5 = 7.”

• Module 10, Lesson 6, 2D shapes: Analyzing attributes of shapes, Differentiation, Extra Challenge, students have the opportunity to extend their thinking around work from a journal page they completed in the previous lesson. “Distribute the paper. Have the students draw very large 2D shapes. They can refer to Student Journal 10.5. They can then write the different descriptions or attributes of each shape inside its outline. The pictures can be displayed around the classroom.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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 2, Lesson 6, Number: Writing numbers just before and just after (up to 10), Whole class lesson notes, Step 2 Starting the lesson, “ELL: Allow time for the students to count forward and backward to fluent English-speaking students.” Step 3 Teaching the lesson, “ELL: Provide the students with connecting cubes to link the language of ten and five more to a visual representation. Ask the students to repeat the number names after you. Listen closely to check that they are saying the n sound at the end of the word. Allow students to speak about their experiences in their native language first, then ask in English.” Step 4 Reflecting on the work, “ELL: Provide sentence stems such as, The number before ___ is ___ ...” Small group 1 lesson notes, “ELL: Pair the students with fluent English-speaking students to enhance language acquisition. Invite the students to explain their just before and just after thoughts to each other.” Small group 2 lesson notes, “ELL: Encourage the students to repeat another fluent English-speaking student. For example, the student repeats, ``We need to look for the number that is just after five.”

• Module 7, Lesson 2, Number: Matching representations for 19, 18, and 15, Whole class lesson notes, Step 2 Starting the lesson, “ELL: Allow the students to watch a few rounds of the activity before joining in.” Step 3 Teaching the lesson, “ELL: Allow time for students to discuss the terms before, just before, after, and just after with fluent English-speaking students before moving on with the activity. Pair the students with fluent English-speaking students to complete the activity, if necessary.” Step 4 Reflecting on the work, “ELL: Provide sentence stems such as, The number before ___ is ___ ...” Small group 1 lesson notes, “ELL: Pair the students with fluent English-speaking students to enhance language acquisition. Invite the students to explain their just before and just after thoughts to each other.” Small group 2 lesson notes, “ELL: Pair students with fluent English-speaking students. Allow them to consider their response before discussing their thoughts with their partner.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten 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 2, Number: Creating groups of objects to match pictures, Whole Class, Step 3 Teaching the lesson, cubes are identified to support students with counting and representing quantities. “Give every student a train of five cubes. As you walk around, say, When you get your cubes, break them apart and put them on the floor in front of you. Roll the large cube into the middle of the formation, and have the students put cubes on their fingers to match the number of dots showing on the large cube. Ask different students to roll the large cube and count the dots rolled. Then have everyone put matching cubes on their fingers.”

• Module 6, Lesson 6, Addition: Developing fact fluency, Whole Class, Step 3 Teaching the lesson, counters and cubes are named as manipulatives to support students with addition equation calculations. “Distribute the cards and have the students work independently to figure out the answer. Some students may be able to figure out the answers mentally. If necessary, allow students to use their fingers, or to self-select tools from the resource center to support their problem solving.”

• Module 9, Lesson 2, Number: Writing numbers that are one greater or one less (up to 20), Step 3 Teaching the lesson, the online Flare tool is identified as a strategy to find one less or one more. “Open the Flare Number Track online tool and hold the toy above the number 12. Ask, What number is one greater than 12? What number is one less than 12? Move the toy and click on the relevant tile to flip it to reveal each number as the students say it. Reinforce this by saying, Twelve, one less is 11 and one greater is 13. Count 11, 12, 13 with the students. Continue until all the numbers on the track have been revealed.”