The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices across the year and they are often explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.

MP1 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 5, Lesson 3, Equality: Identifying two parts that balance a total, Step 3 Teaching the lesson, students think about different balancing problems and persevere to find the solution. “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 groups 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 (MP1) 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?”

• Module 7, Lesson 6, 3D objects: Identifying objects, Maintaining Concepts and Skills, Word Problems, students make sense and persevere in solving an addition word problem with multiple possible answers. “Lisa has 10 blocks. Reece has fewer blocks than Lisa. If they put their blocks together, what number could they show?” The teacher asks, “What is happening in this problem? What do you know about this problem? What do you need to find out? What will we use to solve this problem? How could you show your thinking?”

• Module 8, Lesson 3, Subtraction: Representing situations (take from), Step 3 Teaching the lesson, students make sense and persevere in solving problems when they analyze subtraction situations to determine what they know and what they have to find out. “There are six eggs. Two eggs break. How many are left?” The teacher discusses “the points below (MP1): What is this problem about? What do you have to find out? Will you use addition or subtraction to find the answer? How did you decide? What subtraction sentence can we write to match?”

• Module 9, Lesson 3, Number: Working with position (up to 20), Mathematical practices and processes, students make sense of mystery teen numbers. “MP1 - when students analyze clues to solve mystery number situations, and persevere in their thoughts until they find a possible answer.” Student Journal, page 127, Question a, students are given a number track 1-20, “My number is between 11 and 15.” Teaching the lesson, “If necessary, clarify that a number between 11 and 15 will be greater than 11 and less than 15 (MP1).”

MP2 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 6, Lesson 2, Addition: Writing equations (put together), Step 3 Teaching the lesson, students reason abstractly and quantitatively about addition problems. “Project the first domino showing three and two dots (slide 1). Ask, What numbers are shown on this domino? (MP2) If necessary, remind students that one number is shown on each side of the domino. Confirm that the domino shows the numbers three and two. Ask, What is the total number of dots? What sentence can we write to show the adding? Have the students count all the dots to identify the total. Write 3 add 2 equals 5 on the board. (MP2)”

• Module 8, Lesson 4, Subtraction: Writing equations (take from), Mathematical practices and processes, “MP2 when students create an equation to match a word problem (decontextualize), and relate the equation to a model of the word problem (decontextualize).” Step 4 Reflecting on the work, “Say, Think of a take-away word problem you can create with felt characters. Allow time for the pairs to develop a problem. Then each pair acts out their take-away problem on the felt board for the other students to see, and says how many are left. Invite volunteers to write an equation that corresponds to each word problem on the board (MP2).”

• Module 9, Lesson 1, Number: Making groups that have one more or one fewer (up to 20), Step 3 Teaching the Lesson, students reason abstractly and quantitatively when they “make sense of quantities one more and one fewer than a given quantity, and say the number that each quantity represents.” Students are given a picture of 14 ladybugs, “Make a group of counters to show a quantity that is one more than 14. Allow time for the students to make the group. Ask, What number tells us the number that is one more than 14? (MP2)”

• Module 11, Lesson 3, Addition/Subtraction: Solving word problems (draw pictures), Mathematical practices and processes, “MP2 when students create a word problem to represent an operation”. Step 2 Starting the lesson, “Ask the students to think of and share a word problem that involves addition or subtraction (MP2).”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3. 

Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include:

• Module 1, Lesson 3, Number: Creating groups of pictures to match numerals (1 to 5), Step 2 Starting the lesson, students construct viable arguments as they explain why the total number of objects remains the same despite being rearranged and counted in a different order. “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. (MP3)”

• Module 3, Lesson 6, Capacity: Making comparisons, Step 2 Starting the Lesson, students construct viable arguments as the reason about the capacity of different containers. “Display containers A, B, and C. Say, Imagine that I wanted to fill each of these containers with rice. Which container would hold the most rice? How do you know? Invite students to share and justify their predictions. Encourage them to describe the attributes of the container that helped them form their prediction. For example, Container (B) is tallest, so it must hold more rice. (MP3)”

• Module 9, More Math, Thinking Tasks, Question 3, students construct a viable argument and critique the reasoning of others as they count and represent teen numbers. “Vincent has written that there are 71 bees in total. How do you know Vincent has made a mistake? You can draw a picture to help.” The correct answer is 17.

• Module 10, Lesson 5, 2D shapes: Identifying shapes, Student Journal, page 145, students construct viable arguments as they explain and justify their sorting decisions with 2D shapes. “Cut out the 2D shapes. Then sort and paste them where they belong on page 147.” There are labels for triangles, circles, squares, non-square rectangles, and other shapes. In Step 3 Teaching the lesson, the teacher encourages students “to sort their shapes in a method of their choice. Afterward, organize students into pairs to compare their sorting and describe their sorting rule. (MP3)”

• Module 11, Student Journal, pages 225- 227, Convince a friend, students construct viable arguments and critique the reasoning of others as they join simple 2D shapes to make larger 2D shapes. “Cut out the 5 shapes and join some of them to make the larger shape on page 227. Fatima thinks she can join 3 shapes to make the shape below. Corey thinks it can only be made with 2 shapes. Who do you agree with? Show how you know.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

MP4 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 5, Lesson 1, Equality: Introducing the idea of balance, Whole Group Lesson Notes, Step 3 Teaching the lesson, students model with mathematics as they reason about equality. “Ask everyone to stand. Say, Let’s pretend to be a pan balance. Put your arms straight out to the sides. Hold a stapler in one hand, and the baseball bat in the other, and turn your back to the students so they can copy your movements. Say, The (bat) is heavier. Make your arm with the (bat) go down. Ask, How could you describe the stapler? Encourage several responses such as, “The stapler is lighter than the bat.” Select two different objects and repeat, with the arms moving to match lighter and heavier as you describe the comparison. (MP4 and MP6) Now select two identical items (for example, glue sticks) and hold one in each hand. Say, The (glue sticks) are the same. Extend your arms straight out to show balance. Repeat with different pairs of classroom objects. (MP4)”

• Module 6, Student Journal, page 127 and 129, Mathematical modeling task, students model with mathematics as they connect a picture representation with a matching equation. Students are given 9 ladybugs to cut out. “Cut out these pictures. Then paste them onto the leaves on page 129.” Students are given a picture of 2 leaves. “Paste ladybugs onto both leaves to complete the picture. Share your thinking.” Below the leaves is a blank equation for students to fill in, “___ + ___ = ___.”

• Module 8, Lesson 3, Subtraction: Representing situations (take from), Small group 1, students model with mathematics as they describe how the model relates to the problem situation and a matching equation. Students are given cards with pictures of subtraction situations and subtraction equation cards. “The subtraction equations cards are spread out faceup and the picture cards are placed facedown in a pile. Students take turns to select a picture card and find the matching subtraction equation card.”

• Module 11, Student Journal, page 223, Mathematical modeling task, students model with math as they compare representations for a given context. “Kylie uses 9 rings to make a paper chain. She uses 5 blue rings and some red rings. Blake wants to use 4 red rings and 5 blue rings to make his paper chain. Will their paper chains look the same? Show how you know.”

MP5 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the modules to support their understanding of grade level math. Examples include:

• Module 3, Lesson 3, Number: Comparing numbers (1 to 10), Step 3 Teaching the lesson, students use appropriate tools strategically to compare numbers within 10. “Bring the students together to share their results. Ask, Who used counters to identify the number that is greater? Who used a number track? What about counting? Encourage students to share their strategies. Establish that if using counters, the group that has more represents the greater number. If using a number track, the greater number is on the right because it represents a distance that is farther away from the start of the track. If counting, the greater number is said last (assuming the sequence is correct). (MP5)”

• Module 7, Lesson 4, Number: Analyzing teen numbers, lesson notes state, “MP5 when students choose a tool from the resource center to support their thinking about addition equations”. Step 4 Reflecting on the work, students are given, “10 + 1 = 11, 10 + 2 = 12, 10 + 3 = 13”, “Organize students into pairs and have them work together to prove that the equations are true. Suggest that they work with counters and ten-frames, or draw pictures to verify the equations. (MP5)”

• Module 9, Student Journal, page 185, Mathematical modeling task, students engage with MP5 as they choose appropriate tools and strategies to reason about 3D shapes. Students are given a picture of a basketball, a can of tuna fish, a box of tissues, and a dot cube (die), “Look at these 3D objects. Show other 3D objects that look similar.” Grade K Module 9 Activity notes for MMT and CAF, “Watch for how students determine which aspects of the objects they should attend to, and how the everyday objects relate to the idealized geometric objects. For example, some students may find objects within their room to compare features. Others may use the pictures to look for similarities and differences. Afterward, discuss the different tools, representations, and/or strategies the students used to help them solve the problem.”

• Module 11, Lesson 4, Addition/subtraction: Solving word problems (write equations), “MP5 - when students select and use tools to help them solve word problems”. Student Journal, page 157, Question a, students select and use tools to solve real world problems. “5 friends are playing in the pool. 2 friends get out of the water. How many friends are left in the pool?” Step 3 Teaching the lesson, the teacher asks, “What tool could we use to help figure out the answer? (MP5) Encourage responses such as cubes, counters, coins, and drawing a picture. Remind students that they can select a tool from the resource center to help solve the problem, if needed.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. MP6 is explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes. 

Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Lesson 1, Number: Creating groups of objects, Whole group lesson notes, Step 3 Teaching the lesson, students attend to the precision of mathematics by accurately counting a group of objects. “Ask each student to take five cubes, then sit in a large circle with the other students. Say, I will show and say a number, and you put that many cubes on your fingers. Hold your hand out in front of you. Ready? Show two cubes. Repeat with one, three, four, and five at random. After the students show several numbers of cubes, say, Put one cube on your finger. Now, put another one on. Count one, two. Now put another cube on. Count one, two, three. Continue for four and five. (MP6)”

• Module 2, Lesson 4, Number: Writing numerals 7 to 10, and 0, Student Journal, page 33, Question 1, students attend to the precision of mathematics by accurately writing numerals. “Follow the arrows. Trace then write the numerals.” Students practice writing the number 7, 8 and 9.

• Module 12, More math, Thinking tasks, Question 1, students see a picture of 1 hen in a pen and 4 hens coming into the pen, “Look at the picture. Write the total number of hens. ___”. According to the task rubric, “The precision of MP6 is visible and necessary for an accurate count and to write the matching number.” 

Students have frequent opportunities to attend to the specialized language of math in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 3, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The vocabulary below will be introduced (bolded) and developed throughout this module. The words can be printed as cards from the resource list. The first file contains words that have been introduced in a previous module and the second contains words that are introduced in this module.” These words are also defined in the student glossary at the end of each Student Journal. The words are: Empty, fewer, full, greater, half full, heavier, least, length, lighter, longer, mass, more, number, numeral, shorter. Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.

• Module 6, Lesson 1, Addition: Adding two groups (put together), Whole group lesson notes, Step 3 Teaching the lesson, students attend to the specialized language of math by using terminology accurately. “Reinforce this by saying statements such as, Two put with four makes six. Two and four is six. Two and four equals six. Take this opportunity to introduce the mathematical language for addition, add and plus. Ask, Has anybody heard of the words add and plus before? What do you think these words mean? Lead a whole class discussion. Remind students to listen but not interrupt when others are sharing. Have the students give a thumbs-up if they agree with a suggestion or a thumbs-down if they disagree. Encourage students to explain why they agree or disagree. (MP3) At the end of the discussion, explain that each term involves putting two groups together to figure out a total. (MP6)”

• Module 7, Lesson 6, 3D objects: Identifying objects, Small group 1, Sorting 3D objects by name, students attend to the specialized language of math as they identify 3D shapes by the correct name and sort them. Students are given a box of real-world 3D objects and four large signs: cube, cone, cylinder, and sphere. “Organize students into pairs to sort the objects and name each object as they place it with the matching sign. They then count each sorted group.”

While there are examples of the intentional development of MP6, Attend to precision, throughout materials, there is also evidence of imprecise language. Example include:

• Module 10, Lesson 3, Addition: Exploring the commutative property, Step 3 Teaching the lesson, students “attach clothespins to the 8 hanger to represent 2 + 6. Rotate the hanger around to show 6 + 2 = 8.” The teacher says, “These two equations are addition facts. They are called turnaround facts because the two groups we are adding are the same but are turned around.”

• Module 10, Lesson 4, Addition: Introducing the think big, count small strategy, Step 3 Teaching the lesson, “MP6 - when students use correct language to describe the think big, count small strategy”. Directions include, “Invite a student to take a domino from the bag. Ask them to identify the greater number, then use the think big, count small strategy to figure out the total. Make sure they verbalize the strategy as they work. (MP6) For example, This domino shows four and two. The greater number is four. I do not need to count all the dots to find out the total. I just think big and count on two more: four, five, six. Four add two is six.” 

• Module 11, Lesson 1, Addition/subtraction: Interpreting word problems, Step 3 Teaching the lesson, students use key verbs for addition. “MP6 - when students identify and use precise addition and subtraction language.” Students are given a T-chart (slide 1) with the headers addition and subtraction, the teacher records and reads a student-created addition word problem aloud, “Ask, How do you know the problem is about addition? (MP6) Guide the students to discuss the language in the problem. Take note of any key verbs (for example, join, add, and put together) and record them below the addition heading.”

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year and they are often explicitly identified for teachers in several places:  Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within whole class lesson notes.

MP7 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Module 2, Lesson 5, Number: Introducing the number track, Step 4 Reflecting on the work, students look for and make use of structure while utilizing a number track to count on or back from a given number. “Have the students share their answers to Student Journal 2.5, and describe how they found the missing numbers. Look for students who were able to count on or back from a given number instead of counting from 1 for each example. (MP7)”

• Module 4, Lesson 4, Number: Working with benchmarks of five (Five-frame), Step 3 Teaching the lesson, students look for and make use of structure while answering questions about a five-frame. “Project the five-frame (slide 1) and say, This five-frame helps us see numbers greater than or less than five. Project the five-frame showing three counters (slide 2) and ask, How many counters are there? Are there more than or fewer than five? How many fewer? How do you know? Repeat to show two, four, six, and then eight counters (slides 3 to 6). (MP7)”

• Module 7, Lesson 4, Number: Analyzing teen numbers, Step 3 Teaching the lesson, Big Book, students look for and make use of structure “when they recognize the structure of a teen number (one group of ten and some more) in the scenes of the big book”. In The Bug Day Out, students see a picture of two water slide ride cars, each with ten seats. Ten bugs are in the first car, and 6 bugs are in the second car. The teacher asks, “how are the ladybugs arranged on the boats? Highlight that the ladybugs are seated in a group of ten and some more. Say, 16 is ten and six more. Repeat the discussion for the remaining pages. (MP7)”

• Module 11, Lesson 4, Addition/Subtraction: Solving word problems (write equations), Step 2 Starting the lesson, students look for and make use of structure as they “use the structure of domino arrangements to identify the number dot without counting one by one.” The teacher says, “I am going show a picture of dots. I want you to figure out the number of dots.” “Display one of the domino dot arrangement cards for about three seconds. Have the students share the number of dots they could see. Confirm the number of dots, then repeat the activity with other dot arrangement cards. (MP7)” 

MP8 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:

• Module 3, Lesson 3, Number: Comparing numbers (1 to 10), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally from a given number. “Ask a student to say a number between five and ten. Count from that number to 15. Then have the class repeat the count with you. Repeat with different students choosing the starting number. Invite a student to start counting from eight and stopping at 15. Repeat with other students, starting from other numbers less than ten. Repeat at other times during the day. (MP8)”

• Module 4, Lesson 5, Number: Working with benchmarks of ten (ten-frame), Step 2 Starting the lesson, students look for and express regularity in repeated reasoning by counting orally from a given number. “Have the students count from 1 to 15. Ask, What number will we say after 15? Invite a student to count from 15 to 20. Then have the whole class count from 15 to 20. Count aloud from 1 to 20. Emphasize the n sound in the teen component of the teen numbers. Then have the students repeat the count with you several times. Repeat at other times during the day. (MP8)”

• Module 7, Lesson 2, Number: Matching representations for 19, 18, and 15, Step 3 Teaching the lesson, students look for and express regularity in repeated reasoning when they “identify a quicker way of figuring out the total of finger representations of the numbers 18 and 19. For example, noticing that only one or two fingers are not raised, so they count back one or two from 20.” Students show 18 then 19 with their fingers and the teacher says, “We can start at ten and count the extra ones to figure out the total. Can you think of a quicker way we could figure out the total?” Students discuss and share their methods. “They may suggest counting back from 20 because there are only one or two fingers being held down. (MP8)”

• Module 10, Lesson 6, 2D shapes: Analyzing attributes of shapes, Student Journal, page 149, students look for and express regularity in repeated reasoning when they notice that the number of corners and the number of sides is the same in each 2D shape and then test and prove the generalization that every 2D shape will have the same number of corners as number of sides. Students see a picture of a square and five other polygons, “Write the number of sides and corners for each shape.” Reflecting on the work, “What do you notice about the number of sides and the number of corners for each shape? Do you think that would be true for all 2D shapes? Can you think of any shapes for which it might not be true? (MP8). Encourage students to share and test their ideas.”

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 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.”