## ORIGO Stepping Stones 2.0

##### v1.5
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## Report for Kindergarten

### Overall Summary

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials partially meet expectations for rigor and meet expectations for practice-content connections.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Each Grade Level consists of 12 modules. Each module contains two types of summative assessments. Check-ups assess concepts taught in the module, and students select answers or provide a written response. In Interviews, teachers ask questions in a one-on-one setting, and students demonstrate understanding of a module concept or fluency for the grade. In addition, Quarterly Tests are administered at the end of Modules 3, 6, 9, and 12.

Examples of assessment items aligned to Kindergarten standards include:

• Module 1 Interview, students are given 5 counters and count the number of counters by saying numbers 1-5 aloud in sequence (K.CC.1).

• Module 5 Checkup, students identify which numerals correspond to the number of counters shown, assessing knowledge of number names and counting within 100 (K.CC.1).

• Module 7 Checkup, students connect the names of various 3D shapes to both the model and real world example of the shapes (K.G.2).

There are some assessment items that align to standards above Kindergarten; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include:

• Module 12, Check-Up 1, Problem D, students solve, “13 cents has the same value as ____ dime and  ____ pennies.” In Check-Up 2, Problem C, students solve, “1 dime and ____ pennies has the same value as 17 cents.” In the Interview, “Correctly identified the value of each coin. ___ dime ___ nickel ___ penny. Correctly represented values using coins. 13 cents, 17 cents, 12 cents. Correctly describe the coins required to make a value 14 cents, 19 cents, and 15 cents.” These problems align to 2.MD.8.

• Modules 10-12, Quarterly Assessment, Test A, Question 6, students determine the equivalent for 1 dime and 3 pennies. In Test B, Question 6, students determine the equivalent for 1 dime and 5 pennies. These problems align to 2.MD.8.

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Extensive work is provided as students engage with different types of problems in each Kindergarten lesson. There is a Student Journal with problems aligned to the day’s objective and Maintaining Concepts and Skills page that includes additional practice opportunities with grade level skills. Each Module includes six whole-class lessons and twelve small-group activities and, according to the materials, “It is recommended that Kindergarten teachers teach a whole-class lesson on one day and follow up with the two accompanying small-group activities on the next day.” Examples include:

• Module 2, Lessons 1-5 engage students in extensive work with K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). In Lesson 1, Number: Creating groups to match numerals (6 to 10), Student Journal, page 23, students count to match a quantity to a given numeral. Student’s are asked to, “Color fruit to match each numeral.” In Lesson 3, Number: Writing numerals 1 to 6, Student Journal, pages 29 and 31, students practice writing the numerals 1 through 5 to match a given quantity. Students are directed to, “Follow the arrows. Trace then write the matching numerals.” In Lesson 5, Number: Introducing the number track, Student Journal, page 37, students write a number sequence. Question 1, “Trace over the gray numerals. Then write the numbers that are missing on each number track.”

• Module 3, Lessons 4-6, engage students in extensive work with K.MD.2 (Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, “directly compare the heights of two children and describe one child as taller/shorter.” In Lesson 4, Length: Making comparisons, Student Journal, page 49, students use a piece of string to compare lengths. Directions instruct students to, “Color the pictures blue that are shorter than your string. Color the pictures yellow that are longer than your string.” In Lesson 5, Mass: Making comparisons, Student Journal, page 51, includes six questions with a picture of a balance scale and two different objects on each scale. The scale is not equally balanced, as one object is higher in the air than the object on the other side. The materials instruct students to, “Circle the toy that is lighter.” In Lesson 6, Capacity: Making comparisons, Student Journal, page 53, Question 2, “Circle the glass that is holding more water.” Question 3, “Look at all the glasses in question 2. Write L on the glass that is holding the least amount of water.”

• Module 5, Lessons 2-4 and Module 10, Lesson 2 engage students in extensive work with K.OA.3 (Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). In Module 5, Lesson 3, Equality: Identifying two parts that balance a total, students practice decomposing numbers in more than one way. Step 2 Starting the lesson teacher notes, “Show a train of five connecting cubes. Ask two students to come to the front and break the train of five cubes into two groups. The students then identify the number of cubes in each group (for example, two and three). Ask, Who can break the five cubes in a different way? Choose another pair of students to break a second train of five cubes into two different groups (for example, one and four). Repeat the activity and discussion by breaking up a train of eight connecting cubes.” In the same lesson, Student Journal, page 73, students see a picture of a balance scale with quantities of circles on one side, and a different quantity on the other side. Directions instruct students to, “Draw a circle in each empty box to make each balance picture true. Then complete the sentence to match. ___ and ___ is the same value as ___” or “___ is the same value as ___and ___.” In Module 10, Lesson 2, Addition: Decomposing numbers (up to 10), Student Journal, page 139, students color a unifix cube train to show decomposing a number. Students now progress to writing an equation to match their cube train. Directions ask students to, “Color some of the blocks. Then write an equation to match.”

The instructional materials provide opportunities for all students to engage with the full intent of Kindergarten standards through a consistent lesson structure. Examples of meeting the full intent include:

• Module 5, Word Problems, Module 10, Word Problems, and Module 11, Lessons 2, 3, and 6 engage students with the full intent of K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.) In Module 5, More Math, Word Problems, “Natalie has 9 counters in total. Some of the counters are red, and some of the counters are blue. How many blue and how many red counters could Natalie have?” In Module 10, More Math, Word Problems, “Morgan has 8 stickers. She gives some stickers to her friend Antonio, and some stickers to her sister Susan. She has no stickers left. How many stickers could she have given to each person?” In Module 11, Lesson 2, Addition/Subtraction: Solving word problems (act out), Student Journal, page 153, “Use blocks to act out each problem. Then write an equation to show the answer.” Question 2a, “7 birds were sitting on the fence. One bird flew away. How many birds are left?” Question 2b, “Claire counts 3 blue cars and 3 red cars. How many cars did she count in total?”

• Module 8, Lesson 2 and Module 10, Lesson 4, engage students with the full intent of K.CC.2 (Count forward beginning from a given number within the known sequence). In Module 8, Lesson 2, Subtraction: Writing equations (take apart), Starting the Lesson, “Say the counting sequence from 20 to 50. Then have the students say the sequence with you a number of times. Invite a student to start counting by 20. Repeat with other students, starting from 30 or 40. Then invite students to count from 26, 36, or 46.” In Module 10, Lesson 4, Addition: Introducing the think big, count small strategy, Starting the Lesson, students count from 1 to 100. “Start the counting sequence from one, with each student saying just one number name as the count moves around the circle. Stop the sequence at 30. Start the count at 20 and move in the opposite direction around the circle stopping at 50. Repeat at other times of the week with other number ranges between 1 and 100.”

• Module 9, Lesson 5 and Module 11, Lesson 5 engage students with the full intent of K.G.5 (Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.) In Module 9, Lesson 5, 3D Objects: Identifying and using objects, Small Group 1 activity, “Each student uses the 3D objects as models to help them make at least three 3D objects from the modeling clay.” In Module 11, Lesson 5, 2D Shapes: Drawing shapes, Step 2 Starting the Lesson, the teacher describes a 2D shape. students draw the shape and the teacher asks “for a volunteer to share their shape and explain how it matches all the clues”.

Materials do not provide opportunities to engage all students with the full intent of one standard that is major work of the grade:

• K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.) The full intent of K.NBT.1 is not realized as students do not have the opportunity to compose or decompose teen numbers into ten ones and some further ones by using objects and drawings. Students are given picture prompts on cards or in the Student Journal to show the composition or decomposition. In Module 7, Lesson 4, Number: Analyzing teen numbers, teen numbers are identified as having 1 ten and some ones instead of ten ones and some extra ones. For example, Student Journal, page 101, Question b, students are given a picture of a filled ten frame and five circles outside the ten frame. “Write the number of tens and ones. ___ ten and ___ ones.”

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

##### Indicator {{'1c' | indicatorName}}

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of modules devoted to, or supporting, major work of the grade is 8 out of 12, which is approximately 67%.

• The approximate number of lessons devoted to major work of the grade is 49 out of 72, which is approximately 68%.

• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 71 out of 96, which is approximately 74%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 74% of the instructional materials focus on major work of the grade.

##### Indicator {{'1d' | indicatorName}}

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers on a document titled, “Grade __ Module __ Lesson Contents and Learning Targets” for each module. Examples of connections include:

• Module 1, Lesson 6, Data: Making yes/no graphs, Step 3 Teaching the lesson, connects the supporting work of K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.) to the major work of K.CC.5 (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) and to the major work of K.CC.4 (Understand the relationship between numbers and quantities; connect counting to cardinality.) Students use sticky notes to create a graph and then answer questions about the data. “Discuss the information on the yes/no graph. Ask, What do you see happening on this yes/no graph? What do the faces tell us? Encourage the students to discuss their ideas. Ask a student to count the number of faces in each column. Make sure the correct number name is assigned to each sticky note and that they know the last number name said tells the total number of sticky notes. Ask, do we have more or fewer students who like dogs, or do not like dogs?”

• Module 9, Lesson 5, 3D objects: Identifying and using objects, Small Group 2, connects the supporting work of K.G.5 (Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.) to the major work of K.CC.5 (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) Students build and count shapes. “Organize students into pairs to create a stack of five to eight blocks. They take a photo of their stack, then disassemble it, and lay the objects on the ground to take a photo of the blocks. At a later time, the photos can be shared with the whole class. The other students can identify the number and type of blocks used in the picture of the stack, before the second photo is shown.”

• Module 10, Lesson 6, 2D shapes: Analyzing attributes of shapes, Student Journal, page 149, connects the supporting work of K.G.4 (Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length) to the major work of K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Students see a picture of a square. Question a, “Write the number of sides and corners for each shape.” On the journal page, students practice with 5 additional shapes.

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

Materials are coherent and consistent with the Standards. Examples of connections include:

• Module 4, Lesson 4, Number: Working with benchmarks of five (five-frame), Students work in partners for the whole group time to count the number of objects on cards and then recognize that the last number stated is the total (K.CC.4). The program states that it also addresses K.CC.3, in which students write numerals up to 20 connecting to K.CC.B, Count to tell the number of objects, to K.CC.A, Know number names and the count sequence.

• Module 7, Lesson 7, Number: Matching representations for 19, 18, and 15, Teaching the lesson, connects K.CC.A as students write the numerals and K.CC.B as students draw a given number of objects. Two students show 15 fingers to the class. Students count the fingers. The teacher says, “Just like the numbers, 14, 16, and 17, these numbers are written with the 1 at the start to remind us there is one group of ten. Work with the students to write the numerals 15, 18, and 19.”

• Module 8, Lesson 8.2, Subtraction: Writing equations (take apart), Teaching the lesson, Lesson notes connects K.CC.A with K.OA.A as students count the numbers and represent a given situation as a subtraction equation.

##### Indicator {{'1f' | indicatorName}}

Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Materials relate grade-level concepts from Kindergarten explicitly to prior knowledge from earlier grades. These references are consistently included within the Topic progression portion of Lesson Notes and within each Module Mathematics Focus. At times, they are also noted within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 3, Lesson 6, Capacity: making comparisons, Lesson Notes connect K.MD.2 (Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.) “In early years, children may have had experience with describing the amount of liquid they see in a container, such as a drinking glass or a bath. In this lesson (3.6), students make direct comparisons to compare the capacity of three different containers. Language associated with capacity and liquid volume is then explored.”

• Module 7, Mathematics, Focus, “Students coming to your classroom from a formal Pre-Kindergarten or early childhood curriculum may have experience and exposure to the following concepts: Naming common 3D objects (sphere, cube, cylinder, rectangular-based prism, and pyramid), Joining 3D objects to compose 3D structures, Describing and sorting 3D objects”.

• Module 12, Lesson 1, Money: Identifying coins, Lesson Notes connect K.NBT.A (Work with numbers 11-19 to gain foundations for place) to the work from early years. “In early years, children may have had experience with money, coins, and their values. In this lesson (12.1) students describe the distinguishing features of a penny, nickel, dime, and quarter. They then identify each of these coins.”

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Topic Progression portion of Lesson Notes and within the Coherence section of the Mathematics Overview in each Module. Examples include:

• Module 4, Lesson 6, Number: Working with unstructured arrangements, Lesson Notes connect K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).), K.CC.4 (Understand the relationship between numbers and quantities; connect counting to cardinality.), and K.CC.5 (Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) to the work of grade 1 (1.NBT.1). “In this lesson - Students identify numbers that are represented in unstructured arrangements on a ten-frame. The lesson builds upon Lessons 4.4 and 4.5, as students visualize the counters being moved to form a representation that is more familiar. In Lesson 1.1.1, students identify numerals and number names that match collections of up to ten objects.”

• Module 9, Mathematics Overview, Coherence “Lessons 9.1-9.4 focus on working with numbers through 20, including work with comparison and relative position.” This “serves as a foundation to representing two-digit numbers (1.3.1-1.3.8).”

• Module 10, Lesson 4, Addition: Introducing the think big, count small strategy, Lesson Notes connect K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem) to the work of grade 1 (1.OA.6, 1.OA.8,1.NBT.1). “Students use the technique of starting with the greater number and counting on the lesser number, regardless of the order presented in the addition fact. In Lesson 1.2.1, students review the concepts of add to and put together addition.”

##### Indicator {{'1g' | indicatorName}}

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten foster coherence between grades and can be completed within a regular school year with little to no modification.

According to the Program Overview Program Components, “Carefully crafted lesson notes ensure a successful learning experience. For Kindergarten, each module has six whole-class lessons and 12 small-group activities. It is recommended that Kindergarten teachers teach a whole-class lesson one day and follow up with the two accompanying small-group activities the next day. Following this recommendation will provide 144 days of lessons.” While there are no clear recommendations for time to implement assessments, there is a description of assessment types within the materials. According to the Program Overview, “Summative assessment generally takes place at planned intervals after instruction. If used strategically, summative assessment can also serve a formative role to modify future instruction. Stepping Stones 2.0 provides three options for summative assessment.” Check-ups, Interviews, and Quarterly tests (after modules 3, 5, 9, and 12) account for 1 asssessment day per module and 4 assessment days for quarterlies. When assessments are added in, there are 160 days of instruction.

Included in the 160 days:

• 144 lesson days

• 12 module assessment days

• 4 quarterly test days

### Rigor & the Mathematical Practices

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor and Balance

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for rigor. The materials give attention throughout the year to procedural skill and fluency and spend sufficient time working with engaging applications of mathematics. The materials partially develop conceptual understanding of key mathematical concepts and partially balance the three aspects of rigor.

##### Indicator {{'2a' | indicatorName}}

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include some problems and questions that develop conceptual understanding throughout the grade level. Students have few opportunities to independently demonstrate conceptual understanding throughout the grade.

Cluster K.OA.A includes understanding addition as putting together and adding to, and understanding subtraction as taking apart and taking from. Modules 6, 7, 8, and 9 explore a variety of real-world applications using a few mathematical representations.

Some opportunities exist for students to work with addition and subtraction that address conceptual understanding through the use of some visual representations and different strategies. Examples include:

• Module 3, Lesson 1, Number: Making groups that have more or fewer (up to 10), Whole Class, Step 3 Teaching the lesson, “Each student collects 10 counters, then sits in a large circle. Show the students the number picture card for four. Say, This group shows four. Make a group of counters to show more than four. Invite different students to describe the number group they made. Prompt several different answers to highlight there are many ways to show more than four.”

• Module 7, Lesson 4, Number: Analyzing teen numbers, Whole Class, Step 3 Teaching the lesson, “Students read their numeral, then show the matching number using a strategy of their choice (MP5). These strategies could include pairing with another student to show the number with fingers, drawing pictures or showing the number with counters or other classroom resources. Look for students who use the ten-frame to represent the number. Ask these students to share their thinking with the class. Ask, How do you know [fifteen] is shown? Focus on the fact that each teen number is composed of one group of 10 ones and some leftover ones. Repeat the activity. This time encouraging students to show their number using the ten-frame.”

• Module 8, Lesson 1, Subtraction: Representing situations (take apart), Whole Class, Step 3 Teaching the lesson, “Distribute the connecting cubes. Explain to the students that they will use the cubes to model put together (addition), and take apart (subtraction) problems, as shown. After each problem, invite students to share the solution and to identify whether they used addition or subtraction thinking to figure it out. Encourage them to refer to the problem and explain what helped them decide. For example, for the first problem, students may explain, "I knew the number of dogs in the water and the number of dogs on the beach. I had to find out the total so I had to put the two numbers together."

• Module 9, Lesson 1, Number: Making groups that have one more or one fewer (up to 20), Whole Class, Step 3 Teaching the lesson, “Place the number picture cards in an array, facedown, on a table. Invite one student to turn over a picture card, and another student to roll the cube. All of the students make a group of counters to match the picture and words rolled. For example, if the picture shows 18 and the cube “one fewer”, the students make a group of 17 counters. Continue until every student has turned over a picture or rolled the cube.”

However, the instructional materials do not regularly provide students opportunities to independently demonstrate conceptual understanding throughout the grade-level. Examples include:

• Module 8, Lesson 2, Subtraction: Writing equations (take apart), Student Journal, page 113, “Write the total. Cover 1 or 2 dots. Then write the number of dots that are left.” Each problem shows a number of dots with an equation under it. The equation has students subtracting 1 or 2 from the dots. The worksheet addresses filling in the equation not conceptual understanding of subtraction.

• Module 10, Lesson 4, Addition: Introducing the think big, count small strategy, Student Journal, page 185, Questions a-f, “Have the student figure out and write the totals, then draw a line from each key to a matching door. There are two keys for each door.” Each problem has a key with an addition equation to solve. Students match their sums with numbers already written on the page. The worksheet addresses filling in the sums  and matching equal numbers but does not address  the conceptual understanding of addition.

• Module 11, Lesson 1, Addition/subtraction: Interpreting word problems, Whole Class, Step 3 Teaching the lesson, “Point to the Subtraction heading and ask Who can share a word problem about subtraction? Choose a volunteer to share their problem, and you record the problem on the board. Read the problem aloud, and have the students raise their hand if they agree that it involves subtraction. Ask, How do you know that the problem is about subtraction? Guide students to discuss the language in the problem, highlighting any key verbs (for example, take, cut, chop, run away, lost, and eat). Say, We know this problem is about subtraction because it wants us to (take) an amount from the (total). Repeat the activity with a few more subtraction word problems.” This lesson addresses keywords for solving problems, not conceptual understanding.

##### Indicator {{'2b' | indicatorName}}

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the Kindergarten expected fluencies, add and subtract within 5.

The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.

The materials attend to the Kindergarten expected fluencies: K.OA.5 fluently add and subtract within 5. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include:

• Module 6, Lesson 6, Addition: Developing fact fluency, Student Journal, “Addition: Developing fact fluency.” Students are given addition problems within 5 to practice and solve fluency.

• Module 8, Lesson 6, Subtraction: Developing fact fluency, Student Journal, “Write the answers on the race track.” Students are given different subtraction problems within 5 to solve and practice fluency.

• Module 8, Lesson 6, Subtraction: Developing fact fluency, Small group 1, “Organize students into pairs and distribute the cards. They mix the cards and place them face up on a flat surface. They take turns to match the subtraction expression with the answer. Extend the activity by placing the cards face down to play a memory game.” Students are practicing subtraction fluency within 5 by playing this game.

• Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills, such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 8’s Interview 1 has students counting from 21 to 50 and Interview 2 has students demonstrate fluency of adding within 5.

• “Fundamentals Games” contain a variety of computer/online games that students can play to develop grade level fluency skills. For example Add ‘em up, students demonstrate fluency of adding within 5 (K.OA.5).

• Some lessons provide opportunities for students to practice the procedural fluency of the concept being taught in the “Step Up” section of the student journal.

##### Indicator {{'2c' | indicatorName}}

Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Teachers routinely engage students in engaging single and multi-step application problems during whole group and small group portions of lessons. Examples include:

• Module 3, Lesson 2, Number: Identifying groups that have more or fewer (up to 10), Small Group 1, students solve non-routine application problems by comparing quantities. (K.CC.6) “Organize students into small groups and distribute the resources. Ask each group to place a different number of blocks in each cup. Make sure the number is ten or fewer. Have them write the number of cubes in each cup on the cup itself. Then compare the number of cubes in their cups with those of other groups. Extend the activity by asking individual students to find another student who has a great number of cubes, the same number of cubes, or fewer cubes.”

• Module 6, Lesson 4,  Addition: Writing equations (add to), Small Group 2, students solve non-routine addition problems and write matching equations. (K.OA.1) “Organize students into pairs and distribute the resources. One student rolls the cube and places that number of counters on one side of the card. The other student repeats the action, placing the matching counters on the other side of the card. Together, the students count the total and say an addition equation to match. For example, “Three add two equals five.” The counters are removed from the card, and the activity is repeated several times.”

• Module 11, Lesson 2, Addition/subtraction: Solving word problems (acting out), Whole Class, Step 3 Teaching the Lesson, students use concrete tools to solve routine real-world problems involving addition and subtraction. (K.OA.1 and K.OA.2) “Slide 1: There are 9 leaves. 2 leaves blow away. How many leaves are left? Slide 2: 5 cars are in the parking lot. 4 cars drive away. How many cars are left? Slide 3: Kevin has 2 pennies? He finds 3 more pennies. How many pennies does he now have?”

Materials provide opportunities throughout the grade level, within Thinking Tasks and Word Problems, for students to independently demonstrate multiple routine and non-routine applications of the mathematics. Example include:

• Module 6, More Math, Thinking Task, Question 3, students count and match a quantity with a picture in a non-routine problem. (K.CC.1 and K.OA.3) “Draw dots in each empty box to make the balance picture true. Write an equation to match.” An image shows a balance scale with seven dots on one side and two empty boxes on the other side of the balance.

• Module 9, More Math, Word Problems, students use place value reasoning to identify and describe quantities in number puzzles in a routine problem. (K.CC.1, K.CC.2, and K.NBT.1) “Selena and Jamar have each written a number. Selena’s number is 2 less than Jamars’s number. Jamar’s number can be shown with a group of 10 counters and 2 more counters. What number did Selena write?”

• Module 12, More Math, Thinking Task, Question 3, students use the commutative property to reason about and represent a non-routine problem. (K.OA.1 and K.OA.2) “Draw a picture to show 1 + 4 has the same total as 4 + 1.”

##### Indicator {{'2d' | indicatorName}}

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

The curriculum addresses conceptual understanding, procedural skill and fluency, and application standards, when called for, and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials emphasize fluency, procedures, and algorithms.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• Module 7, Lesson 4, Number: Analyzing teen numbers, students develop understanding of a teen number as a group of ten and some ones. The lesson focuses on conceptual understanding by using ten frames to show a ten and some ones for numbers such as 16, 13, 15, and 14.

• Module 8, Lesson 1, Subtraction: Representing situations (take apart), Student Journal, students practice procedural skill as they are shown a picture and then asked to “Cross out the number shown. Then complete the sentence. b. 6 books are shown, ____ cross out 3 is ____.”

• Module 9, Lesson 4, Number: Solving number puzzles, Student Journal, students use conceptual understanding to solve number puzzles using a number track. For example, “has 1 ten and 6 ones.”

• Module 10, More Math, Word Problems, “Kasem collects three shells at the beach. He already has 4 shells at home. How many shells does Kasem have now?” (K.OA.2)

Examples of students having opportunities to engage in problems that use two or more aspects of rigor include:

• Module 5, Lesson 3, Equality: Identifying two parts that balance a total, combines conceptual understanding and application. Step 3, Teaching the lesson, students balance a pan balance using cubes.

• Module 8, Lesson 3, Subtraction: Representing situations (take from), combines conceptual understanding and application. Step 3, Teaching the lesson, students use the book Ten Happy Hens to solve subtraction problems using cubes to act out the story. For example, “There are ten hens. Two hens run away. There are eight left.”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Indicator {{'2e' | indicatorName}}

Materials support 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.

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).”

##### Indicator {{'2f' | indicatorName}}

Materials support 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.

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.”

##### Indicator {{'2g' | indicatorName}}

Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

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.”

##### Indicator {{'2h' | indicatorName}}

Materials attend to 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.

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.”

##### Indicator {{'2i' | indicatorName}}

Materials support 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 the grade-level content standards, as expected by the mathematical practice standards.

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.”

### Usability

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, do not meet expectations for Criterion 2, Assessment, and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain 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; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

##### Indicator {{'3a' | indicatorName}}

Materials provide 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.

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 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.”

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Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

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.”

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Materials include standards correlation information that explains the role of the standards in the context of the overall series.

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.

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Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provides strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

ORIGO ONE includes 1-minute videos, in English and Spanish that can be shared with stakeholders. They outline big ideas for important math concepts within each grade. Each module also has a corresponding Newsletter, available in English and Spanish, that provides a variety of supports for families, including the core focus for each module, ideas for practice at home, key glossary terms, and helpful videos. Newsletter examples include:

• Module 3, Resources, Preparing for the module, Newsletter, Core Focus, “Number: Identifying quantities that are more or less (up to 10), Number: Comparing numbers (1 to 10) represented as numerals, Measurement: Comparing length, mass, and capacity. Numbers 0–10 - Students build on the sense of numerical relationships developed from real-life experiences. Students use these new skills to recognize numerical displays in everyday life, such as noticing the page numbers in a book, counting days on a calendar, and reading the face of a clock. These experiences help students learn which of two numbers comes later or earlier in a number sequence, and therefore which is larger or smaller. Measurement - Students use comparison language like tall, taller, tallest, or big, bigger, biggest to compare and order three or more things. They learn they can compare lengths just by looking at objects, or by comparing them directly (placing the objects side by side). Students compare the weight of objects by lifting them and identifying which are heavy and which are light. They confirm their observations by using a pan balance to compare the objects. Students learn through experience that sometimes we want to compare the capacity of two or more objects at the same time. They use comparison language like more, less, least, full, half full, empty to compare three containers. Students learn that capacity relates to the amount that something can hold. They compare the capacity of the glasses by comparing the filling of the containers directly.”

• Module 11, Resources, Preparing for the module, Newsletter, Glossary, “Addition stories focus on one or more things joining another one or more things. Subtraction stories focus on one or more things leaving or going away from another one or more things. Students use 2D shape names to describe pictures (e.g. “The cat’s tail is a triangle”).” Module 11, Newsletter, Helpful videos, “View these short one-minute videos to see these ideas in action. go.origo.app/pjagw. go.origo.app/pjdmq.”

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Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

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.”

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Materials provide a comprehensive list of supplies needed to support instructional activities.

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”

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This is not an assessed indicator in Mathematics.

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This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Origo Stepping Stones 2.0 Kindergarten partially meet expectations for Assessment. The materials identify the standards, but do not identify the mathematical practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

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Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

While Check-ups, Quarterly tests, and Interviews consistently and accurately identify grade level content standards within each Module assessment overview, mathematical practices are not identified. Examples from formal assessments include:

• Module 2, Preparing for the module, Module assessment overview, Interview 1, denotes standards addressed. K.CC.1 and K.CC.2, “Steps: Say to the students, Start at 1 and count aloud to 10. If successful, say an incorrect counting sequence from a range within 10, such as 2, 4, 5, 6. Have students identify the mistake made and then say the correct counting sequence. Ask students to start at 10 and count aloud backward to 1. If successful, say an incorrect counting sequence from a range within 10, such as 8, 7, 5, 4. Draw a ✔ beside the learning the student has successfully demonstrated.”

• Module 5, Preparing for the module, Module assessment overview, Check-up 2, denotes standards addressed for each question, K.G.1. “Look at the objects on the shelves. a. Circle in green the object that is just above the (image of) car. b. Circle in red the object that is just under the (image of) bear. c. Circle in blue the objects that are beside the (image of) abc blocks. d. Circle in purple that object that is just before the (image of) baseball.”

• Module 9, Assessment, Quarterly test, Test A, denotes standards for each question. Question 7, K.NBT.1. “Circle 10 shapes. Count the extra shapes and write numbers to match. Ten and ___ ones.”

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Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Origo Stepping Stones 2.0 Kindergarten partially meets expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Summative Assessments, such as Check-ups and Quarterly tests, provide an answer key with aligned standards. Performance Tasks include an answer key and a 2-point rubric, which provides examples of student responses and how they would score on the rubric. A student achievement recording spreadsheet for each module learning target is available that includes: Individual Achievement of Learning Targets for this Module, Whole Class Achievement of Learning Targets for this Module and Individual Achievement of Learning Targets for Modules 1 to 12. While some scoring guidance is included within the materials, there is no guidance for teachers to interpret student performance or suggestions for teachers that could guide follow-up support for students. Examples from the assessment system include:

• Module 3, Assessments, Check-up 2, “Question 1. Color green the pictures that are shorter than your string. Question 2. Color red the pictures that are longer than your string. Answers: Green - eraser and blocks. Red- pencil.” The answer key aligns this question to K.MD.2.

• Module 4, Assessments, Performance task, students place counters on numbers as they say the number name and then match their numeral card. “Ask the student to place counters on a ten-frame card to show a number. They say the number name then identify the numeral card to match. Repeat three times. Place counters on the ten-frame to show 10. Ask the student to say the number name. Look for students who say the number without counting each counter. Repeat by showing 5. Place counters on the ten-frame to show 6. Ask the student to say the number name. Look for students who say the number without counting each counter. Repeat by showing 9, 4, and 8.” The Scoring Rubric and Examples state, “2 Meets requirements. Shows complete understanding. Identified the numeral to match a number. Accurately recognized benchmark numbers of 5 and 10, without counting. Showed evidence of using benchmark of 5 or 10 to identify other numbers, without counting or with minimal counting. 1 Partially meets requirements. Shows some understanding. Identified the numeral to match a number. Accurately recognized a benchmark number of 5 or 10, without counting. Identified other numbers with some accuracy but relied on counting each object. 0 Does not meet requirements. Shows no understanding.”

• Module 6, Assessments, Quarterly test B, Question 7, “Look at the balance picture. Complete the addition sentence to keep the pans balanced. Draw circles to help your thinking. 4 and ___ balances 6.” The answer key shows the answer is 2 and aligned K.OA.3.

• Module 10, Assessments, Performance task, students color beads to make ten. “Question 1. a. Color some beads blue. Color the rest of the beads red. b. Write an equation to show the number of blue beads, the number of red beads, and the total number of beads. ___ + ___ = 10. Question 2. a. Color some beads blue. Color the rest of the beads red. b. Write an equation to match the picture. ___ + ___ = ___.” The Scoring Rubric and Examples state, “2 Meets requirements. Shows complete understanding. Accurately identified an equation to match a picture. Showed more than one way to make ten. 1 Partially meets requirements. Shows some understanding. Accurately identified an equation to match a picture. Attempted to show another way to make ten but made a computational or counting error. 0 Does not meet requirements. Shows no understanding.”

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

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.”

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Origo Stepping Stones 2.0 Grade K do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

There are no accommodations on student assessments.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics, multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity, and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

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.”

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

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.”

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide various approaches to learning tasks over time and variety in how students are expected to demonstrate their learning, but do not provide opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways: Student Journal Steps, Small Group Activities, and within Thinking Tasks, a key component for the program. According to the Program Overview, “ORIGO Thinking Tasks break this mold by presenting students with rigorous, problem- solving opportunities. These problems may become messy and involve multiple entry points as students carve out a solution path. By placing emphasis on the complexity of problem solving, we strive to create a culture for all learners that engages and inspires while developing their confidence and perseverance in the face of challenging problems.” Examples of varied approaches include:

• Module 4, Lesson 3, Number: Representing 0 to 10, Student Journal, pages 79 and 81, students match numeral images to their numeral names. “Cut out these cards. Then paste them on the matching pictures on page 81. Paste the numeral and number name on the matching quantity.”

• Module 9, More Math, Thinking Tasks, Question 2, students use drawing strategies to represent one more. “[Repeat bee image from Q1]. Draw one more bee. Write the new total.”

• Module 11, Lesson 6, 2D shapes: Creating shapes, Small group 1, Making jigsaw puzzles, students make a new shape from joining or splitting 2D shapes. “Each student draws lines to split their square into five parts. They write their name on each part, cut the pieces apart, and place them in the bag. Organize students into pairs. Have them exchange bags and use the pieces to remake the square.”

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide opportunities for teachers to use a variety of grouping strategies.

Suggested grouping strategies are consistently present within lesson notes and include guidance for whole group, small group, pairs, or individual activities. Examples include:

• Module 1, Lesson 1, Number: Creating groups of objects, Small Group 2, Matching quantities, “Organize students into pairs. Have each pair select a bag, place a bear counter on each star sticker, then put those counters inside the bag.”

• Module 6, Lesson 5, Addition: Relating concepts, Step 2 Starting the lesson, “Organize students into four groups and allocate one group to each of the workstations. Ask each student to take one of the answer slips from their workstation.“ Small Group 1, Counting two groups, “Organize students into pairs and distribute the resources.”

• Module 11, Lesson 4, Addition/subtraction: Solving word problems (write equations), Step 1 Preparing the lesson, “Each small group of students will need: 2 strips of paper (approximately 2 in by 8 in) and 1 sheet of paper and pencil. Each student will need: access to resources such as connecting cubes, counters, coins, and other small objects, for example, buttons or stones. Step 3 Teaching the lesson, “Organize students into small groups and distribute the resources. Have the students work together to write a word problem that involves addition and a word problem that involves subtraction. Small group 1, Matching sentences to word problems, “organize students into pairs and distribute the resources. They write an addition or subtraction word problem. You may need to help them write the problems. The word problems are exchanged with another pair, who write an equation to solve it.”

##### Indicator {{'3q' | indicatorName}}

Materials provide 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.

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.”

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the student journal represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Names include multi-cultural references such as Hugo, Fatima, Jacinta, and Anoki and problem settings vary from rural, to urban, and international locations. Each module provides Cross-curricula links or Enrichment activities that provide students with opportunities to explore various demographics, roles, and/or mathematical contexts.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

While there are supports in place to help students who read, write, and/or speak in a language other than English, there is no evidence of intentionally promoting home language and knowledge. Home language is not specifically identified as an asset to engage students in the content nor is it purposefully connected within mathematical contexts.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0, Kindergarten provide some guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Spanish materials are consistently accessible for a variety of stakeholders, including ORIGO ONE Videos, the Student Journals, the glossary, and the Newsletters for families.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide some supports for different reading levels to ensure accessibility for students.

Each module provides support specific to vocabulary development, called ‘Building vocabulary’. Each Building vocabulary activity provides: “Vocabulary term, Write it in your own words, and Show what it means”. While the Lesson overview, Misconceptions, and Steps within each lesson may include suggestions to scaffold vocabulary or concepts to support access to the mathematics, these do not directly address accessibility for different student reading levels. Examples of vocabulary supports include:

• Module 1, Lesson 5, Data: Sorting into two categories, Lesson overview and focus, Misconceptions, “When sorting objects, students may not perceive some attributes. Use mathematical language to highlight the attribute in focus. Ask one student to state the attribute and another to point to it. Another effective strategy is to ask one student to sort a set of objects by an attribute and ask the class to guess the attribute. In the beginning, limit the sorts to only two categories.”

• Module 5, Lesson 4, Equality: Developing the language of equality, Whole group lesson notes Step 3 Teaching the lesson, “Continue to reinforce the meaning of the equals symbol (=): balance, is the same value as, is equal to, and equals. (MP6)”

• Module 11, Mathematics overview, Common errors and misconceptions, Word problems, “The goal of this module is to build students’ skills in making sense of and representing problem situations through interpreting actions, acting out situations, drawing pictures and equations, and matching the situation to the correct operation (addition or subtraction). Therefore, it is important to continue to use concrete objects or pictures to act out the problem contexts. Students need many opportunities to recognize that a problem that describes losing, leaving, or flying away are take from situations, and are represented by the subtraction symbol. Similarly, students should learn to recognize part-part-total situations and use objects with different attributes to represent them. If students are struggling to write appropriate equations, identify which problem type (join, separate, or part-part-total) may be the most problematic and focus class discussions on acting out that particular type.”

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. Examples include:

• While all components of the materials can be accessed digitally, some are only accessible digitally, such as ORIGO Big Books, Interactive Student Journal, Fundamentals Games and Flare Online Tools.

• ORIGO ONE videos describe the big math ideas across grade level lessons in one minute clips. There is a link for each video that makes them easy to share with various stakeholders.

• Every lesson includes an interactive Student Journal, with access to virtual manipulatives and text and draw tools, that allow students to show work virtually. It includes the Step In, Step Up, Step Ahead, and Maintaining Concepts and Skills activities, some of which are auto-scored, others are teacher graded.

• The digital materials do not allow for customizing or editing existing lessons for local use, but teachers can upload assignments or lessons from the platform.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

While teacher implementation guidance is included for Fundamentals games and Flare online tools, there is no platform where teachers and students collaborate with each other. There is an opportunity for teachers to send feedback to students through graded assignments.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within modules and lessons that supports student understanding of the mathematics. Examples include:

• Each lesson follows a common format with the following components: Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, Maintaining Concepts and Skills, Lesson focus, Topic progression, Observations and discussions, Journals and portfolios, and Misconceptions. The layout for each lesson is user-friendly as each component is included in order from top to bottom on the page.

• Each Kindergarten lesson also has two corresponding small group activities.

• The font size, amount and placement of directions, and print within student materials is appropriate.

• The digital format is easy to navigate and engaging. There is ample space in the Student Journal and Assessments for students to capture calculations and write answers.

• The ORIGO ONE videos are engaging and designed to create light bulb moments for key math ideas. They are one minute in length so students can engage without being distracted from the math concept being presented.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Program Overview includes a description of embedded tools, how they should be incorporated, and when they can be accessed to enhance student understanding. Examples include:

• Program Overview, Additional practice tools, “This icon shows when Fundamentals games are required.” Lessons provide this icon to show when and where games are utilized within lesson notes.

• Program Overview, Additional practice tools, “This icon shows when Flare tools are required.” Lessons provide this icon to show when and where these tools are utilized within lesson notes.

• Program Overview, ORIGO Big Books, “This icon shows when ORIGO Big Books are required.” Lessons provide this icon to show when and where these tools are utilized within lesson notes. “Characters and concepts from the Big Books are brought to life in ORIGO Big Book online tools. These easy-to-use tools set the stage for purposeful play and learning.” Lessons provide opportunities for teachers and students to utilize the Big Book and tools. Each Big Book includes lesson notes for the teacher to use within the classroom.

## Report Overview

### Summary of Alignment & Usability for ORIGO Stepping Stones 2.0 | Math

#### Math K-2

The materials reviewed for Origo Stepping Stones 2.0 Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 1 and 2 meet expectations for Usability, Gateway 3, and the materials reviewed for Origo Stepping Stones 2.0 Kindergarten partially meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

###### Alignment
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###### Usability
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