The instructional materials 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.

Opportunities exist for students to work with addition and subtraction addressing conceptual understanding through the use of some visual representations and different strategies. For example:

• In Module 3, Lesson 1, Step 3, Teaching the Lesson, “Each student collects 10 counters, and sits in a large circle. Say, This group shows four. Make a group of counters to show more than four.”
• In Module 7, Lesson 4, Whole Class, Step 3, Teaching the Lesson, “Students read their number, then show the matching number of counters. The counters are used to fill the ten-frame, with the leftover counters placed to the side. Ask questions such as, Which number did you show? How many counters are on the frame? How many counters are beside the frame? How do you read the number that is shown on the ten-frame? Focus on the fact that each teen number is composed of one ten and some leftover ones, and that these values are put together to read the number.”
• In Module 8, Lesson 1, Step 3, Teaching the Lesson, “Provide each student with a handful of connecting cubes. Ask the students to use the cubes to model put together (addition), and take apart (subtraction) stories. After each story, the students will identify the operation they used. Use stories such as the examples below: 4 dogs are in the water. 3 dogs are on the beach. What is the total number of dogs? There are 6 eggs in the carton. 2 eggs are broken. How many eggs are not broken?”
• In Module 9, Lesson 1, 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.

• In Module 8, Lesson 2, Student Journal 8.2, “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 one or two from the dots. The worksheet addresses filling in the equation not conceptual understanding of subtraction.
• In Module 10, Lesson 4, Student Journal 10.4, “Complete the equation. Write the greater number first.” Each problem has two domino cards, each card has the number written and represented with dots, the students fill out the equation with the bigger number first. The worksheet addresses filling in the equation using the bigger number first not the conceptual understanding of addition.
• In Module 11, Lesson 1, Whole Class, Step 3, Teaching the Lesson, “Point to the subtraction heading and ask Who can share a word problem about subtraction? Record the problem on the board and work with the students to pull out any key verbs (e.g. take, cut, chop, run away, lost, 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.

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

The instructional materials have few opportunities for students to engage in non-routine application throughout the grade-level. There is little variety in situational contexts/problem types. Engaging applications include single and multi-step word problems presented in a context in which the mathematics is applied, however, these problems are often routine, and students have few opportunities to engage with non-routine application problems.

Examples of routine application problems include, but are not limited to:

• In Module 5, More Math, Word Problems, addresses standard K.OA.2, students are work together to find the solution to 3 word problems. “Ang has 8 toy cars. He was given 5 toy cars on Monday. He was given the rest of the toy cars on Friday. How many toy cars was Ang given on Friday?”.
• In Module 6, More Math, Word Problems, addresses standard K.OA.2, students work together to find the solution to 3 word problems. “Liam is given 5 coins to put in his wallet. He already has 3 coins. How many coins does Liam have now?”.
• In Module 6, More Math, Enrichment, Activity 1 and addresses standard K.OA.2, students represent two groups that make ten and write the matching equation.
• In Module 7, More Math, Word Problems, addresses standard K.OA.2, “Lisa has 10 blocks. Reece has fewer blocks than Lisa. If they put the blocks together, what number could they show?” (K.OA.2)
• In Module 8, More Math, Word Problems, addresses standard K.OA.2, “The pet shop has 9 puppies for sale. Three of the puppies are sleeping. The rest are playing. How many of the puppies are playing?”.
• In Module 10, Lesson 1, Whole class, addresses standard K.OA.2, the book Scaredy Cats is read to the class and the students use connecting cubes to help the cats in the story solve the problem of “trying to arrange ten boxes into two equal stacks to make the boat balance.”.

There are some instances where students engage with non-routine problems. For example, in Module 9, More Math, Word Problems, addresses standard K.OA. 2, “Selena and Jamar have each written a number. Selena’s number is 2 less than Jamar’s number. Jamar’s number can be shown with a group of 10 counters and 2 more counters. What number did Selena write?”.

The instructional materials 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:

• In Module 7, Lesson 4, students develop understanding of a teen number as a group of ten and some ones. The lesson focuses on the conceptual understanding by using ten frames to show a ten and some ones for numbers such as 13, 14, 15, and 16.
• In Module 8, Lesson 1, Student Journal 8.1, 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 ______.”
• In Module 9, Lesson 4, Student Journal 9.4, students are using conceptual understanding to solve number puzzles using a number track. For example, “has 1 ten and 6 ones.”
• In 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, combines conceptual understanding and application. Step 3, Teaching the Lesson, students balance a pan balance using cubes.
• Module 8, Lesson 3, 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.”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for carefully attending to the full meaning of each practice standard. The materials do not attend to the full meaning of MP4.

For MP4, students are given models to use and have few opportunities to develop their own mathematical models. In addition, students have few opportunities to compare different models in problem contexts, for example:

• In Module 1, Lesson 6, Whole Class, Step 3, Teaching the Lesson, “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. Summarize by counting the number of faces for each answer. Ask, Do we have more students who like dogs, or who do not like dogs? Encourage the students to explain their thinking. (SMP4)”
• In Module 7, Lesson 4, Whole Class, Step 3, Teaching the Lesson, “Organize students into pairs and distribute the resources. Students read their numeral, then show the matching number of counters. The counters are then used to fill the ten-frame, with the leftover counter placed to the side. Move around the room to observe the students. Ask questions such as, Which number did you show? How many counters are on the frame? How many counters are beside the frame? How do you read the number that is shown on the ten-frame? Focus on the fact that each teen number is composed of one ten and some leftover ones, and that these values are put together to read the number. (SMP 4)”
• In Module 8, Lesson 3, Whole Class, Step 3, Teaching the Lesson, “Distribute the cubes. Share a subtraction problem then record it on the board. For example, 6 take away 2 equals _____. Have the students model the problem with cubes to figure out the answer. Move between the students asking questions such as, How many cubes did you start with, in your group? How many cubes did you take away? How many cubes are left? Ask for a volunteer to complete the sentence on the board. Then repeat the activity with other examples. (Note: Include examples that involve subtraction with zero, e.g. 4-4=0, or 4-0=4.) (SMP 4)”
• In Module 9, Lesson 3, Whole Class, Step 2, Starting the Lesson, “Have students sit in a circle in an open area of the classroom. Place the numeral cards facedown on the floor, and tell the students that they are going to work together to build a number track. Invite a volunteer to choose one of the cards, share the number with the class and then place it face up on the floor. Another volunteer comes to the front and selects a card. Ask, Where will you put your number? Is it more or less than (Fatima’s) number? Continue until the number track nears completion, and ask What numbers are left to pick up? How do you know? (SMP 4)”

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials, however, while vocabulary is identified throughout the materials, there is no explicit directions for instruction of the vocabulary for the teacher in the Steps portion of the lesson. Examples include but are not limited to:

• Vocabulary for each module is found under Mathematics, Vocabulary Development. Vocabulary identified in bold print is developed throughout the module. The targeted module vocabulary words can be printed onto cards under the Resources tab. For example, in Module 1, vocabulary includes words such as number, numeral, and how many.
• The vocabulary words do not have definitions.
• Not all the vocabulary words are in the glossary, for example, curved surface.
• Each module contains a parent newsletter. The newsletter highlights key vocabulary and provides the definition for parents in the Glossary section of the newsletter.
• In Module 1, Lesson 3, the term numeral is present in the Student Journal, but the definition is not introduced in any lesson in Module 1.