2022

Open Up Resources K-5 Math

Publisher
Open Up Resources
Subject
Math
Grades
K-5
Report Release
07/05/2023
Review Tool Version
v1.5
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.

Alignment (Gateway 1 & 2)
Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
Meets Expectations
Our Review Process

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Report for Kindergarten

Alignment Summary

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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 meet expectations for practice-content connections.

Kindergarten
Alignment (Gateway 1 & 2)
Meets Expectations
Gateway 3

Usability

25/27
0
17
24
27
Usability (Gateway 3)
Meets Expectations
Overview of Gateway 1

Focus & Coherence

The materials reviewed for Open Up Resources K-5 Math 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.

Criterion 1.1: Focus

06/06

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 Open Up Resources K-5 Math 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
02/02

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

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The curriculum is divided into eight units, and each unit contains an End-of-Unit Assessment. While Unit 1 includes an End-of-Unit Assessment as an Interview, all other units include a written assessment for individual student completion. Additionally, the Unit 8 Assessment is an End-of- Course Assessment and includes problems from across the grade. Examples from End-of-Unit Assessments include: 

  • Unit 2, Numbers 1-10, End-of-Unit Assessment, Problem 4, “a. Circle the number that is more. 4, 6. b. Circle the number that is less. 8, 5.” (K.CC.7)

  • Unit 5, Composing and Decomposing Numbers to 10, End-of-Unit Assessment, Problem 3, “Mai has a train of 7 connecting cubes. She snaps the train into two pieces. Show 1 way to snap the cubes. Show a different way to snap the cubes.” A picture of seven snap cubes is shown. (K.OA.3)

  • Unit 6, Numbers 0 - 20, End-of-Unit Assessment, Problem 1, ”Draw 17 dots. Use the 10-frame if it helps you.” An image of a ten frame is provided. (K.NBT.1)

  • Unit 7, Solid Shapes All Around Us, End-of-Unit Assessment, Problem 3, “Consider the ball and box your teacher has displayed. How are the shapes the same? How are they different? Show your thinking with drawings or words.” (K.G.4) 

  • Unit 8, Putting it All Together, End-of-Course Assessment and Resources, Problem 4, “a. How many dots are there? b. How many triangles are there? c. How many counters are there?” There is a picture of 11 dots; 14 triangles arranged in a circle, and 17 counters on ten frames. (K.CC.5)

Indicator 1B
04/04

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

The instructional materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The instructional materials provide extensive work in Kindergarten as students engage with all CCSSM standards within a consistent daily lesson structure. Per the Kindergarten Course Guide, “A typical lesson has four phases: a Warm-up, one or more instructional activities, the lesson synthesis, a Cool-down. In kindergarten, most lessons do not include Cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson. Since activities are shorter, each lesson includes 15–25 minutes of time for centers.” Examples of extensive work include:

  • Unit 1, Math in Our World, Lesson 12; Unit 3, Flat Shapes all Around Us, Lesson 4; Unit 4, Understanding Addition and Subtraction, Lesson 12; Unit 5, Composing and Decomposing Numbers to 10 Lesson 9; Unit 6, Numbers 0-20, Lesson 11; and Unit 7, Solid Shapes all Around Us, Lesson 9 engage students in extensive work with K.CC.1 (Count to 100 by ones and by tens). Unit 1, Section D, Lesson 12, How Many Are There (Part 1), Activity 2, Student Work Time, students work on the verbal count sequence to 10, “‘Let’s count to 10 all together.’ Count to 10 all together. ‘Let’s count to 10 and clap our hands when we say each number.’ Count to 10 and clap all together. ‘Let’s count to 10 and touch the table when we say each number.’ Count to 10 and touch the table all together. ‘Let’s count to 10 and put up 1 finger when we say each number.’ Count to 10 and put up each finger all together.” Throughout Kindergarten, students build to count to 100. Unit 3, Section A, Lesson 4, Describe, Compare and Sort Shapes, Warm-up: Choral Count: Extent the Count Sequence, Student Work Time, students continue the counting up to 30, “Count to 30 together. Record as students count. Count to 30 1–2 times. Point to the numbers as students count.” Unit 4, Section B, Lesson 12, Compare Addition and Subtraction Story Problems, students and the teacher count to 40 together. Warm-up: Choral Count: Count to 40, Student Work Time, “Count to 40 together. Record as students count. Count to 40 1–2 times. Point to the numbers as students count.” As students progress to Unit 5, they count up to 70, count to 90 in Unit 6, and count to 100 in Unit 7. Unit 5, Section B, Lesson 9, All of the Story Problems, Warm-up: Choral Count: Count to 70 and Count On, Launch, “Let’s count to 70. Count to 70 1–2 times as a class.” Unit 6, Section C, Lesson 11, Count Images (Part 1), Warm-up: Choral Count: Count to 90 and Count On, Launch, “Let’s count to 90. Count to 90 1–2 times as a class.” Unit 7, Section B, Lesson 9, Compare Capacity, Warm-up: Choral Count: Count by 10, Launch,  “Display numbers from 1 to 100. ‘Let’s count to 100.’ Point to the numbers as students count to 100.”

  • Unit 2, Numbers 1-10, Section A, Lesson 5, and Section B, Lessons 8 and 10 engage students in extensive work with K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Include groups with up to ten objects). Section  Lesson 5, Make Groups of More, Fewer, or the Same, Warm-up: How Many Do You See: Fingers on Two Hands, Student Work Time, students recognize quantities represented on fingers, without having to count, ‘Discuss your thinking with your partner.’, 30 seconds: partner discussion, Share responses., ‘Use your fingers to show how many there are.’, Repeat with 6 fingers and 7 fingers.How many do you see? How do you see them?” Lesson 8, Compare Matching Images, Activity 1, Launch, students compare groups of images that are lined up and decide which group has more or fewer items. Directions state, “Groups of 2, Display the image from the student book. ‘What do you notice? What do you wonder? (There are people and apples. There are 6 people. How many apples are there? Are there enough apples for each person to get one?) Have you ever helped to set the table for a meal or pass out a snack? What did you do?’” Lesson 10, Find More or Fewer, Cool-down: Unit 2, Section B Checkpoint, Student Responses, students use the structure of 5 (in 5-frames or fingers) to count on from 5 to tell how many, “Use ‘more,’ ‘fewer,’ and ‘the same number’ to describe comparisons.”

  • Unit 5, Composing and Decomposing Numbers to 10, Section B, Lessons 7 and 8, and Unit 8, Putting It All Together, Section A, Lesson 3 engage students in the extensive work with 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). Unit 5, Lesson 7, Solve Both Addends Unknown Story Problems, Activity 1, Student Work Time, students notice multiple ways to solve a Put Together/Take Apart, Both Addends Unknown story problem. Student Facing, “Jada made 6 paletas with her brother. They made two flavors, lime and coconut. How many of the paletas were lime? Then how many of the paletas were coconut?” Unit 5, Lesson 8, More Than One Way, Activity 2, Student Work Time, students solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. Student Facing, “Andre and his older brother have 8 dates.They stuff some of the dates with cheese. They stuff the rest of the dates with almonds. How many of the dates did they stuff with cheese? Then how many of the dates did they stuff with almonds? Expression:” In Unit 8, Lesson 3, Count to Add and Subtract, Activity 2, Student Work Time, students complete and solve numberless Add To, Result Unknown and Take From, Result Unknown story problems. Student Facing, “a. ___ students were singing. Then 1 more student came to sing with them. How many students are singing now? Show your thinking using objects, drawings, numbers, or words. b. ___ students were singing. Then 1 student stopped singing and went home. How many students are singing now? Show your thinking using objects, drawings, numbers, or words.”

The instructional materials provide opportunities for all students to engage with the full intent of Kindergarten standards through a consistent lesson structure. According to the Grade 1 Course Guide, “The first event in every lesson is a Warm-up. Every Warm-up is an Activity Narrative. The Warm-up invites all students to engage in the mathematics of the lesson… After the Warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class… After the activities for the day, students should take time to synthesize what they have learned. This portion of class should take 5-10 minutes before students start working on the Cool-down.” “In Kindergarten, most lessons do not include Cool-downs like those common in other grades. During these lessons, checkpoints are used to formatively assess understanding. Since activities are shorter, each lesson includes 15-25 minutes of time for centers.” Examples of meeting the full intent include:

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 8, and Unit 7, Solid Shapes All Around Us, Section B, Lesson 7 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 Unit 3, Lesson 8, Draw Shapes, Activity 1, Launch and Student Work Time, students draw lines to connect dots and practice drawing shapes. In Launch,  “‘These dots will help us draw shapes. I need to connect the red dots using straight lines.’ Demonstrate drawing a straight line between 2 of the red dots. ‘Where should I draw the next line?’ Repeat until the rectangle is drawn. ‘What shape did I draw?’ (A rectangle.)” In Student Work Time, “‘Draw straight lines to connect the dots. When you’re finished, color in the shape and tell your partner about the shape you drew.’” In Unit 7, Lesson 7, Flat and Solid Shapes, Activity 1 Launch and Student Work Time, students build and compare flat and solid shapes using clay. In Launch, “Groups of 2, Give each student a piece of clay. ‘Use your clay to make a shape that you know.’ 1 minute: independent work time. ‘Share your shape with your partner. How are they the same? How are they different?’ (The shapes are different. I made a circle and my partner made a triangle.)” In Student Work Time, “Display a cylinder. ‘Make this shape with your clay.’ 2 minutes: independent work time, Display a cone. ‘Make this shape with your clay.’ 2 minutes: independent work time, ‘Describe the shape that you made to your partner. What does it look like?’ (It looks like an ice cream cone. It’s tall. It has a point on the bottom).”

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 14, and Unit 5, Composing and Decomposing Numbers to 10,Section A, Lesson 4 engage students with the full intent of K.CC.2 (Count forward beginning from a given number within the known sequence). In Unit 4, Lesson 14, Expressions and Story Problems, Warm-up: Choral Count: Count On, Launch and Student Work Time, students count on from a given number. In Launch,  “‘Let’s count to 10.’ Count to 10.” In Student Work Time, “‘Now start at the number 3 and count to 10.’ Count on from 3 to 10. Repeat 3–4 times starting with other numbers within 10.” In Unit 5, Lesson 4, Find All the Ways, Warm-up: Choral Count: Count On, Launch and Student Work Time, students count on when given a number. In Launch, “‘Let’s count to 60.’ Count to 60.” In Student Work Time, “‘Now, start at the number 9 and count to 20.’ Count on from 9 to 20. Repeat 3–4 times starting with other numbers within 10.”

  • Unit 3, Flat Shapes All Around Us, Section A, Lessons 6 and 7, and Unit 7, Solid Shapes All Around Us, Section B, Lessons 8 and 9 engage students with the full intent of 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 Unit 3, Lesson 6, Rectangles and Squares, Activity 2, Student Work Time, students use the language longer and shorter to compare the lengths of rectangles, “Circle the rectangle that is longer. Tell your partner how you know which rectangle is longer.’ 1 minute: partner work time, Repeat the steps with the second problem. ‘Circle the rectangle that is shorter. Tell your partner how you know which rectangle is shorter.’” In Unit 3, Lesson 7, Build With Straws, Activity 1, Launch, students compare two objects to determine which object is longer or shorter, “Groups of 2, Give each group of students a bag of straws. ‘Today we will use these straws to build shapes. First let’s compare the lengths of the straws and figure out which is longer. Work with your partner to compare the length of the straws to the line on your paper. If the straw is shorter than the line, put it on the left side of the page. If the straw is longer than the line, put it on the right side of the page. Tell your partner about each straw using ‘longer than’ and ‘shorter than’.’” In Unit 7, Lesson 8, Compare Weight, Activity 1, Student Work Time, students work in pairs to describe and compare the weight of objects, “Display bags 1 and 2. ‘Here are 2 bags, but we can’t see what is inside. Which bag is heavier?’ 30 seconds: quick think time, Share responses. ‘How could we figure out which bag is heavier?’ (We could pick them up and feel which one is heavier.) 30 seconds: quiet think time, 1 minute: partner discussion, Share responses. Pass the bags around so that each student can hold both bags to compare the  weights.” In Unit 7, Lesson 9, Compare Capacity, Activity 1, Student Work Time, students think about and compare the capacity of containers, “Display 2 cups and give each student a sticky note. ‘Which of these cups do you think would hold more lemonade? Put your sticky note by the cup that you think would hold more lemonade.’ 3 minutes: Independent work time. ‘People had different answers about which cup would hold more lemonade. What can we do to figure out which cup can hold more lemonade?’ 1 minute: quick think time, 1 minute: partner discussion, Share and record responses. Demonstrate filling one of the cups with water and then slowly pour that water into the other cup. ‘I filled up the red cup and poured the same water into the blue cup, but the blue cup overflowed. Which cup do you think can hold more lemonade?’ 30 seconds: quick think time, 1 minute: partner discussion, Share responses. ‘The red cup can hold more lemonade than the blue cup.’”

Criterion 1.2: Coherence

08/08

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

The materials reviewed for Open Up Resources K-5 Math 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
02/02

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

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65% of instructional time to the major clusters of the grade: 

  • The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 8, approximately 75%.

  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 123 out of 145, approximately 85%. The total number of lessons devoted to major work of the grade include: 115 lessons plus 8 assessments for a total of 123 lessons.

  • The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 131 out of 138, approximately 95%.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 85% of the instructional materials focus on major work of the grade.

Indicator 1D
02/02

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

The materials reviewed for Open Up Resources K–5 Math Grade 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 listed for teachers on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed on a document titled “Scope and Sequence”. Examples of connections include:

  • Unit 1, Math in Our World, Section A, Lesson 4, Activity 1, Student Work Time, 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.4 (Understand the relationship between numbers and quantities; connect counting to cardinality). Students are introduced to geoblocks and explore, sort, and count the geoblocks. The activity states, “10 minutes: partner work time, ‘Share with your partner one thing you did or made with the blocks.’ 2 minutes: partner discussion. Sample responses: Students use geoblocks to build towers, buildings, and other things. Students sort the geoblocks by shape. Students use comparison language like more, bigger, or smaller when discussing their creations. Students use shape names to describe the blocks.”

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 5, Activity 1, Student Work Time, connects the supporting work of K.G.5 (Model shapes in the world by building shapes from components…) 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.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 identify examples of circles and triangles. The activity states, “‘4 minutes: independent work time, Choose 1 triangle that you colored in. Tell your partner 1 thing that you know about that shape.’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘Write a number to show how many triangles you colored. Write a number to show how many circles you colored.’ 1 minute: independent work time. ‘Did you color more triangles or more circles? How do you know?’ 30 seconds: quiet think time, 30 seconds: partner discussion.” 

  • Unit 8, Putting It All Together, Section A, Lesson 1, Activity 1, Launch and Student Work Time, connects 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.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 sort objects into categories and represent and compare the number of objects in each category. The Launch states, “Give each student a bag of beads. ‘Sort your beads into two groups.’ 1 minute: independent work time.” Student Work Time states, “How many beads are in each group? Show your thinking using drawings, numbers, or words. 3 minutes: independent work time. ‘Compare the number of beads in each group. Which has more beads? Which has fewer beads? Circle the group that has fewer beads.’ 1 minute: independent work time. ‘Tell your partner which group has fewer beads using this sentence: There are fewer ___ than ___.’” Student Facing states, “How many beads are in each group? Show your thinking using drawings, numbers, or words. Circle the group that has fewer beads.”

Indicator 1E
02/02

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 instructional materials for Open Up Resources K–5 Math 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. These connections can be listed for teachers in one or more of the four phases of a typical lesson:  instructional activities, lesson synthesis, or Cool-down. Examples of connections include:

  • Unit 4, Understanding Addition and Subtraction, Section A, Lesson 4,  connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.OA.A (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from). Students count two groups of numbers to find a total. The activity states, “‘How many students would rather be a bird? How do you know?’ 30 seconds: quiet think time, 30 seconds: partner discussion, Share responses. Demonstrate or invite students to demonstrate counting. ‘How many students would rather be a fish? How do you know?’ 30 seconds: quiet think time, 30 seconds: partner discussion, Share responses. Demonstrate or invite students to demonstrate counting.”

  • Unit 6, Numbers 0–20, Section B, Lesson 5, Activity 1, Launch and Student Work Time, connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.NBT.A (Work with numbers 11-19 to gain foundations for place value). Students count to answer “how many” questions about images displayed on fingers. The Launch states, “Groups of 2. Display the student page. ‘Let’s practice reading numbers.’ Point to and read each written number. Invite students to chorally repeat each written number 1–2 times. ‘Now, figure out how many fingers there are. Draw a line from the fingers to the number that shows how many there are.’” In Student Work Time, Student Facing shows questions 1-5 with a pair of hands with fingers corresponding to numbers 13 to 19. 

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 11, Activity 2, Launch and Student Work Time, connects the supporting work of K.G.B (Analyze, compare, create, and compose shapes) to the supporting work of K.MD.B (Classify objects and count the number of objects In each category). Students determine defining characteristics for sorting solid shapes into groups. The Launch states, “Groups of 2, Give each group of students a collection of at least 6-8 solid shapes. ‘Work with your partner to sort the shapes into two groups. Write a number to show how many shapes are in each group.’ 1 minute: quiet think time, 3 minutes: partner work time” Student Work Time states, “‘Think of a name for each group of shapes that describes why you put those shapes together. You can write the name above each group.’ 1 minute: independent work time, ‘Pair up with another group. Explain to them which shapes you put together and why.’ 4 minutes: small-group work time, ‘Sort your shapes in a different way.’ 1 minute: quiet think time, 3 minutes: partner work time, Monitor for students who sort the shapes based on attributes, as described in the activity narrative.”

  • Unit 8, Putting It All Together, Section A, Lesson 2, Activity 1, Launch and Student Work Time, connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects). Students count collections of up to 20 objects and represent their count with drawings and numbers. The Launch states, “Give each student a collection of objects and access to 10-frames.” In Student Work Time, Student Facing states, “How many objects are in your collection? Show your thinking using drawings, numbers, or words.”

Indicator 1F
02/02

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 instructional materials reviewed for Open Up Resources K–5 Math 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. 

Prior and Future connections are identified within materials in the Course Guide, Scope and Sequence Section, within the Dependency Diagrams which are shown in Unit Dependency Diagram and Section Dependency Diagram. An arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section. While future connections are all embedded within the Scope and Sequence, descriptions of prior connections are also found within the Preparation tab for specific lessons and within the notes for specific parts of lessons. 

Examples of connections to future grades include:

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 3, Preparation connects 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 and other attributes) to work defining attributes of shapes in Grade 1. Lesson Narrative states, “Students look at pictures of objects in the environment as well as common flat shapes. They describe and compare shapes. This lesson is an opportunity to see what attributes of shapes students notice and attend to. Students notice and describe both defining (number of sides and corners, flat or straight sides) and non-defining (size, color, orientation) attributes of shapes. This allows teachers to see the vocabulary students use to describe shapes (MP6). In grade 1 students will distinguish between these defining and non-defining attributes of shapes.”

  • Unit 6, Numbers 0-20, Section B, Lesson 7, Preparation connects 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 work with relating counting to addition and subtraction in 1.OA.5. Lesson Narrative states, “Students write a number to represent a quantity greater than 10 for the first time. Students use full 10-frames and some more to identify and create numbers 11–19. Students may count all of the dots or counters to determine the teen number, or they may count on from 10. Counting on to determine the total is not an expectation in kindergarten.”

  • Grade K Course Guide , Scope and sequence, Unit 7, Solid Shapes All Around Us, Unit Learning Goals connect K.G.5 (Model shapes in the world by building shapes from components and drawing shapes) and K.G.6 (Compose simple shapes to form larger shapes) to the work of creating composite shapes in Grade 1. Narrative states, “Students use their own language to describe attributes of solid shapes as they identify, sort, compare, and build them, while also learning the names for cubes, cones, spheres, and cylinders. The work here prepares students to identify defining attributes of shapes and to use flat and solid shapes to create composite shapes in grade 1.”

Examples of connections to prior knowledge include:

  • Grade K Course Guide, Scope and Sequence, Unit 1, Math in Our World, Unit Learning Goals connect K.CC.A (Know number names and the count sequence), K.CC.B (Count to tell the number of objects), and K.G.A (Identify and describe shapes) to previous work with counting. Narrative states, “Students enter kindergarten with a range of counting experiences, concepts, and skills. This unit is designed to be accessible to all learners regardless of their prior experience. To that end, no counting is required for students to engage in the activities in the first three sections, though students may choose to count. Students also have opportunities to work with math tools and topics related to geometry, measurement, and data through a variety of centers.”

  • Unit 2, Numbers 1–10, Section A, Lesson 4, Preparation connects K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group) to previous work comparing quantities in Kindergarten. Lesson Narrative states, “In a previous lesson, students identified groups that had more or fewer objects than a given group. The number of objects in the groups made it easy to compare the groups visually. For example, students could tell by looking that a group of two cubes was fewer than a group of nine cubes. In this lesson, students compare groups of objects that are closer in quantity. Students also practice using the words fewer, more, and the same in sentences that compare quantities (MP6). For example, students hear and repeat statements such as, “There are fewer red counters than yellow counters.”

  • Unit 5, Composing and Decomposing Numbers to 10, Section A, Lesson 2, Preparation connects K.OA.3 (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from) to work composing shapes in Kindergarten Unit 3. Lesson Narrative states, “In a previous unit, students made designs with pattern blocks and counted how many of each pattern block they used. In this lesson, students make and share a design with the same total number of pattern blocks but different numbers of individual pattern blocks.”

Indicator 1G
Read

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 Open Up Resources K–5 Math Kindergarten foster coherence between grades and can be completed within a regular school year with little to no modification. 

According to the Kindergarten Course Guide, About These Materials, “Each grade level contains 8 or 9 units. Units contain between 8 and 28 lesson plans. Each unit, depending on the grade level, has pre-unit practice problems in the first section, checkpoints or checklists after each section, and an end-of-unit assessment. In addition to lessons and assessments, units have aligned center activities to support the unit content and ongoing procedural fluency. The time estimates in these materials refer to instructional time. Each lesson plan is designed to fit within a class period that is at least 60 minutes long. Some units contain optional lessons, and some lessons contain optional activities that provide additional student practice for teachers to use at their discretion.”

According to the Kindergarten Course Guide, Scope and Sequence, Pacing Guide, “Number of days includes 2 days for assessments per unit. Upper bound of the range includes optional lessons.” For example: 

  • 138 days (lower range) to 153 days (upper range).

Per the Kindergarten Course Guide, A Typical Lesson, “A typical lesson has four phases: 1. a Warm-up 2. one or more instructional activities 3. the lesson synthesis 4. a Cool-down. In kindergarten, most lessons do not include Cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson. Since activities are shorter, each lesson includes 15–25 minutes of time for centers.” In Kindergarten, each lesson is composed of the following:

  • 5-10 minutes Warm-up

  • 10-25 minutes (each) for one to three Instructional Activities

  • 5-10 minutes Lesson Synthesis

  • 0-5 minutes Cool-down

  • 15-25 minutes Centers

Overview of Gateway 2

Rigor & the Mathematical Practices

The materials reviewed for Open Up Resources K-5 Math 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).

Criterion 2.1: Rigor and Balance

08/08

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 Open Up Resources K-5 Math Kindergarten meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.

Indicator 2A
02/02

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

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials develop conceptual understanding throughout the grade level. According to the Kindergarten Course Guide, Design Principles, conceptual understanding is a part of the design of the materials. Balancing Rigor states, “There are three aspects of rigor essential to mathematics: conceptual understanding, procedural fluency, and the ability to apply these concepts and skills to mathematical problems with and without real-world contexts. These aspects are developed together and are therefore interconnected in the materials in ways that support student understanding. Opportunities to connect new representations and language to prior learning support students in building conceptual understanding. Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Additionally, Purposeful Representations states, “Across lessons and units, students are systematically introduced to representations and encouraged to use representations that make sense to them. As their learning progresses, students are given opportunities to make connections between different representations and the concepts and procedures they represent.” Examples include:

  • Unit 2, Numbers 1-10, Section B, Lesson 9, Warm-up, Student Work Time, students develop conceptual understanding as they identify groups that have more, less, or the same number as a given group of images. Activity states, “‘How can we figure out how many students like apples better?’ 30 seconds: quiet think time. 30 seconds: partner discussion. Share responses. Demonstrate or invite students to demonstrate counting. ‘How many students like apples better? How can we figure out how many students like bananas better?’ 30 seconds: quiet think time. 30 seconds: partner discussion. Share responses. Demonstrate or invite students to demonstrate counting. ‘How many students like bananas better?’” (K.CC.B)

  • Unit 3, Flat Shapes Around Us, Section A, Lesson 1, Activity 2, Launch, students develop conceptual understanding as they use informal language to describe shapes and share what they know about different shapes. An image of a Backgammon game is shown. Launch states, “Groups of 2, ‘What games do you play with your family?’ 30 seconds: quiet think time. 30 seconds: partner discussion. Share responses. ‘Backgammon is a popular game in many different countries, such as Iraq, Lebanon, Egypt, and Syria. Lots of people play Backgammon in our country, too. Have you ever played this game or a game like this? Tell your partner about a shape you see in the backgammon game. Take turns describing the shapes you see in the picture with your partner.’ 30 seconds: quiet think time.” (K.G.4)

  • Unit 8, Putting It All Together, Section A, Lesson 2, Warm-up, Launch and Activity Synthesis, students develop conceptual understanding of 10 as they subitize or use grouping strategies to describe the images they see. Dot images are provided, and Student Facing states, “How many do you see? How do you see them?” Activity Synthesis states, “‘How is the 10-frame helpful when figuring out how many dots there are?”’ (I know that there are 10 dots on the 10-frame and 10 and 5 is 15. I start counting at 10 and count the rest of the dots.)” (K.NBT.1)

According to the Grade Kindergarten Course Guide Guide, materials were designed to include opportunities for students to independently demonstrate conceptual understanding, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:

  • Unit 1, Math In Our World, Section D, Lesson 12, Activity 1, Student Work Time, students demonstrate conceptual understanding as they count collections of objects and say one number for each object. Activity states, “Give each student a bag of objects. Give students access to 5-frames and a counting mat. ‘Figure out how many objects are in your collection. Use the tools if they are helpful.’ 2 minutes: independent work time. ‘Switch collections with a partner. Figure out how many objects are in your new collection.’ 2 minutes: independent work time. Monitor for students who say one number for each object.” (K.CC.4a)

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 16, Cool-down, students demonstrate conceptual understanding as they find the value of and represent an expression. Student Facing states, “Find the value of the expression 1+41+4. Show your thinking using objects, drawings, numbers, or words.” (K.OA.1)

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 14, Activity 2, Launch and Activity Synthesis, students demonstrate conceptual understanding as they build and describe figures composed of solid shapes. Launch states, “Groups of 2. Give students access to solid shapes and geoblocks. ‘Choose who will build first. The first partner will use the solid shapes to build something. Watch as your partner builds.’ 2 minutes: independent work time. ‘Use the solid shapes to build the same thing as your partner.’ 1 minute: independent work time. Repeat the steps above, with students switching roles.” Activity Synthesis states, “Invite students to share how they changed their building using positional words and names of shapes.” (K.G.1, K.G.6)

  • Unit 8, Putting It All Together, Lesson 21, Activity 2, Launch and Student Work Time, students demonstrate conceptual understanding as they compose and decompose numbers 11–19. Launch states, “Groups of 2, Give students access to connecting cubes or two-color counters, 10-frames, and bead tools. Display the student book. ‘Kiran wrote equations to show the total number of students and how many students sat at the table and how many sat on the rug, but he didn’t finish the equations. Finish filling in each equation. You can use connecting cubes or two-color counters if they are helpful.’” In Student Work Time, Student Facing states, “17=10+17=10+___. 19=19=___+9+9. 10+10+___=14=14. ___+2=12+2=12. 11=11=___+1+1. 15=10+15=10+___.” (K.NBT.1)

Indicator 2B
02/02

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

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 

According to the Kindergarten Course Guide, Design Principles, Balancing Rigor, “Warm-ups, practice problems, centers, and other built-in routines help students develop procedural fluency, which develops over time.” Examples include: 

  • Unit 2, Numbers 1-10, Section A, Lesson 6, Warm-up, Launch and Student Work Time, students develop procedural skill and fluency as they recognize quantities represented with fingers. Launch states, “Groups of 2. ‘How many do you see? How do you see them?’ Display 4 fingers.” Student Work Time states, “‘Discuss your thinking with your partner.’ 30 seconds: partner discussion. Share responses. Repeat with 8 fingers and 10 fingers.” An image of two hands is shown with one hand showing four fingers and one hand balled in a fist. (K.CC.6)

  • Unit 6, Numbers 0- 20, Section A, Lesson 3, Activity 3, students develop fluency with addition and subtraction within 5 as they find the number that makes 5 when added to a given number. Launch states, “Groups of 2. Give each student a set of cards, a recording sheet, and access to two-color counters, 5-frames, and 10-frames. ‘We’re going to learn a center called Find the Pair. Put your cards in a pile in the middle of the table. You and your partner will both draw 5 cards. Keep your cards hidden from your partner.’ Demonstrate drawing 5 cards. Invite a student to act as the partner and draw 5 cards. ‘I am going to look at my cards. I need to choose 1 card and figure out which number I need to make 5 with the card.’ Display a card with the number 4. ‘My card says 4. What card do I need to go with it to make 5? (1) I need a 1 card. I’m going to ask my partner if they have a 1 card. If my partner has a 1 card, they will give it to me. I will put the 4 card and 1 card down as a match and write an expression. If I have a 4 card and a 1 card, what expression should I write?’ (4+14+1 or 1+41+4).” (K.OA.5)

  • Unit 8, Putting It All Together, Section A, Lesson 1, Warm-up, Launch, students develop procedural skills and fluency as they practice counting and finding patterns in the count. Launch states, “‘Count by 1, starting at 57.’ Record as students count. Stop counting and recording at 77.” (K.CC.2, K.CC.4c)

According to the Kindergarten Course Guide, materials were designed to include opportunities for students to independently demonstrate procedural skill and fluency, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.” Examples include:

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 17, Activity 1, Launch, students demonstrate fluency as they find the value of addition expressions with +0 and +1. Launch states, “Groups of 2, Display a tower of 3 connecting blocks:, ‘Mai has a tower with 3 cubes. Mai wants to add 0 cubes to the tower. What should Mai do?’ (Nothing. When you add 0, you don’t add anything.) 30 seconds: quiet think time. Share responses. Give each group of students a copy of the blackline master and a connecting cube. Give students access to connecting cubes and two-color counters. ‘Take turns with your partner. Roll the cube to figure out if you need to add 0 or 1. Fill in the expression. Find the value of the expression and write the number on the line. You can use objects or drawings if they are helpful.’” (K.OA.5)

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 6, Activity 3, Launch, students demonstrate procedural skill and fluency as they use addition and subtraction within 5. Launch states, “Groups of 2. Give each group of students a cup, 5 two-color counters, and 2 copies of the blackline master. ‘We are going to learn a new way to do the Shake and Spill center. It is called Shake and Spill, Cover. Let’s play a round together. I am going to put 3 counters in the cup and shake them up. Before I spill the counters, you will close your eyes so I can cover all the yellow counters with the cup. Then you will open your eyes and figure out how many counters are under the cup.’ Put 3 counters in a cup and shake them up. ‘Close your eyes.’ Spill the counters and cover 1 yellow counter. Leave 2 red counters on the table. ‘Open your eyes. Look at the counters on the table. How many counters are under the cup? How do you know?’ (One because there are 2 on the table and 2 and 1 more makes 3.) 30 seconds: partner discussion. Share responses. Pick up the cup showing the 1 counter that was covered. ‘Now we fill in the recording sheet. We had 3 counters total. Then we fill in the expression that matches the parts we broke 3 into. There were 2 counters outside the cup and 1 counter in the cup.’ Demonstrate completing the recording sheet. ‘Take turns with your partner spilling and covering the yellow counters. On each turn you can decide to use 3, 4, or 5 counters. Make sure you and your partner agree on how many total counters you are using before you shake, spill, and cover.’”(K.OA.5)

  • Unit 8, Putting It All Together, Section C, Lesson 12, Cool-down: Unit 8, Section C Checkpoint, students demonstrate their fluency as they use strategies to find sums and differences. Student Response states, “Students count all to find the sum. Students use their knowledge of the count sequence to find certain sums. Students know certain sums. Students represent all, then cross off or remove to find the difference. Students use their knowledge of the count sequence to find certain differences. Students know certain differences.” (K.OA.5)

Indicator 2C
02/02

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

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of mathematics. 

According to the Grade K Course Guide, Design Principles, Balancing Rigor, “Access to new mathematics and problems prompts students to apply their conceptual understanding and procedural fluency to novel situations.” Multiple routine and non-routine applications of the mathematics are included throughout the grade level, and these single- and multi-step application problems are included within Activities or Cool-downs. 

Students have the opportunity to engage with applications of math both with teacher support and independently. According to the Kindergarten Course Guide, materials were designed to include opportunities for students to independently demonstrate application of grade-level mathematics, when appropriate. Design Principles, Coherent Progress states, “Each activity starts with a launch that gives all students access to the task. This is followed by independent work time that allows them to grapple with problems individually before working in small groups. The activity ends with a synthesis to ensure students have an opportunity to consolidate their learning by making connections between their work and the mathematical goals.” A Typical Lesson states, “The Cool-down task is to be given to students at the end of the lesson. Students are meant to work on the Cool-down for about 5 minutes independently and turn it in. The Cool-down serves as a brief formative assessment to determine whether students understood the lesson. Students’ responses to the Cool-down can be used to make adjustments to further instruction.”

Examples of routine applications of the math include:

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 4, Activity 2, Launch and Student Work Time, students consider and describe attributes of shapes and sort shapes into categories. Launch states, “Groups of 2, Give each group a set of shape cards. ‘In the last activity we sorted our objects into groups. We put the objects together based on something that was the same about them.’ Display a couple of shape cards. ‘You and your partner will sort the shape cards into two groups. You can decide how to sort the shapes. Put each shape in one of your groups. Talk to your partner about why each shape fits in the group.’” Student Work Time states, “5 minutes: partner work time, Monitor for groups that sort the shapes in different ways. ‘Write a number to show how many shapes are in your groups.’ 2 minutes: independent work time. ‘Which group has more shapes? How do you know?’” (K.G.4, K.MD.3)

  • Unit 4, Understanding Addition and Subtraction, Section B, Lesson 11, Activity 1, Student Work Time, students draw a picture to represent and solve a story problem. In Student Work Time, Student Facing states, “There were 7 kids playing soccer in the park. 3 of the kids left to go play on the swings. How many kids are playing soccer in the park now?” There is an image of four kids playing soccer. Student Work Time states, “3 minutes: independent work time, Monitor for students who draw pictures with details to represent the story. Monitor for students who use symbols such as circles.” (K.OA.2)

  • Unit 8, Putting It All Together, Section D, Lesson 18, Cool-down, students solve a real-world problem by composing and decomposing within 10. Student Facing states, “There are 10 birds on the wire. Some of the birds are red. The rest of the birds are blue. How many of the birds are red? Then how many of the birds are blue? Show your thinking using objects, drawings, words, or numbers. Find more than 1 solution to the problem.” (K.OA.2, K.OA.3)

Examples of non-routine applications of the math include:

  • Unit 2, Numbers 1- 10, Section A, Lesson 5, Activity 1, Launch, students make groups that have more, fewer, or the same number of objects as another group. Launch states, ”Groups of 2, Give each group a mat and access to collections of between 2–9 objects and connecting cubes. ‘Choose a group of objects and place them in the box at the top of the mat. Use cubes to make a new group of objects for each box below. Make a group that has fewer objects, a group that has the same number of objects, and a group that has more objects. Discuss with your partner how you know each group has more, fewer, or the same number of objects.’” (K.CC.6)

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 5, Activity 2, Student Work Time, students connect the action in the story to the meaning of the addition and subtraction signs. Student Work Time states, “Reread the first story problem. ‘Show your thinking using objects, drawings, numbers, or words.’ 2 minutes: independent work time. 2 minutes: partner discussion. ‘Lin began writing this equation but didn’t finish it. Finish her equation to show what happened in the story problem.’ 2 minutes: independent work time. Repeat the steps with the second story problem. Display 93=9-3=___ for students to complete the equation.” Student Facing states, ”a. Andre put together 4 pattern blocks to make a shape. Then Andre put 4 more pattern blocks on the shape. How many pattern blocks are in Andre’s shape? ___ equation: 8=8=___++___ b. Elena used 9 pattern blocks to make a train. Then she took 3 of the pattern blocks off of the train and put them back in the bucket. How many pattern blocks are in Elena's train now? ___ equation 93=9-3=___.” (K.OA.1, K.OA.2)

  • Unit 8, Putting It All Together, Section A, Lesson 3, Activity 1, Launch and Student Work Time, students use their knowledge of the count sequence to solve Add To, Result Unknown and Take From, Result Unknown story problems where one is added or taken away. Launch states, “Groups of 2, Give students access to connecting cubes and 10-Frames. ‘Today you are going to solve two story problems about people on a bus.’” In Student Work Time, Student Facing states, “a. There were 7 people on the bus. Then 1 more person got on the bus. How many people are on the bus now? Show your thinking using objects, drawings, numbers, or words. b. There were 10 people on the bus. Then 1 person got off the bus. How many people are on the bus now? Show your thinking using objects, drawings, numbers, or words.” (K.CC.2, K.CC.4, K.OA.2)

Indicator 2D
02/02

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 Open Up Resources K–5 Math Kindergarten meet expectations in that 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.

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:

  • Unit 4, Understanding Addition and Subtraction, Section A, Lesson 4, Activity 1, Launch, students extend their conceptual understanding as they use objects to represent addition. Launch states, “Give each student at least 10 counters and access to 5-frames. ‘Count out 3 counters. You can use a 5-frame if it is helpful.’ 30 seconds: independent work time. ‘Now add 4 more counters.’ 30 seconds: independent work time. ‘How many counters are there altogether?’ Write ‘There are 7 counters altogether. This sentence now says, There are 7 counters altogether. We are going to continue to work on problems where we add more counters to the group we started with. Let’s add and find the total number of counters.’” (K.CC.5, K.OA.1)

  • Unit 5, Composing and Decomposing Numbers to 10, Section A, Lesson 1, Activity 1, Student Work Time, students develop procedural skill and fluency as they decompose 6 into two parts using connecting cubes. Student Work Time states, “‘You have 6 cubes. Put some of the cubes in your hand and some on your desk.’ 30 seconds: independent work time. ‘Tell your partner how many cubes are in your hand. Show them the cubes. Tell your partner how many cubes are on your desk. Show them the cubes. Tell your partner how many cubes you have altogether.’” (K.OA.3, K.OA.5)

  • Unit 8, Putting It All Together, Section B, Lesson 11, Activity 1, Launch and Student Work Time, students apply their understanding of addition and subtraction as they represent and solve a story problem about their school community. Launch states, “Give each student a piece of chart paper and access to connecting cubes or two-color counters and crayons. ‘Tell your partner the story problem that you came up with yesterday. Today you are going to make a poster to show your story problem. Solve the story problem. Show your thinking using drawings, numbers, or words.’” Student Work Time states, “10 minutes: independent work time. ‘If you have time, you may want to show different ways to solve the problem using pictures, numbers, words, or symbols.’ 10 minutes: independent work time.” (K.OA.1, K.OA.2)

Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of a single unit of study or topic. Examples include:

  • Unit 2, Number 1-10, Section A, Lesson 2, Activity 2, Launch, students develop conceptual understanding alongside procedural skill and fluency as they recognize that the arrangement of a group of objects does not change the number of objects. Launch states, “Groups of 2, Give each group 1 cup and 10 two-color counters. Give students access to 5-frames. ‘We are going to learn about a new center called Shake and Spill. Let's play a round together. Choose who will go first and start with all of the counters in the cup. Shake the cup and spill the counters on the table.’ 30 seconds: partner work time. ‘Take turns figuring out how many counters there are. When you know how many counters there are, tell your partner and see if you both agree.’ 1 minute: partner work time. ‘Put the counters back into the cup, shake them and spill them again. Take turns figuring out how many counters there are and share with your partner.’ 1 minute: partner work time. ‘Now you can take turns playing with your partner. Take some of the counters out of the cup and put them away so that you are using a different number of counters this time. Remember to spill the counters, figure out how many there are, spill the counters again, and figure out how many there are.’” (K.CC.4, K.CC.5)

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 14, Activity 1, Launch and Student Work Time, students develop conceptual understanding alongside application as they explain how a subtraction expression represents a story problem. Launch states, “Groups of 2, Give students access to connecting cubes or two-color counters. Read and display the task statement. ‘Tell your partner what happened in the story.’ 30 seconds: quiet think time. 1 minute: partner discussion. Monitor for students who accurately retell the story. Choose at least one student to share with the class. Write the expression 10 - 6. ‘How does this expression show what happens in the story problem?’” In Student Work Time, Student Facing states, “There were 10 people riding bikes in the park. Then 6 of the people stopped riding to have lunch. How many people are riding bikes now?” (K.OA.1, K.OA.2)

  • Unit 6, Numbers 0-20, Section A, Lesson 2, Activity 2, Launch and Student Work Time, students develop conceptual understanding alongside procedural skill and fluency as they keep track of objects counted in order to accurately count groups up to 20. Launch states, “Groups of 2, Give each student a collection of objects and access to 10-frames and a counting mat. Display a 10-frame mat and a counting mat. ‘How can you use the counting mat to help you figure out how many objects are in your collection?’ (I can put all of the objects on one side and say a number as I move each object to the other side.) 30 seconds: quiet think time. 30 seconds: partner discussion, Share responses. ‘How can you use the 10-frame to help you figure out how many objects there are in your collection?’ (I can put one object in each box and line up the rest of the objects. Then I can count them.) 30 seconds: quiet think time. 30 seconds: partner discussion. Share responses. ‘Choose either the 10-frame or the counting mat to help you figure out how many objects are in your collection.’” Student Work Time states, “4 minutes: independent work time. ‘Find a partner who used a different tool to help them count their collection. If you used a 10-frame to help you count your collection, find a partner who used the counting mat. Show your new partner how you counted your collection.’ 4 minutes: partner work time.” (K.CC.4a)

Criterion 2.2: Math Practices

10/10

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

The materials reviewed for Open Up Resources K-5 Math 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
02/02

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 Open Up Resources K–5 Math 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 within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

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 units. Examples include:

  • Unit 1, Math In Our World, Section C, Lesson 11, Activity 1, Activity Narrative and Student Work Time, students think of different ways to represent a story. Student Facing states, “4 little speckled frogs sat on a speckled log, eating the most delicious bugs. Yum! Yum! 1 jumped into the pool, where it was nice and cool. Now there are 3 green speckled frogs. Glub! Glub!” An image of a green frog is shown. Activity Narrative states, “Acting out gives students opportunities to make sense of a context (MP1). Monitor for suggestions of acting out the story with concrete objects such as cubes, fingers, or students, as well as representing the story with pictures.”

  • Unit 2, Numbers 1-10, Section A, Lesson 4, Activity 1, Activity Narrative, Launch and Student Work Time, students identify a group of objects that has more. Launch states, “Groups of 2. Give each group of students access to connecting cubes and two-color counters. ‘We have been learning about different tools that we use at home and in our classroom. What kind of tools do you use when you eat at home?’ (Spoons, forks, chopsticks, plates, bowls, napkins, cups, straws). 30 seconds: quiet think time. 1 minute: partner discussion. Share and record responses. ‘We use many different tools when we eat.’ Display and read the story. ‘What is the story about?’ (A family eating dinner, Priya’s family, spoons for dinner). 30 seconds: quiet think time. Share responses. Read the story again. ‘How can you act out this story?’ (We can pretend we are sitting at the table and pretend to hand out spoons. We can use the cubes to show the people and the counters to show the spoons. We can draw a picture.). 30 seconds: quiet think time. 1 minute: partner discussion. Share responses.” Student Work Time states, “‘Act out the story with your partner.’ 3 minutes: partner work time. ‘Are there more people or spoons? How do you know?’ (There are more spoons than people. Each person gets one spoon and then there are some more spoons.). 2 minutes: partner work time. Monitor for students who matched one spoon to each person to see if there were enough spoons and which there was more of.” In Student Work Time, Student Facing states, “Priya and her family are sitting down at the table for dinner. There are 4 people sitting at the table. There are 6 spoons. Are there enough spoons for each person to get one?” Activity Narrative states, “The context of family mealtimes that is introduced in this activity will be revisited throughout the unit. Acting it out gives students an opportunity to make sense of a context (MP1).”

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 5, Warm-up, Student Work Time and Activity Narrative, students reason about a problem context involving quantities within ten. In Student Work Time, Student Facing states, “What do you notice? What do you wonder? Elena used 9 pattern blocks to make a train. Then she took 3 of the pattern blocks off of the train and put them back in the bucket.” Activity Narrative states, “This Warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (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 units. Examples include:

  • Unit 1, Math in Our World, Section A, Lesson 5, Warm-up, Launch, Student Work Time, and Activity Narrative, students reason about tools and consider different representations. Launch states, “Groups of 2. Display the image.” In Student Work Time, Student Facing states, “What do you notice? What do you wonder?” Activity Narrative states, “The purpose of this Warm-up is for students to consider how different tools can be used to represent the same thing. When students describe how each object represents a house and make connections between the objects, they show their ability to reason abstractly and quantitatively (MP2).”

  • Unit 3, Flat Shapes All Around Us, Section B, Lesson 10, Activity 2, Launch, Student Work Time, and Activity Narrative, students use pattern blocks to fill in simple puzzles. Student Facing shows an image of a pattern puzzle, with different pattern blocks shown to make the figure. Launch states, “Groups of 2. Give each group of students pattern blocks. ‘In the last activity we put together pattern blocks to make quilts. We can also use pattern blocks to make things that we see in real life. Close your eyes and think about something that you see at home or in your community. Use the pattern blocks to make what you see.’ 2 minutes: independent work time. ‘Tell your partner about what you made and why.’ 2 minutes: partner discussion. Share responses. ‘Each puzzle looks like something we see in real life. Use the pattern blocks to fill in each puzzle. Write a number to show how many of each pattern block you used. Ask your partner a question about each puzzle using the word “fewer”.’ Student Work Time states, “6 minutes: partner work time.” Activity Narrative states, “When students make connections between the pattern blocks and the shape outlines in the puzzle, they show their ability to reason abstractly and quantitatively (MP2).”

  • Unit 6, Numbers 0-20, Section C, Lesson 11, Activity 2, Launch, Student Work Time, and Activity Narrative, students show that numbers 11-19 consist of 10 ones and and some more ones as they color images to match expressions. Launch states, “Groups of 2. Give each student access to at least two different colored crayons. ‘Color the shapes to show each expression. Then complete the equation to show how many shapes there are altogether.’” Student Work Time states, “2 minutes: independent work time. 3 minutes: partner work time. Monitor for students who count on from 10.” In Student Work Time, Student Facing states, a1. Color the squares to show 10+210+2. 10+2=10+2=____. An image of 12 squares is shown. b. Color the triangles to show 10+810+8. 10+8=10+8=____. An image of 18 triangles is shown. c. Color the hexagons to show 10+410+4. 10+4=10+4=____. An image of 14 hexagons is shown. d. Color the circles to show 10+910+9. 10+9+10+9+____. Two images are shown: a rectangular shape with 10 circles and 9 circles.” Activity Narrative states, “Because students are coloring in the shapes to show 10+10+____, students may count on from 10 to determine the total number of shapes. It is important that students connect their equations to the corresponding representations (MP2).”

Indicator 2F
02/02

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 Open Up Resources K–5 Math 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 engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Activity Narratives and Lesson Activities’ Activity Narratives).

According to the Kindergarten Course Guide, Design Principles, Learning Mathematics By Doing Mathematics, “Students learn mathematics by doing mathematics, rather than by watching someone else do mathematics or being told what needs to be done. Doing mathematics can be defined as learning mathematical concepts and procedures while engaging in the mathematical practices - making sense of problems, reasoning abstractly and quantitatively, making arguments and critiquing the reasoning of others, modeling with mathematics, making appropriate use of tools, attending to precision in their use of language, looking for and making use of structure, and expressing regularity in repeated reasoning. By engaging in the mathematical practices with their peers, students have the opportunity to see themselves as mathematical thinkers with worthwhile ideas and perspectives.”

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

  • Unit 1, Math in Our World, Section D, Lesson 13, Warm-up, Launch, Student Work Time, and Activity Narrative, students construct viable arguments as they count collections of objects, focused on keeping track of which objects have been counted. Launch states, “‘We need to figure out how many of us are here. How can we make sure that we count each person one time?’ 30 seconds: quiet think time. Share responses. Monitor for students who suggest a way to organize the students, such as having all of the students line up.” Student Work Time states, “Count the students using two of the methods suggested by students. ‘How many of us are here today?’” Activity Narrative states, “As students share answers to questions such as ‘How can we figure out how many of us are here?’ and ‘Did I count the students correctly?’ they are beginning to construct viable arguments and attend to precision (MP3, MP6).”

  • Unit 3, Flat Shapes Around Us, Section A, Lesson 1, Warm-up, Launch, Student Work Time, and Activity Narrative, students construct arguments as they compare four different images and analyze the characteristics or attributes of the images. Launch states, “Display the image. ’What is the same and what is different about the teddy bears?’ 30 seconds: quiet think time. 30 seconds: partner discussion. Share responses.” Student Work Time states, “Which one doesn’t belong? Display the image. 30 seconds: quiet think time. ‘Tell your partner which teddy bear doesn’t belong and why.’ 30 seconds: partner discussion. In Student Work Time, Student Facing states, “2. Which one doesn’t belong?” Images of teddy bears are provided. Activity Narrative states, “In this Warm-up, students only work with three images of teddy bears. By the end of the section, students will compare four images of shapes. Emphasize to students that there is no right answer to the question and that it is important to explain their choice. Listen to how students create an argument and use or revise their language to make their argument clear to others (MP3).”

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 16, Activity 2, Launch, Student Work Time, Activity Synthesis, and Activity Narrative, students construct arguments as they use solid shapes to make a model of the classroom. Launch states, “When a classmate comes to your model, tell them all about your model and what the shapes represent.” Student Work Time states, “Invite half of the class to stand by their models while the other half walks around. 5 minutes: gallery walk. Switch groups. 5 minutes: gallery walk. ‘Were there any things that you saw in your classmates’ models that gave you an idea for things you want to add to or change about your model?’ 1 minute: quiet think time. 2 minutes: partner discussion. Share responses. ‘Work on your model.’ 4 minutes: independent work time. Monitor for changes students make to their models including changing the shapes that they use, changing the relative position of the shapes, or putting in more shapes to represent additional features.” Activity Synthesis states, “Invite selected students to share changes that they made to their models and why they made them.” Activity Narrative states, “Describing their model to their peers and seeing other models helps students develop ideas for how to add to or change their model (MP3).”

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

  • Unit 3, Flats Shapes All Around Us, Section A, Lesson 5, Activity 2, Launch, Student Work Time, and Activity Synthesis, students construct arguments and begin to critique the reasoning of others as they distinguish triangles from other shapes. Launch states, “Groups of 4, Give each group a set of cards. ‘Work with your group to sort the shapes into 2 groups. Put the shapes that are triangles on the left side of your page. Put the shapes that are not triangles on the right side of your page. When you place a shape, tell your group why you think the shape belongs in that group.’” Student Work Time states, “4 minutes: small-group work time. Monitor for students who discuss attributes of triangles when sorting. ‘Write a number to show how many shapes are in each group.’ 1 minute: independent work time. ‘Walk around to see how the other groups organized their shapes. Did they organize them the same way that your group did?’ 6 minutes: work time.” In Student Work Time, Student Facing states, “Let’s put the shapes into 2 groups.Triangle, Not a Triangle” Activity Synthesis states, “Display cards O, K, and G next to each other. ‘Noah says that the shape in the middle is not a triangle because it is pointing down and triangles have to point up. Do you agree with Noah? Why or why not?’”

  • Unit 5, Composing and Decomposing Numbers to 10, Section A, Lesson 1, Activity 2, Launch, Student Work Time and Activity Synthesis, students construct arguments and begin to critique the reasoning of others as they decompose numbers into two groups. Launch states, “Groups of 2. Give students access to connecting cubes. ‘Diego and Lin also put some cubes in their hands and some on their desks. Diego has 3 in his hand and 1 on his desk. He says he has 4 cubes altogether. Lin has 2 in her hand and 2 on her desk. She also says she has 4 cubes total. Can they both have 4 cubes altogether?’” Student Work Time states, “3 minutes: partner discussion. Monitor for students who count the groups to determine that both students have 4 even though they are broken into different parts.” Activity Synthesis states, “Do Diego and Lin both have 4 cubes? Invite previously identified students to share. ‘What parts did Diego break 4 into? (3 and 1)’ Write 3+13+1. ‘What parts did Lin break 4 into?’ (2 and 2) Write 2+22+2. ‘Diego and Lin showed us that we can break numbers apart in different ways.’”

  • Unit 8, Putting It All Together, Section B, Lesson 7, Cool-down, students critique the work of others as they use numbers to create a number book using objects in their environment. Student Facing states, “Choose 1 object in our classroom. Create a number book page about the object. Include a number, a drawing, and letters, a word, or words.” Preparation, Lesson Narrative states, “When students represent objects in their school with pictures and numbers, the reason abstractly and quantitatively (MP2).”

Indicator 2G
02/02

Materials support 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.

The materials reviewed for Open Up Resources K–5 Math Kindergarten meet expectations for supporting 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. 

Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Instructional Routines and Lesson Activities’ Instructional Routines).

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, model situations with appropriate representations, and describe what they do with the model and how it relates to the problem. Students model with mathematics as they work with support of the teacher and independently throughout the units. Examples include:

  • Unit 3, Flat Shapes All Around Us, Section B, Lesson 14, Activity 2, Launch, Student Work Time, and Instructional Routine, students put shapes together to form larger shapes. Launch states, “Give each student a sheet of construction or white paper. Give students access to cut out shapes, glue, crayons, colored pencils, and markers. ‘We noticed that artists use shapes in different ways to create art. Some artists make patterns and designs. Some put shapes together to form people or animals. Now you are going to make your own piece of artwork using shapes. You can use any of these materials. Think about how you can draw or put shapes together to make larger shapes.’” Student Work Time states, “8 minutes: independent work time.” Instructional Routine states, “When students recognize mathematical features of objects in the real world, they model with mathematics (MP4).”

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 3, Cool-down, Section A Checkpoint, students compose shapes from pattern blocks. The teacher observes to capture evidence of student thinking on the checkpoint checklist. Student Response states, “Count all to determine the total. Use objects, drawings, or equations to represent a story problem.” Preparation, Lesson Narrative states, “In this lesson, students create a shape out of pattern blocks and brainstorm questions that they could ask about other students’ shapes. Students create and solve story problems about shapes made out of pattern blocks (MP2, MP4).”

  • Unit 8, Putting It All Together, Section B, Lesson 8, Activity 2, Launch, Student Work Time, and Instructional Routine, students recognize different ways math is all around them in their community. In Student Work Time, Student Facing states, “a. Find something that you can count. b. Find 2 objects that you can compare the weight of. c. Find something that you know how many there are without counting. d. Find something that there are 5 of. e. Find 2 groups of objects that make 10 objects altogether. f. Find a group of objects that you could use to fill in a 10-frame. g. Find something that you could make using solid shapes. h. Find 2 groups of objects that you can compare the number of. i. Find something that has a number on it. j. Find 2 objects that you can compare the length of.” Launch states, “Groups of 2, Give students access to 10-frames, geoblocks, and solid shapes. ‘Work with your partner to find an object or objects that goes with each prompt.’” Student Work Time states, “‘Find something that you can count.’ 30 seconds: quiet think time. 2 minutes: partner work time. ‘Now count what you found.’ 1 minute: partner work time. Repeat the steps with the rest of the prompts.” Instructional Routine states, “When students identify objects in the classroom that fit different constraints they are taking an important step toward modeling with mathematics (MP4).”

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 units to support their understanding of grade-level math. Examples include:

  • Unit 1, Math In Our World, Section D, Lesson 13, Activity 1, Launch, Student Work Time, and Instructional Routine, students count collections of objects, and the focus is saying one number for each object. Launch states, “Today you’re going to count another collection of objects. As you’re working, think about how to make sure you count each object.” Student Work Time states, “Give each student a bag of objects. Give students access to 5-frames and a counting mat. ‘Figure out how many objects are in your collection.’ 2 minutes: independent work time. ‘Switch collections with a partner. Figure out how many objects are in your new collection.’ 2 minutes: independent work time. Monitor for students who have a method of keeping track of which objects have been counted, such as moving and counting or lining up the objects and counting them in order.” Instructional Routine states, “Students use appropriate tools strategically as they choose which tools help them count their collections (MP5).”

  • Unit 2, Numbers 1 - 10, Section D, Lesson 21, Activity 1, Launch, Student Work Time, and Instructional Routine, students compare numbers in a way that makes sense to them. In Student Work Time, Student Facing states, “Circle the number that is more. a. 5, 8, b. 9, 4,” Launch states, “Groups of 2, Give students access to connecting cubes or counters. ‘Work with your partner to figure out which number is more. Circle the number that is more.’” Student Work Time states, “5 minutes: partner work time. Monitor for students who create representations of the numbers using cubes or a drawing and use these representations to compare. Monitor for students who counted to figure out which number is more.” Instructional Routine states, “Students can use physical objects or make drawings to represent each number (MP5), and match or count to compare.”

  • Unit 4, Understanding Addition and Subtraction, Section B, Lesson 8, Cool-down, Section B checkpoint, students represent and solve story problems using a strategy that makes sense to them. Teachers observe and capture evidence of student thinking on the checkpoint checklist. Student Response states, “Accurately retell a story problem in their own words. Understand the action in a story problem and act it out or demonstrate it with objects or drawings. Use objects or drawings to represent a story problem.” Preparation, Lesson Narrative states, “Students may use objects, math tools, or drawings to represent and solve the story problem (MP5).”

Indicator 2H
02/02

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 Open Up Resources K–5 Math 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. 

Students have opportunities to engage with the Math Practices across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

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

  • Unit 1, Math in Our World, Section A, Lesson 4, Warm-up, Activity Narrative, Launch, Student Work Time, and Activity Synthesis, students use specialized language to describe shapes. Activity Narrative states, “The purpose of this activity is to elicit ideas students have about geoblocks. This allows teachers to see what language students use to describe shapes (MP6). There is no need to introduce formal geometric language at this point since this will happen in a later unit.” Launch states, “Groups of 2. Give each student a few geoblocks and display a collection of geoblocks or the image in the student book. ‘What do you notice?’ 30 seconds: quiet think time.” Student Work Time states, “‘Tell your partner what you noticed.’ 1 minute: partner discussion. Share and record responses. ‘What do you wonder?’ 1 minute: quiet think time. ‘Tell your partner what you wondered.’ 30 seconds: quiet think time. 1 minute: partner discussion. Share and record responses.” Activity Synthesis states, “‘These are called geoblocks. What is one thing that you think you could do or make with the geoblocks?’”

  • Unit 1, Math In Our World, Section B, Lesson 8, Activity 2, Launch, Student Work Time and Activity Narrative, students attend to precision as they recognize, name, and match groups with the same number of images. Launch states, “Groups of 2. Display the image from the student book. ‘When I point to each group, show your partner with your fingers and tell your partner how many things there are.’ Point to the ducks. 30 seconds: partner work time. Repeat the steps with the cats and dogs. ‘Which groups have the same number of things? How do you know?’ (There are 3 ducks and 3 dogs. They are both 3.) 30 seconds: quiet think time. Share responses. Display or write “3”. ‘There are 3 ducks and 3 dogs. They both have the same number of things.’” Student Work Time states, “Give each group of students a set of cards. ‘Work with your partner to match the cards that have the same number of things. Explain to your partner how you know.’ 4 minutes: partner work time.”  Activity Narrative states, “When students say that two cards match because they have the same number of objects, they attend to precision in their language (MP6).”

  • Unit 2, Numbers 1- 10, Section B, Lesson A, Cool Down, students attend to precision as they compare groups of objects and describe their comparisons using “more,” “fewer,” and “the same number.” Student Responses states, “Compare the number of objects in groups. Use ‘more,’ ‘fewer,’ and ‘the same number’ to describe comparisons. Make groups with more, fewer, or the same number of objects than a given group.” Activity Narrative (from Activity 2) states, “In making comparisons, students have a reason to use language precisely (MP6).”

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 9, Warm-up, Launch, Activity Narrative, and Activity Synthesis, students attend to precision as they compare attributes of shapes to determine which one does not belong. Launch states, “Groups of 2. Display the image. ‘Pick one that doesn’t belong. Be ready to share why it doesn’t belong.’ 1 minute: quiet think time.” Activity Narrative states, “This Warm-up prompts students to carefully analyze and compare the attributes of 4 shapes. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the words students know and how they talk about attributes of shapes.” Activity Synthesis states, “Display the image of the square. ‘Noah said that this shape doesn’t belong because it is not a rectangle. What do you think?’ 30 seconds: quiet think time. Share responses. ‘A square is a special kind of rectangle.’”

  • Unit 5, Composing and Decomposing Numbers to 10, Section B, Lesson 5, Cool-down, students use grade appropriate math terms to restate and represent story problems. Student Responses states, “Accurately retell a story problem in your own words. Use objects or drawings to represent a story problem. Explain how objects or drawings represent a story problem. Use labels, colors, numbers, or other methods to represent the two groups in a story problem.” Activity Narrative (from Activity 2) states, “Students are encouraged to use clear and precise language to explain how their representation shows the story problem (MP6).”

  • Unit 7, Solid Shapes Around Us, Section B, Lesson 13, Activity 1, Launch, Student Work Time, Activity Synthesis, and Activity Narrative, students use specific mathematical language to describe the solid shapes. Launch states, “Groups of 2. Give students access to solid shapes. ‘Choose 2 solid shapes.’ 30 seconds: independent work time.” Student Work Time states, “‘We are going to go for a walk. Your job is to look for objects that look like your solid shapes. Tell your partner about the shapes you find.’ 10 minutes: shape walk. Monitor for students who use positional words to describe the location of shapes. ‘Tell your partner about your favorite object. Where did you see it?’ 30 seconds: quiet think time. 1 minute: partner discussion. Share responses.” Activity Narrative states, “The purpose of this activity is for students to identify and describe solid shapes in their environment (MP4, MP6).” Activity Synthesis states, “Invite students who used positional words to describe the location of shapes to share. ‘____ saw a round light bulb below the lamp shade. It looked like a sphere. _____ saw a book on the bookshelf. It looked like a box.’ Display image: ‘Which shape does this clock look like?’ (Students say “cylinder” or hold up a cylinder.) Display image: ‘Which shape does this party hat look like? (Students say “cone” or pick up a cone.) In the next activity, we are going to use clay to make shapes that show the objects we saw.’”

Indicator 2I
02/02

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 Open Up Resources K–5 Math 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 across the year, and they are often explicitly identified for teachers within the Course Guide (How to Use These Materials). A chart is provided within this section that highlights several lessons that showcase particular Mathematical Practices. The Mathematical Practices are also identified within specific lessons (Lesson Preparation Narratives and Lesson Activities’ Narratives).

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 to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently throughout the units. Examples include:

  • Unit 2, Numbers 1–10, Section B, Lesson 8, Activity 2, students look for and make use of structure while they compare groups of images. Launch states, “Groups of 2. Display the student page. ‘How are these pictures different from the ones we worked with in the first activity?’ (There are different pictures. The pictures aren’t matched up.)” Student Work Time states, “‘Are there enough cartons of milk for each student? How do you know?’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘Are there more students or cartons of milk? How do you know?’ 30 seconds: independent work time. 30 seconds: partner discussion. ‘There are more cartons of milk than students. How many students are there? How many cartons of milk are there?’ 1 minute: independent work time. ‘8 cartons of milk is more than 7 students.’ Repeat the steps with each group of images. Switch between asking students ‘Are there more _____ or _____?’ and ‘Are there fewer _____ or _____?’ Monitor for students who draw lines to match each image. Activity Narrative states, “Matching the images helps students relate the comparisons to the situation they just worked with where the images were already matched (MP7).”

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 15, Cool-down: Unit 4, Section C Checkpoint, students look for and make use of structure while they connect expressions to drawings. Student Facing states, “Lesson observations. Student Observations, Explain how an expression connects to a drawing or story problem. Fill in an expression to represent a drawing.” Activity 1 Narrative states, “The purpose of this activity is for students to match drawings to expressions. Students use the structure of the dots to decide whether they represent an addition or subtraction expression and then identify that expression (MP2, MP7).” The Cool-down also assesses students’ ability to connect expressions to drawings. Teacher Instructions state, “For this Checkpoint Assessment, a full checklist for observation of students can be found in the Assessments for this unit. The content assessed is listed below for reference. Relate addition and subtraction expressions to story problems. Explain how an expression connects to a drawing or story problem. Fill in an expression to represent a drawing. Find the value of addition and subtraction expressions within 5. Use fingers, objects, or drawings to find the value of an expression. Count all to determine the total when 0 or 1 are added. Use knowledge of the count sequence to determine the total when 1 is added.”

  • Unit 5, Composing and Decomposing Numbers to 10, Section C, Lesson 13, Warm-up, Student Work Time and Activity Synthesis, students look for and make use of structure while they subitize or use grouping strategies to describe the images they see. In Student Work Time, Student Facing states, “How many do you see? How do you see them?” Student Work Time states, “Display image. ‘Discuss your thinking with your partner.’ 1 minute: partner discussion. Record responses. Repeat for each image.” Activity Synthesis states, “Display the hands showing 8 fingers. ‘How many fingers are up? (8) How many fingers need to go up so there are 10 fingers?’ (2). Repeat the steps with the rest of the images.” Activity Narrative states, “When students think about quantities in relation to 5 and 10, they look for and make use of structure (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 to use repeated reasoning in order to make generalizations and build a deeper understanding of grade-level math concepts as they work with support of the teacher and independently throughout the units. Examples include:

  • Unit 1, Math in Our World, Section C, Lesson 11, Cool-down, students use repeated reasoning using one-to-one correspondence as they make groups of objects. Student Facing states, “Lesson observations.” Sample Student Responses include, “Say the count sequence to 10. Say one number for each object. Answer how many without counting again. Recognize and name groups of 1, 2, or 3 objects or images without counting. Recognize and name groups of 4 objects or images without counting. Show quantities on fingers.Identify groups with the same number of objects (for groups of up to 4 objects).” Preparation, Lesson Narrative states, “As students notice that when you get enough of an object for each student to have one, the number of students and the number of objects are the same, they look for and express regularity in repeated reasoning (MP8).”

  • Unit 5, Composing and Decomposing Numbers to 10, Section C, Lesson 12, Activity 2, Launch and Student Work Time, students use repeated reasoning to find how many counters are needed to fill a 10-frame. Launch states, “Groups of 2. Give students access to two-color counters. ‘Figure out how many counters are needed to fill each 10-frame. Write a number to show how many counters are needed to fill it. Circle the equation that shows the number of counters in the 10-frame and the number of counters needed to fill the 10-frame.’” In Student Work Time, Student Facing states, “a. (A ten frame with 7 counters is shown) 10=7+310=7+3, 10=8+210=8+2, 10=5+510=5+5 b. (A ten frame with 4 counters is shown) 10=8+210=8+2, 10=1+910=1+9, 10=4+610=4+6 c. (A ten frame with 9 counters is shown) 10=9+110=9+1, 10=5+510=5+5, 10=7+310=7+3 d. (A ten frame with 3 counters is shown) 10=5+510=5+5, 10=3+710=3+7, 10=2+810=2+8 e. (A ten frame with 5 counters is shown) 10=9+110=9+1, 10=6+410=6+4, 10=5+510=5+5 f. (A ten frame with 2 counters is shown) 10=1+910=1+9, 10=2+810=2+8, 10=4+610=4+6.” Activity Narrative states, ”With repeated experience composing 10 in many ways, students may begin to know the combinations to make 10 (MP8).”

  • Unit 6, Numbers 0–20, Section A, Lesson 4, Warm-up, Launch, Student Work Time, and Activity Synthesis, students count collections of objects and understand that the number of objects in a collection stays the same, regardless of how they are arranged. In Student Work Time, Student Facing states, “What do you notice? What do you wonder?” Launch states, “Groups of 2. Display the image. ‘What do you notice? What do you wonder?’ 1 minute: quiet think time.” Student Work Time states, “‘Discuss your thinking with your partner.’ 1 minute: partner discussion. Share and record responses.” Activity Synthesis states, “Which arrangements do you think would be easiest to count? Why? (The lined up dots would be easy to count. I could count one line and then the other line.).” Preparation, Lesson Narrative states, “Students will count the same collection of objects in different arrangements to build this conservation of number, which develops through experience over time. While developing conservation of number, students may need to recount the objects each time they are rearranged. With repeated practice, some students may know that the number of objects is the same without recounting (MP8).”

Overview of Gateway 3

Usability

The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports.

Criterion 3.1: Teacher Supports

09/09

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 Open Up Resources K-5 Math 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
02/02

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 Open Up Resources K-5 Math Kindergarten meet expectations for providing teachers 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. 

Within the Course Guide, several sections (Design Principles, A Typical Lesson, How to Use the Materials, and Key Structures in This Course) provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include but are not limited to:

  • Resources, Course Guide, Design Principles, Learning Mathematics by Doing Mathematics, “A problem-based instructional framework supports teachers in structuring lessons so students are the ones doing the problem solving to learn the mathematics. The activities and routines are designed to give teachers opportunities to see what students already know and what they can notice and figure out before having concepts and procedures explained to them. The teacher has many roles in this framework: listener, facilitator, questioner, synthesizer, and more.”

  • Resources, Course Guide, A Typical Lesson, “A typical lesson has four phases: 1. a warm-up; 2. one or more instructional activities; 3. the lesson synthesis; 4. a cool-down.” “A warm-up either: helps students get ready for the day’s lesson, or gives students an opportunity to strengthen their number sense or procedural fluency.” An instructional activity can serve one or many purposes: provide experience with new content or an opportunity to apply mathematics; introduce a new concept and associated language or a new representation; identify and resolve common mistakes; etc. The lesson synthesis “assists the teacher with ways to help students incorporate new insights gained during the activities into their big-picture understanding.” “In kindergarten, most lessons do not include cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson. Since activities are shorter, each lesson includes 15–25 minutes of time for centers.”

  • Resources, Course Guide, How to Use the Materials, “The story of each grade is told in eight or nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson in the unit also has a narrative. Lesson narratives explain: the mathematical content of the lesson and its place in the learning sequence; the meaning of any new terms introduced in the lesson; how the mathematical practices come into play, as appropriate. Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.”

  • Resources, Course Guide, Scope and Sequence lists each of the eight units, a Pacing Guide to plan instruction, and Dependency Diagrams. These Dependency Diagrams show the interconnectedness between lessons and units within Kindergarten and across all grades. 

  • Resources, Course Guide, Course Glossary provides a visual glossary for teachers that includes both definitions and illustrations. Some images use examples and nonexamples, and all have citations referencing the unit and lesson in which the definition is found. 

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. Examples include:

  • Unit 2, Numbers 1-10, Section B, Lesson 8, Warm-up, Instructional Routine, “This warm-up focuses on cardinality, or knowing that the last number tells us how many, and keeping track of which images have been counted.” Suggestions to maximize preparation of the materials include: “For example, if there are 23 students in the class, cut out four 5-frames and 3 squares out of a fifth 5-frame. Consider laminating the display and using a dry erase marker to write the two choices and record students’ responses. If available, the provided images can also be enlarged.” Each step of the Warm-up includes what to ask/say, time to wait, and expectations of student responses. 

  • Unit 4, Understanding Addition and Subtraction, Overview, outlines procedures and vocabulary use. “Previously, students built their counting skills and represented quantities in a group with their fingers, objects, drawings, and numbers. Here, they relate counting to the result of two actions: putting objects together or taking objects away. Students enact addition by counting the total number of objects in two groups, and subtraction by counting what remains after some objects are taken away. (The word “total” is used here instead of “sum” to reduce potential confusion with the word “some” or part of a whole.)”

  • Unit 6, Numbers 0-20, Lesson 8, Lesson Narrative, "In previous lessons, students saw numbers 11–19 as ten ones and some more ones as they counted, composed, and represented these numbers. The purpose of this lesson is for students to use the understanding that a full 10-frame contains 10 ones to compose numbers 11–19. Using a 10-frame encourages students to count on from 10. While this lesson highlights counting on as a strategy, students need significant practice working with 10-frames before they are able to count on to determine the total with understanding. Students can complete the activities by counting all. Counting on to determine the total is not an expectation in kindergarten."

Indicator 3B
02/02

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 Open Up Resources K-5 Math 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. 

Unit Overviews and sections within lessons include adult-level explanations and examples of the more complex grade-level concepts. Within the Course Guide, How to Use the Materials states, “Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.” Examples include:

  • Unit 2, Numbers 1-10, Section B, Lesson 10, Activity 2, “The purpose of this activity is for students to learn stage 2 of the Less, Same, More center. Students compare groups of images in different arrangements. The activity synthesis highlights that numbers that are fewer than 5 come before 5 in the count sequence and numbers that are more than 5 come after 5 in the count sequence. This idea will be revisited in future sections and units. Students need repeated experiences comparing groups of objects, images, and numbers to be able to notice, articulate, and use the connection between the counting sequence and comparing the size of numbers (MP7, MP8).”

  • Unit 3, Flat Shapes All Around Us, Overview, “Students explore differences in shapes and use informal language to describe, compare, and sort them. Circle, triangle, rectangle, and square are four shapes that students study and name here. (They will not describe what makes each shape so until grade 1.) Students also learn a key idea, that congruent shapes are still “the same” even if they are in different orientations.”

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 9, Compare Capacity, Lesson Narrative, “In previous units and lessons, students compared the lengths and weights of objects. Students learned that three-dimensional shapes are solid. In this lesson, students learn about an attribute of solid shapes: capacity. Initially students compare two containers where it is visually obvious which one holds more. After this initial discussion, the cups or containers that students are comparing should have capacities that are not obviously different. For example, a shorter, wider cup and a taller, thinner cup.”

Also within the Course Guide, About These Materials, Further Reading states, “The curriculum team at Open Up Resources has curated some articles that contain adult-level explanations and examples of where concepts lead beyond the indicated grade level. These are recommendations that can be used as resources for study to renew and fortify the knowledge of elementary mathematics teachers and other educators.” Examples include:

  • Resources, Course Guide, About These Materials, Further Reading, K-2, “Units, a Unifying Idea in Measurement, Fractions, and Base Ten. In this blog post, Zimba illustrates how units ‘make the uncountable countable’ and discusses how the foundation built in K-2 measurement and geometry around structuring space allows for the development of fractional units and beyond to irrational units.”

  • Resources, Course Guide, About These Materials, Further Reading, Entire Series, “The Number Line: Unifying the Evolving Definition of Number in K-12 Mathematics. In this article, the authors (Lahme, McLeman, Nakamaye, and Umland) focus their attention on the selection of definitions, notation, and graphical conventions surrounding the development of the real numbers from kindergarten to grade 12, and address the work that students might do in later years.”

Indicator 3C
02/02

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

The materials reviewed for Open Up Resources K-5 Mathematics Kindergarten meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. 

 Correlation information can be found within different sections of the Course Guide and within the Standards section of each lesson. Examples include:

  • Resources, Course Guide, About These Materials, CCSS Progressions Documents, “The Progressions for the Common Core State Standards describe the progression of a topic across grade levels, note key connections among standards, and discuss challenging mathematical concepts. This table provides a mapping of the particular progressions documents that align with each unit in the K–5 materials for further reading.”

  • Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in the Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.”

  • Resources, Course Guide, Scope and Sequence, Dependency Diagrams, All Grades Unit Dependency Diagram identifies connections between the units in grades K-5. Additionally, a “Section Dependency Diagram” identifies specific connections within the grade level.

  • Resources, Course Guide, Lesson and Standards, provides two tables: a Standards by Lesson table, and a Lessons by Standard table. Teachers can utilize these tables to identify standard/lesson alignment.

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 4, Standards, “Addressing: K.G.B.6 Compose simple shapes to form larger shapes. For example, ‘Can you join these two triangles with full sides touching to make a rectangle?’ K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Building Towards: K.G.B.6.”

 Explanations of the role of specific grade-level mathematics can be found within different sections of the Resources, Course Guide, Unit Overviews, Section Overviews, and Lesson Narratives. Examples include:

  • Resources, Course Guide, Scope and Sequence, each Unit provides Unit Learning Goals, for example, “Students recognize numbers and quantities in their world.” Additionally, each Unit Section provides Section Learning Goals, “Explore and use math tools. Share mathematical ideas with a partner.”

  • Unit 3, Flat Shapes All Around Us, Overview, “This unit introduces students to the foundational concepts of geometry, with a focus on familiar flat (two-dimensional) shapes. Students may initially associate names of shapes with everyday objects. For example, a rectangle is a shape that looks like a door. Students need to see and interact with many examples of a shape to accurately relate what’s in their environment to the geometric term. For instance, students may say that only one of these two shapes is a triangle—the isosceles triangle sitting on its base—because they have seen examples like it being referred to as triangles. They may not consider a scalene triangle sitting on a vertex as a part of the same shape category because, in their experience, a shape like it hasn’t been associated with the term “triangle.” 

  • Unit 4, Understanding Addition and Subtraction, Section C, Lesson 16, Lesson Narrative, “In previous lessons, students interpreted expressions and connected expressions to story problems and drawings. This is the first lesson where students begin by working with only expressions. Because students have matched expressions to drawings in previous lessons, students may create a drawing to find the value of the expression. Students may also use their fingers or objects to represent the expression and count to find the total or difference.”

  • Unit 5, Composing and Decomposing Numbers to 10, Section B, Overview, “In this section, students represent and solve Put Together/Take Apart story problems—first where the total is unknown, and later where both addends are unknown. Students also see equations and learn the term for the first time. Jada made 6 paletas with her brother. They made two flavors, lime and coconut. How many of the paletas were lime? Then how many of the paletas were coconut? Problems where both addends are unknown may be more challenging because there is no action in the story and more than one solution is possible. Students work to find multiple solutions but are not expected to find all the solutions in kindergarten. To represent and solve story problems, students continue to use math tools and drawings, and to explain how their representation shows the story. They may use methods such as clearly separating the groups, using 2 colors, or using letter, word, and number labels to make their drawings easier for others to understand. Students also write expressions independently to record the solutions to the story problems.”

Indicator 3D
Read

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 Open Up Resources K-5 Math Kindergarten 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 include a Family Letter, found under Resources, that provides an introduction to the math curriculum, available in English and Spanish. Each unit has corresponding Family Support Materials, in English and Spanish, that provide a variety of supports for families. These supports are found on the main website: https://access.openupresources.org/curricula/our-k5-math/index.html, and are accessible through the Family and Student Roles. Examples include:

  • Resources, Family Letter, provides information about: “What is a problem-based curriculum?; What supports are in the materials to help my student succeed?; and What can my student do to be successful in this course?”

  • Student Role, Unit 1, Math in Our World, Section D, Section Summary, Counting Collections, “In this section, we counted collections of objects. We counted each object and kept track of which objects we’ve counted. We used 5-frames and counting mats to help us. We said a number to tell us how many objects there are.” 

  • Family Role, Unit 2, Numbers 1–10, Family Materials, “In this unit, students answer questions about how many objects there are. Students count out and compare groups within 10 and write numbers to represent how many. Near the end of the unit, ask your student to compare two amounts of objects (pencils, cups, fruit, etc.) Questions that may be helpful as they work: How many ___do you have? (Repeat for both sets of objects.) Which one has more? Which one has fewer? How do you know?”

  • Family Role, Unit 3, Flat Shapes All Around Us, Section A, “Students do not need to use formal vocabulary to describe or name shapes. However, they are asked to identify circles, squares, rectangles, and triangles. They are introduced to the idea that a square is a special kind of rectangle with all 4 sides the same length. Students see a wide range of examples of specific shapes, to help them develop an understanding of what the shapes are.”

Indicator 3E
02/02

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

The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The materials explain and provide examples of instructional approaches of the program and include and reference research-based strategies. Both the instructional approaches and the research-based strategies are included in the Course Guide under the Resources tab for each unit. Design Principles state, “It is our intent to create a problem-based curriculum that fosters the development of mathematics learning communities in classrooms, gives students access to mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, student thinking, and their own teaching practice.” Examples include:

  • Resources, Course Guide, Design Principles, “In order to design curriculum and professional learning materials that support student and teacher learning, we need to be explicit about the principles that guide our understanding of mathematics teaching and learning. This document outlines how the components of the curriculum are designed to support teaching and learning aligning with this belief.” Principles that guide mathematics teaching and learning include: All Students are Capable Learners of Mathematics, Learning Mathematics by Doing Mathematics, Coherent Progression, Balancing Rigor, Community Building, Instructional Routines, Using the 5 Practices for Orchestrating Productive Discussions, Task Complexity, Purposeful Representations, Teacher Learning Through Curriculum Materials, and Model with Mathematics K-5.

  • Resources, Course Guide, Design Principles, Community Building, “Students learn math by doing math both individually and collectively. Community is central to learning and identity development (Vygotsky, 1978) within this collective learning. To support students in developing a productive disposition about mathematics and to help them engage in the mathematical practices, it is important for teachers to start off the school year establishing norms and building a mathematical community. In a mathematical community, all students have the opportunity to express their mathematical ideas and discuss them with others, which encourages collective learning. ‘In culturally responsive pedagogy, the classroom is a critical container for empowering marginalized students. It serves as a space that reflects the values of trust, partnership, and academic mindset that are at its core’ (Hammond, 2015).”

  • Resources, Course Guide, Design Principles, Instructional Routines, “Instructional routines provide opportunities for all students to engage and contribute to mathematical conversations. Instructional routines are invitational, promote discourse, and are predictable in nature. They are ‘enacted in classrooms to structure the relationship between the teacher and the students around content in ways that consistently maintain high expectations of student learning while adapting to the contingencies of particular instructional interactions.’ (Kazemi, Franke, & Lampert, 2009)”

  • Resources, Course Guide, Key Structures in This Course, Student Journal Prompts, Paragraph 3, “Writing can be a useful catalyst in learning mathematics because it not only supplies students with an opportunity to describe their feelings, thinking, and ideas clearly, but it also serves as a means of communicating with other people (Baxter, Woodward, Olson & Robyns, 2002; Liedke & Sales, 2001; NCTM, 2000).”

Indicator 3F
01/01

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

The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for including a comprehensive list of supplies needed to support the instructional activities.

In the Course Guide, Materials, there is a list of materials needed for each unit and each lesson. Lessons that do not have materials are indicated by none; lessons that need materials have a list of all the materials needed. Examples include:

  • Resources, Course Guide, Key Structures in This Course, Representations in the Curriculum, provides images and explanations of representations for the grade level. “5-frame and 10-frame (K-2): 5- and 10-frames provide students with a way of seeing the numbers 5 and 10 as units and also combinations that make these units. Because we use a base-ten number system, it is critical for students to have a robust mental representation of the numbers 5 and 10. Students learn that when the frame is full of ten individual counters, we have what we call a ten, and when we cannot fill another full ten, the ‘extra’ counters are ones, supporting a foundational understanding of the base-ten number system. The use of multiple 10-frames supports students in extending the base-ten number system to larger numbers.”

  • Resources, Course Guide, Materials, includes a comprehensive list of materials needed for each unit and lesson. The list includes both materials to gather and hyperlinks to documents to copy. “Unit 2, Lesson 22 - Gather: Colored pencils or crayons; Copy: Pizza Orders.”

  • Unit 6, Section B, Lesson 6, Preparation, Materials Needed, “Activities: 10-frames (Activity 2), Counters (Activity 2), Colored pencils, crayons, or markers (Activity 3), Connecting cubes (Activity 3), Materials from previous centers (Activity 3).”

Indicator 3G
Read

This is not an assessed indicator in Mathematics.

Indicator 3H
Read

This is not an assessed indicator in Mathematics.

Criterion 3.2: Assessment

08/10

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 Open Up Resources K-5 Math Kindergarten partially meet expectations for Assessment. The materials identify the content standards and mathematical practices assessed in 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 following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series. 

Indicator 3I
02/02

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

The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for having assessment information in the materials to indicate which standards are assessed.

The materials consistently and accurately identify grade-level content standards for formal assessments for the Section Checkpoints and End-of-Unit Assessments within each assessment answer key. Examples from formal assessments include:

  • Resources, Course Guide, Summative Assessments, End of Unit Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.”

  • Unit 4, Understanding Addition and Subtraction, Assessments, End-of-Unit Assessment, Problem 2, “K.OA.A.2: Students solve an Add To, Results Unknown story problem. Students may use objects to represent and solve the problem or they may make a drawing. The provided drawing distinguishes the 3 stickers that were first on the book and the 2 more that Jada put on the book by using different colors. Students may distinguish them by physically separating them or they might not distinguish them, that is, they might draw 3 circles and 2 more that are altogether.” Problem 2, “There are 3 stickers on the book. Then Jada puts 2 more stickers on the book. How many stickers are on the book now? Show your thinking using drawings, numbers, words, or objects.”  

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 8, Cool-down, “Assessing K.MD.A, Which is lighter: your workbook or your pencil? Select the one that is lighter.” Images of a workbook and pencil are shown.

  • Unit 8, Putting It All Together, Assessments, Section D Checkpoint, Teacher Instructions, “For this Checkpoint Assessment, the content assessed is listed below for reference. Use understanding of 10 to work with numbers to 20. Given a number, find how many more are needed to make 10; Use 10 as a benchmark to estimate and count; Use 10 as a benchmark to compose and decompose numbers in different ways; Relate equations to compositions and decompositions of numbers.” (K.OA.3)

Guidance for assessing progress of the Mathematical Practices can be found within the Resources, Course Guide, How to Use These Materials, Noticing and Assessing Student Progress in Mathematical Practices, How to Use the Mathematical Practices Chart, “Because using the mathematical practices is part of a process for engaging with mathematical content, we suggest assessing the Mathematical Practices formatively. For example, if you notice that most students do not use appropriate tools strategically (MP5), plan in future lessons to select and highlight work from students who have chosen different tools.” In addition, “...a list of learning targets for each Mathematical Practice is provided to support teachers and students in recognizing when engagement with a particular Mathematical Practice is happening…the ‘I can’ statements are examples of types of actions students could do if they are engaging with a particular Mathematical Practice.” Examples include:

  • Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade K, MP2 is found in Unit 4, Lessons 7, 9, and 12. 

  • Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade K, MP4 is found in Unit 7, Lessons 3, 13, and 16. 

  • Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP1: I Can Make Sense of Problems and Persevere in Solving Them. I can ask questions to make sure I understand the problem. I can say the problem in my own words. I can keep working when things are going well and try again. I can show at least one attempt to figure out or solve the problem. I can check that my solution makes sense.”

Indicator 3J
02/04

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 Open Up Resources K-5 Math Kindergarten partially meet the 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. 

The assessment system provides multiple opportunities to determine students' learning. Each summative, End-of-Unit or End-of-Course Assessment, provides an explanation about the assessment item, potential student misconceptions, answer key, and standard alignment. According to the Resources, Course Guide, Summative Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.” Suggestions to teachers for following up with students are general, as teachers are encouraged to return to previously taught lessons. While teachers can refer back to specific lessons, it is incumbent on the teacher to determine which additional practice meets the needs of individual students. Examples include:

  • Unit 4, Understanding Addition and Subtraction, Assessments, End-of-Unit Assessment, Problem 1, “K.CC.B: Students count 2 sets of objects, in this case squares and trapezoids. While they are not asked to identify the count with the operation of addition, accurately counting 2 sets of objects is a vital skill before thinking about the count as representing addition. Students who answer 3 or 4 may have misinterpreted the question as asking for the number of squares or trapezoids respectively. ‘How many shapes are there?’ Solution: 7. Additional Support:If a student struggles with counting and knowing the number names and the count sequence, provide additional instruction either in a small group or individually using OUR Math Kindergarten Unit 1 Lesson 17. If a student struggles with writing numerals to represent what was counted, provide additional instruction and opportunities for students to practice counting with manipulatives or objects and writing the numeral to represent what they counted either in a small group or individually. Additional practice can be done using OUR Math Kindergarten Unit 2 Lesson 16.”

  • Unit 6, Numbers 0—20, Assessments, End-of-Unit Assessment, Problem 1. “K.NBT.A.1. Students draw 17 dots. They are given a blank 10-frame which they may use but do not need to. If they do fill the 10-frame, they may draw the extra 7 dots below the 10-frame, as in the sample response, or somewhere else. The sample response is the representation students have most often seen in the materials.‘Draw 17 dots. Use the 10-frame if it helps you.’ Solution: (Student has drawn 17 dots in the 10-frame provided.) Sample response: (Shows one way to draw 17 dots in two 10-frames.) Additional Support: If a student struggles when counting objects and saying the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object, provide additional instruction using OUR Math Kindergarten Unit 1 Lesson 13.”

  • Unit 7, Solid Shapes All Around Us, Assessments, End-Of-Unit Assessment, Problem 3, “K.G.B.4: For this problem, display a ball and a box for all students to see. Students will describe how the two 3-dimensional shapes are the same and how they are different. While students may use the words sphere or box to describe the objects, this is not required. Students should use the language that makes sense to them to describe how the objects are the same and how they are different.” Problem 3, “Consider the ball and box your teacher has displayed. How are the shapes the same? How are they different? Show your thinking with drawings or words.” “Solution, Sample response: They both take up space, they’re not flat. The ball is round. The box has corners and has flat surfaces. Additional Support: If a student struggles using informal language to describe shapes and their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length), provide additional instruction and opportunities in a small group or individually allowing students to practice sorting shapes with shape manipulatives and identifying why they were sorted in that way to help students recognize shape attributes. Additional practice can be done using OUR Math Kindergarten Unit 3 Lesson 9 & Lesson 11.”

Formative assessments include Section Checkpoints, Lesson Cool-downs, and Practice Problems. While these assessments provide multiple opportunities to determine students’ learning and sufficient guidance to teachers for interpreting student performance, there are minimal suggestions to teachers for following-up with students. Examples of formative assessments include: 

  • Unit 2, Numbers 1-10, Assessments, Section A Checkpoint, Sample Observation Checklist, Teachers are provided with two checklists to document skills they observe as students “Count up to 10 objects and know the number remains the same regardless of the arrangement of objects.” and “Compare the number of objects in groups of up to 10 objects.”

  • Unit 3, Flat Shapes All Around Us, Assessments, Section A Checkpoint, Sample Observation Checklist, Teachers are provided with two checklists to document skills they observe as students “Recognize and describe shapes in the environment” and “Use informal language to describe and compare shapes and their attributes.”

Indicator 3K
04/04

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 Open Up Resources K-5 Math Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

Formative assessments include instructional activities, Practice Problems and Section Checkpoints in each section of each unit. Summative assessments include End-of-Unit Assessments and End-of-Course Assessments. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types including multiple choice, multiple response, short answer, restricted constructed response, and extended response. Examples include:

  • Unit 2, Numbers 1-10, Assessments, End-of-Unit Assessment, Problem 3, K.CC.6, “a.) Circle the group that has more things.” Two images are shown: one 5-frame with 5 dots plus one more and two hands with 8 fingers raised. “b.) Circle the group that has fewer things.” Two images are shown, 7 dots in a line and 9 dots in a circular pattern.

  • Unit 3, Understanding Addition and Subtraction, Assessments, End-of-Unit Assessment, Problem 3, K.OA.2, “Students represent and solve a Take From, Result Unknown story problem. Students may use objects to represent and solve the problem. The drawing provided shows the 6 circles representing the kids playing in the park and then two of them are crossed out representing the two kids who go home. Students may represent the kids going home by using color or separating them from the others. Unlike the previous item where the picture solves the problem even if it is not organized, in this case an appropriate picture needs to distinguish the two kids who are going home from the 4 who are staying in order to help solve the problem. It won’t always be possible, from the written student work, to determine how a student envisions their drawing representing the story. In these cases, a personal interview may be needed. There are 6 kids playing in the park. 2 of the kids leave the park to go home. How many kids are playing in the park now? Show your thinking using drawings, numbers, words, or objects.”

  • Unit 7, Solid Shapes All Around Us, Assessments, Section A Checkpoint, Problem 1, K.OA.A.1, K.OA.A.2, “Clare used 10 pattern blocks to make a puzzle. She used trapezoids and triangles. How many trapezoids did Clare use? Then how many triangles did Clare use?”

  • Unit 8, Putting It All Together, Assessments, Section A Checkpoint, supports the full intent of MP2 (Reason abstractly and quantitatively) as students connect objects to written numbers. “Represent and write quantities and numbers up to 20. Count, read, and write numbers up to 20. Use objects, drawings, numbers, words, and expressions or equations to represent quantities up to 20.”

Indicator 3L
Read

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

The materials reviewed for Open Up Resources K-5 Math Kindergarten provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The general accommodations are provided in the Course Guide in the section Universal Design for Learning and Access for Students with Disabilities. These assessment accommodations are offered at the program level and not specific to each assessment. Examples include:

  • Course Guide, How to Assess Progress, Summative Assessment Opportunity, “In K-2, the assessment may be read aloud to students, as needed.”

  • Course Guide, Universal Design for Learning and Access for Students with Disabilities, Action and Expression, Develop Expression and Communication, “Offer flexibility and choice with the ways students demonstrate and communicate their understanding; Invite students to explain their thinking verbally or nonverbally with manipulatives, drawings, diagrams.”

  • Course Guide, Universal Design for Learning and Access for Students with Disabilities, Accessibility for Students with Visual Impairments, “It is important to understand that students with visual impairments are likely to need help accessing images in lesson activities and assessments, and prepare appropriate accommodations. Be aware that mathematical diagrams are provided in scalable vector graphics (SVG format), because this format can be magnified without loss of resolution. Accessibility experts who reviewed this curriculum recommended that students who would benefit should have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams would be inadequate for supporting their learning. All diagrams are provided in SVG file type so that they can be rendered in Braille format.”

Criterion 3.3: Student Supports

08/08

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

The materials reviewed for Open Up Resources K-5 Math 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
02/02

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 Open Up Resources K-5 Math Kindergarten meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics as suggestions are outlined within each lesson. According to the Resources, Course Guide, Universal Design for Learning and Access for Students with Disabilities, “Supplemental instructional strategies that can be used to increase access, reduce barriers and maximize learning are included in each lesson, listed in the activity narratives under ‘Access for Students with Disabilities.’ Each support is aligned to the Universal Design for Learning Guidelines (udlguidelines.cast.org), and based on one of the three principles of UDL, to provide alternative means of engagement, representation, or action and expression. These supports provide teachers with additional ways to adjust the learning environment so that students can access activities, engage in content, and communicate their understanding.” Examples of supports for special populations include: 

  • Unit 5, Composing and Decomposing Numbers to 10, Section C, Lesson 10, Activity 2, Access for Students with Disabilities, “Representation: Language and Symbols, Synthesis: Make connections between the 5-frame representation that can be seen in the 10-frame that is being used. For example “Do you see a 5-frame in the 10-frame we are using here?” Reiterate the fact that when we use the 10-frame we will fill the top row first and then move from left to right. If time allows, show a non-example of what a 10-frame could look like. Provides accessibility for: Visual-Spatial Processing, Conceptual Processing.”

  • Unit 6, Numbers 0-20, Section B, Lesson 7, Activity 2, Access for Students with Disabilities, “Action and Expression: Expression and Communication, Synthesis: Identify connections between the strategy of counting starting at 1 and counting on from 10. For example: ‘Since I know that this 10-frame is full I can start counting at 11. I do not need to count all the dots in the 10-frame again.’ Provides accessibility for: Conceptual Processing”

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 12, Activity 1, Access for Students with Disabilities, “Representation: Language and Symbols, Synthesis: Make connections between the rectangular prism and the shape that is not a rectangular prism. For example, hold them side by side so students can visually see the differences. Provides accessibility for: Conceptual Processing.”

Indicator 3N
02/02

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 Open Up Resources K-5 Math Kindergarten meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-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 for students to investigate grade-level content at a higher level of complexity. These are found where problems are labeled as “Exploration” at the end of practice problem sets within sections, where appropriate. According to the Resources, Course Guide, How To Use The Materials, Exploration Problems, “Each practice problem set also includes exploration questions that provide an opportunity for differentiation for students ready for more of a challenge. There are two types of exploration questions. One type is a hands-on activity directly related to the material of the unit that students can do either in class if they have free time, or at home. The second type of exploration is more open-ended and challenging. These problems go deeper into grade-level mathematics. They are not routine or procedural, and they are not just “the same thing again but with harder numbers. Exploration questions are intended to be used on an opt-in basis by students if they finish a main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in exploration problems, and it is not expected that any student works on all of them. Exploration problems may also be good fodder for a Problem of the Week or similar structure.” Examples include:

  • Unit 2, Numbers 1-10, Section B, Practice Problems, Problem 6 (Exploration), “Make a set of cards with images. Some cards can have the same number of images and some cards can have different numbers of images. Trade your cards with a partner. Turn over two cards and decide if they have the same number or if one has fewer and one has more.”

  • Unit 4, Understanding Addition and Subtraction, Section A, Practice Problems, Problem 5 (Exploration), “Start with a full 5-frame. Player 1 rolls a cube on the number mat and takes away or adds that number of counters while player 2 is not looking. Then player 2 figures out what player 1 did. Players take turns switching roles.”

  • Unit 7, Solid Shapes All Around Us, Section B, Practice Problems, Problem 5 (Exploration), “a. Count out 18 connecting cubes. Can you build a box with your cubes?; b. Count out 20 connecting cubes. Can you build a box with your cubes?”

Indicator 3O
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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 Open Up Resources K-5 Math Kindergarten 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.

Students engage with problem-solving in a variety of ways. According to the Resources, Course Guide, Design Principles, Coherent Progression, “Each lesson starts with a warm-up to activate prior knowledge and set up the work of the day. This is followed by instructional activities in which students are introduced to new concepts, procedures, contexts, or representations, or make connections between them. The lesson ends with a synthesis to consolidate understanding and make the learning goals of the lesson explicit, followed by a cool-down to apply what was learned.” Examples of varied approaches include:

  • Unit 3, Flat Shapes All Around Us, Section A, Lesson 2, Warm-up, “The purpose of this warm-up is to introduce students to the full Which One Doesn’t Belong routine. In this routine, students compare 4 different images and analyze the characteristics or attributes of the images. It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. In this warm-up, students compare 4 images of buttons. By the end of the section, students will compare 4 images of shapes. Listen to how students create an argument and use or revise their language to make their argument clear to others (MP3, MP6).”

  • Unit 5, Composing and Decomposing Numbers to 10, Section B, Lesson 7, Lesson Narrative, “Throughout this section, the teacher records student responses with equations. Equations are read aloud to students as “10 is 5 plus 5.” Students will be asked to interpret and work with equations in the next section.”

  • Unit 7, Solid Shapes All Around Us, Section A, Lesson 5, Cool-down, "Student Responses: Accurately retell a story problem in their own words, use objects, drawings, or equations to represent a story problem, explain connections between objects, drawings, story problems, and equations."

  • Unit 8, Putting it All Together, Section B, Lesson 9, Activity 2, “The purpose of this activity is for students to answer mathematical questions about their school community (MP4). Students work with a partner to choose a question to answer. Students work together to develop a plan for how they will answer the question and what, if any, math tools they will need. Then students have time to work together to answer the question. Students will need an opportunity to go out into the school to answer many of the questions. If necessary, this activity can be adjusted to be completed in one room or one area of the school. If time allows, students can pick multiple questions to answer.”

Indicator 3P
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Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Open Up Resources K-5 Math Kindergarten provide opportunities for teachers to use a variety of grouping strategies.

Suggested grouping strategies are consistently present within the activity launch and include guidance for whole group, small group, pairs, or individuals. Examples include:

  • Unit 2, Numbers 1–10, Section D, Lesson 21, Warm-up, Launch, “Groups of 2. Display and read the story. ‘What is the story about?’ 30 seconds: quiet think time. Share responses. Read the story again. ‘How can you act out the story?’ 30 seconds: quiet thinking time.” Student Work Time, “‘Discuss your thinking with your partner.’ 1 minute: partner discussion. Share responses. Choose a way to represent the story as a class. Read the story together.” 

  • Unit 5, Composing and Decomposing Numbers to 10, Section B, Lesson 7, Activity 3, Student Work Time, “10 minutes: partner work time. “Now you can choose another center. You can also continue playing Math Stories.” Display the center choices in the student book. Invite students to work at the center of their choice. 10 minutes: center work time, If time, invite students to choose another center.”

  • Unit 8, Putting It All Together, Section A, Lesson 1, Activity 1, Launch “Give each student a bag of beads.; ‘Sort your beads into two groups.’ 1 minute: independent work time.” Student Work Time, “‘How many beads in each group? Show our thinking using drawings, numbers, or words.’ 3 minutes: independent work time. ‘Compare the number of beads in each group. Which has more beads? Which has fewer beads? Circle the group that has fewer beads.’ 1 minute: independent work time. " ‘Tell your partner which group has fewer beads using this sentence: ‘There are fewer ____ than ____.’ 1 minute: partner discussion.”

Indicator 3Q
02/02

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 Open Up Resources K-5 Math 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.

Guidance is consistently provided to 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 Resources, Course Guide, Mathematical Language Development and Access for English Learners, “In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” Examples include:

  • Unit 3, Flat Shapes All Around Us, Section B, Lesson 13, Activity 2, “Students use positional words to describe the location of pattern blocks within a larger shape. Access for English Learners - Listening, Speaking: MLR8 Discussion Supports. For each description that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language, specifically position words.”

  • Unit 4, Understanding Addition and Subtraction, Lesson 13, Activity 1, “Access for English Learners - Representing, Listening: MLR2 Collect and Display. Circulate, listen for and collect the language students use as they create story problems. On visible display, record words and phrases such as: ‘more,’ ‘joined,’ ‘went away,’ ‘take away,’ and ‘less.’ Review the language on the display, then ask, ‘Which of these words tell you the story is about addition?’ and ‘Which of these words tell you the story about subtraction?’”

  • Unit 7, Solid Shapes All Around Us, Lesson 3, Warm-up, Instructional Routine, MLR7: Compare and Connect, Notice and Wonder, "The purpose of this warm-up is to elicit the mathematical questions that students produce about shapes composed of pattern blocks, which will be useful when students create and ask questions about shapes in a later activity. While students may notice and wonder many things about the shape, the questions that students can answer about the image are the important discussion points. As students discuss and justify their questions and answers, they share a mathematical claim and the thinking behind it (MP3)."

Indicator 3R
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Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Open Up Resources K-5 Math Kindergarten provide a balance of images or information about people, representing various demographic and physical characteristics.

Materials represent a variety of genders, races, and ethnicities. All are indicated with no biases and represent different populations. Names refer to a variety of backgrounds such as: Priya, Han, Mai, Diego. Settings include rural, urban, and multicultural environments. Examples include:

  • Unit 2, Numbers 1-10, Section A, Lesson 4, Warm-up, “How Many Do You See: Fingers on One Hand.” Drawings portray hands of different colors. Activity 1, “Which Has More? Two students are drawn, Priya and her family are sitting down at the table for dinner.” Drawn are two children placing plates at the table. One has sandy blonde hair, the other has brown hair. 

  • Unit 3, Flat Shapes All Around Us, Section B, Lesson 10, Warm-up, "The purpose of this warm-up is to elicit the idea that shapes can be combined to make patterns and pictures, which will be useful when students put together pattern blocks to make shapes in a later activity. While students may notice and wonder many things about these images, the shapes in the design of the quilt are the important discussion points. The images in this warm-up are of quilts made by a group of women in Gee’s Bend, Alabama. Consider reading the book Stitchin’ and Pullin’: A Gee’s Bend Quilt, by Patricia McKissack, and showing students more examples of quilts as a part of the Notice and Wonder activity. Examples of quilts from the book that are made of different shapes than the one shown in the student workbook will give students the opportunity to notice and wonder different things." There is a picture with a group of African American women around a quilt.

  • Unit 5, Composing and Decomposing Numbers to 10, Assessments, End-of-Unit Assessment, Problem 3, “Mai has a train of 7 connecting cubes. She snaps the train into two pieces. Show 1 way to snap the cubes. Show a different way to snap the cubes.”

Indicator 3S
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Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Open Up Resources K-5 Math Kindergarten partially provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials include a Spanish version of the Family Letter. The Family Role section also includes a Spanish Glossary and Family Materials to provide guidance for each unit.

The Course Guide, Mathematical Language Development and Access for English Learners outlines the program’s approach towards language development, “In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” While language routines are regularly embedded within lessons and support mathematical development, they do not include specific suggestions for drawing on students’ home language.

Indicator 3T
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Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Open Up Resources K-5 Math Kindergarten provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

According to Resources, Course Guide, Design Principles, Authentic Use of Contexts and Suggested Launch Adaptations, “The use of authentic contexts and adaptations provide students opportunities to bring their own experiences to the lesson activities and see themselves in the materials and mathematics. When academic knowledge and skills are taught within the lived experiences and students’ frames of reference, ‘They are more personally meaningful, have higher interest appeal, and are learned more easily and thoroughly’ (Gay, 2010). By design, lessons include contexts that provide opportunities for students to see themselves in the activities or learn more about others’ cultures and experiences. In places where there are opportunities to adapt a context to be more relevant for students, we have provided suggested prompts to elicit these ideas.” Examples include:

  • Unit 2, Numbers 1-10, Lesson 4, Activity 1, Instructional Routines, “The context of family mealtimes that is introduced in this activity will be revisited throughout the unit. Acting it out gives students an opportunity to make sense of a context (MP1). As students share about the tools that they use when eating with their families, record and save their responses to refer to and add to in future lessons. Consider reading picture books about family mealtimes. Some suggestions include: Full, Full, Full of Love by Trish Cooke, Bee-Bim Bop! by Linda Sue Park, Yoko by Rosemary Wells, The Little Red Hen (Makes a Pizza) by Philemon Sturges Rice & Rocks by Sandra L. Richards.”

  • Unit 4, Understanding Addition and Subtraction, Section B, Lesson 6, Lesson Narrative, “In previous lessons, students demonstrated the actions of addition and subtraction with objects and counted to find the total or difference. This lesson introduces students to addition and subtraction in the context of a story, which will be explored throughout this section. The pictures and stories are about students playing at recess, which allows students to relate to and act out the stories directly and helps them understand the connection between what they act out and what happens in the story (MP2).”

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 13, Activity 1, “The purpose of this activity is for students to identify and describe solid shapes in their environment (MP4, MP6). The shape walk can occur in many locations, such as a classroom, school, gym, playground, or library. Additional objects may need to be added to the environment to ensure that there are examples of a variety of solid shapes. Students may identify objects that are not exact examples of solid shapes. If this happens, consider acknowledging similarities between the shapes (“This shape has a point like a cone, but it is not a cone.”). Students use their own language to describe the solid shapes and are not required to use names of solid shapes. As students identify solid shapes, encourage students to describe the location of the object using positional words such as above, below, beside, and next to.”

Indicator 3U
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Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Open Up Resources K-5 Math Kindergarten provide supports for different reading levels to ensure accessibility for students.

In Resources, Course Guide, Universal Design for Learning and Access for Students with Disabilities, Representation, “Teachers can reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports provide students with multiple means of representation, include suggestions that offer alternatives for the ways information is presented or displayed, develop student understanding and use of mathematical language symbols, and describe organizational methods and approaches designed to help students internalize learning.” The supports develop sense-making and accessibility for students. Examples include:

  • Course Guide, Mathematical Language Development and Access for English Learners, Math Language Routine, MLR6: Three Reads, “‘Use this routine to ensure that students know what they are being asked to do, create opportunities for students to reflect on the ways mathematical questions are presented, and equip students with tools used to actively make sense of mathematical situations and information’ (Kelemanik, Lucenta, & Creighton, 2016). This routine supports reading comprehension, sense-making, and meta-awareness of mathematical language. How It Happens: In this routine, students are supported in reading and interpreting a mathematical text, situation, diagram, or graph three times, each with a particular focus. Optional: At times, the intended question or main prompt may be intentionally withheld until the third read so that students can concentrate on making sense of what is happening before rushing to find a solution or method. 1. Read #1: “What is this situation about?” After a shared reading, students describe the situation or context. This is the time to identify and resolve any challenges with any non-mathematical vocabulary. (1 minute); 2. Read #2: “What can be counted or measured?” After the second read, students list all quantities, focusing on naming what is countable or measurable in the situation. Examples: “number of people in a room” rather than “people,” “number of blocks remaining” instead of “blocks.” Record the quantities as a reference to use when solving the problem after the third read. (3–5 minutes); 3. Read #3: “What are different ways or strategies we can use to solve this problem?” Students discuss possible strategies. It may be helpful for students to create diagrams to represent the relationships among quantities identified in the second read, or to represent the situation with a picture (Asturias, 2014). (1–2 minutes).”

  • Unit 3, Flat Shapes All Around Us, Section B, Lesson 12, Activity 1, “Students use pattern blocks to fill in puzzles that don’t show each individual pattern block. Students may experiment with different shapes or begin with a part of the puzzle where they can see what shape looks like it will fit. In either case, as they fill in the puzzle, each choice they make will influence which shapes they can use and whether or not they can fill in the entire puzzle so students will need to persevere and likely go back and make changes. (MP1).” Strategies indicated for students include starting with a smaller shape in the puzzle, and differentiating the degree of difficulty or complexity by allowing students to start with a shape that is familiar to them.

  • Unit 7, Solid Shapes All Around Us, Section B, Lesson 8, Lesson Narrative, “Students are introduced to the terms heavy, light, heavier, and lighter to describe and compare the weights of objects (MP6.) Students initially describe and compare the weights of objects when the comparison is visually obvious and brainstorm ideas for how to compare the weights of objects when they cannot tell by looking at which object is heavier. Then students work in groups to compare the weights of objects and record the comparison.”

Indicator 3V
02/02

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 Open Up Resources K-5 Math Kindergarten meet 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.

Suggestions and/or links to manipulatives are consistently included within materials to support the understanding of grade-level math concepts. Examples include:

  • Unit 2, Numbers 1-10, Section A, Lesson 3, Activity 1, Student Work Time, “Give each group of students a bag of pattern blocks. ‘Take the pattern blocks out of your bag. Are there more orange squares or green triangles?’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘How do you know if there are more orange squares or more green triangles?’ Share responses. ‘Figure out and tell your partner how many orange squares you have. Then figure out how many green triangles you have.’ 2 minutes: partner work time. ‘Switch your bag of objects with another group.’ Repeat the steps above, asking ‘Are there fewer …?’ instead of ‘Are there more …?’”

  • Unit 4, Understanding Addition and Subtraction, Section B, Lesson 9, Activity 1, “Groups of 2. Give students access to two-color counters, connecting cubes, and markers. Read and display the task statement. ‘Tell your partner what happened in the story.’ 30 seconds: quiet think time. 1 minute: partner discussion. Monitor for students who accurately retell the story. Choose at least one student to share with the class. Reread the task statement. ‘Show your thinking using drawings, numbers, words, or objects.’”

  • Unit 6, Numbers 0-20, Section A, Lesson 3, Activity 3, “The purpose of this activity is for students to learn stage 1 of the Find the Pair center. Students develop fluency with addition and subtraction within 5 as they find the number that makes 5 when added to a given number. Each student draws a hand of 5 cards. Students take turns asking their partner for a card that goes with one of their cards to make 5. When students receive a match, they write an expression. Students draw a new card when they do not receive a match. Students may use math tools such as 5-frames or draw a picture to make 5.”

Criterion 3.4: Intentional Design

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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 Open Up Resources K-5 Math Kindergarten do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards; do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other; have a visual design that supports students in engaging thoughtfully with the subject that is neither distracting nor chaotic; and partially provide teacher guidance for the use of embedded technology to support and enhance student learning. 

Indicator 3W
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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 Open Up Resources K-5 Math Kindergarten do not 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. According to the Course Guide, About These Materials, “Teachers can access the teacher materials either in print or in browser as a digital PDF. When possible, lesson materials should be projected so all students can see them.” While this format is provided, the materials are not interactive.

Indicator 3X
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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 Open Up Resources K-5 Math Kindergarten do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

According to the Course Guide, Key Structures in this Course, Developing a Math Community, “Classroom environments that foster a sense of community that allows students to express their mathematical ideas—together with norms that expect students to communicate their mathematical thinking to their peers and teacher, both orally and in writing, using the language of mathematics—positively affect participation and engagement among all students (Principles to Action, NCTM).” While the materials embed opportunities for mathematical community building through student task structures, discourse opportunities and journal/reflection prompts do not reference digital technology.

Indicator 3Y
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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 Open Up Resources K-5 Math Kindergarten have a visual design (whether print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within units and lessons that supports student understanding of the mathematics. According to the Course Guide, Design Principles, “Each unit, lesson, and activity has the same overarching design structure: the learning begins with an invitation to the mathematics, is followed by a deep study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.” Examples from materials include:

  • Each lesson follows a common format with the following components: Warm-up, one to three Activities, Lesson Synthesis, and Cool-down (when included in lessons). The consistent structure includes a layout that is user-friendly as each lesson component is included in order from top to bottom on the page.

  • Student materials, in printed consumable format, include appropriate font size, amount and placement of direction, and space on the page for students to show their mathematical thinking.

  • Teacher digital format is easy to navigate and engaging. There is ample space in the printable Student Task Statements, Assessment PDFs, and workbooks for students to capture calculations and write answers.

Indicator 3Z
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Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Open Up Resources K-5 Math Kindergarten partially provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable. Lessons include links to Community Created Resources that provide teachers with Google Slides for each lesson. No additional guidance is provided within the slide decks. For example, Unit 1, Math in Our World, Section A, Lesson 1, Preparation, Downloads, “Community Created Resources: Google Slides.”