The big ideas in IM Kindergarten include: representing and comparing whole numbers, initially with sets of objects; understanding and applying addition and subtraction; and describing shapes and space. In IM Kindergarten, more time is devoted to numbers than to other topics. The materials, particularly units that focus on addition and subtraction, include problem types, such as Add To, Take From, Put Together or Take Apart, Compare, Result Unknown, and so on. These problem types are based on common addition and subtraction situations, as outlined in Table 1 of the “Mathematics Glossary” section of the Common Core State Standards (NGA & CCSSO).
In this unit, students explore mathematical tools and notice numbers and quantities around them. Teachers gather information about students’ counting skills and understanding of number concepts.
Students enter kindergarten with a range of counting experiences, concepts, and skills. So, this unit is designed to be accessible to all learners regardless of their prior experience. In the first three sections, activities do not require counting, 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.
In the last section, students count collections of objects and groups of people to answer, “how many?” questions. These questions reinforce the idea that counting is a way to tell how many objects there are. Counting up to 10 objects will support students in the next unit, which will focus more deeply on numbers 1–10.
The content of this unit is designed to establish the structures and routines for centers, to create norms for classroom learning, and to begin building a mathematical community. In the first section, lessons are shorter to give students time to learn these routines and norms and to develop a mathematical community.
At different points throughout the unit, consider asking individual students to count a small group of objects. As the student works, observe the skills or understandings in the Checklist provided at the beginning of each section and in the Unit 1 Sections A–D Checkpoint document in the teacher resource packet. The end-of-unit assessment (a one-on-one interview) is another opportunity to find out what students know and can do. This assessment is not necessary for students who have demonstrated the skills on the checklist throughout the unit.
Lesson 1: Explore Connecting Cubes
Lesson 2: Explore Pattern Blocks
Lesson 3: Explore 2-Color Counters and 5-Frames
Lesson 4: Explore Geoblocks
Lesson 5: Explore Math Tools
Lesson 6: Look for Small Groups
Lesson 7: Classroom Scavenger Hunt
Lesson 8: Different Groups, Same Quantity
Lesson 9: Create Picture Books
Lesson 10: Are There Enough?
Lesson 11: Get Enough
Lesson 12: How Many Are There? (Part 1)
Lesson 13: How Many Are There? (Part 2)
Lesson 14: Answer “How Many?” Questions
Lesson 15: Explain How You Counted
Lesson 16: Represent Our Collections
Lesson 17: Model with Math Tools
In this unit, students continue to develop counting concepts and skills, including comparing groups of objects and images, and representing quantities with objects, pictures, and numbers.
Previously, students learned structures and routines for activities and centers. They counted up to 10 objects to answer “how many?” questions. They also answered “are there enough?” questions—the basis of comparing quantities.
Here, students rely on familiar activity structures to build counting skills and an understanding of the connection between quantities and numbers. Students first count groups of objects. Then they count groups of images. Objects and images appear in different arrangements, such as lines, arrays, number cube patterns, and on 5-frames. This helps build an understanding that changing the arrangement doesn’t change the quantity.
Use of fingers and 5-frames to represent numbers are emphasized to help students see the structure of numbers 6–10 as \(5+n\). Fingers are also always available and help with counting.
These fingers show 3.
These fingers show 8.
Students also compare numbers of objects and images. To describe the comparisons, students start by using the terms “fewer” and “more.” Later, when comparing written numbers, the term “less” is introduced. In general, “less” is used to compare numerals, and “fewer” is used to compare groups of objects. Students may use these terms interchangeably at first, but they will develop proficiency with the distinction over time.
Lesson 1: Fingers as a Math Tool
Lesson 2: Count and Arrange
Lesson 3: Groups That Look Very Different
Lesson 4: Groups That Look Alike
Lesson 5: Make Groups of More, Fewer, or the Same
Lesson 6: Use “More,” “Fewer,” or “the Same Number” to Describe Groups
Lesson 7: Write Numbers 1–5
Lesson 8: Write Numbers 6–10
Lesson 9: Count Images in Different Arrangements
Lesson 10: Compare Matching Images
Lesson 11: More, Fewer, or the Same
Lesson 12: Find More, Fewer, or the Same
Lesson 13: Create Groups of Images
Lesson 14: Connect Quantities and Numbers
Lesson 15: Numbers in Many Ways
Lesson 16: Count Out Objects
Lesson 17: Draw Groups of Things
Lesson 18: Write Numbers to Represent Quantities
Lesson 19: Order Towers and Numbers
Lesson 20: 1 More or 1 Less with Towers and Numbers
Lesson 21: Compare Numbers and Images
Lesson 22: Represent and Compare Numbers
Lesson 23: Compare Numbers
Lesson 24: Set the Table
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 objects in their environment to the geometric term.
For instance, students may say that only one of the two shapes is a triangle—the isosceles triangle sitting on its base—because they have seen examples like it 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.”
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 defines each shape until grade 1.) Students also learn a key idea, that congruent shapes are still “the same” even if they are in different orientations.
Later in the unit, students use pattern blocks to make larger shapes. They reinforce their counting and comparison skills as they count and compare the pattern blocks used to create larger shapes. Students also use positional words (above, below, next to, beside) to describe the shapes they compose.
Lesson 1: What We Know about Shapes
Lesson 2: Match Shapes
Lesson 3: Describe and Compare Shapes
Lesson 4: Describe, Compare, and Sort Shapes
Lesson 5: Circles and Triangles
Lesson 6: Rectangles and Squares
Lesson 7: Build with Straws
Lesson 8: Draw Shapes
Lesson 9: Shapes Are Everywhere
Lesson 10: Put Together Pattern Blocks
Lesson 11: Same Shapes
Lesson 12: More than 1 Way to Make a Shape
Lesson 13: Describe and Match Shapes
Lesson 14: Shapes in Art
Lesson 15: Animal Shape Stamp Art
In this unit, students develop their understanding of addition and subtraction as they represent and solve story problems.
Previously, students developed their counting skills. Students learn addition as an extension of counting through joining two groups and counting to find the total. Students also extend their counting through subtraction. They count to find and remove objects within a collection and then count what remains. (The word “total” is used instead of “sum” to avoid confusion with the word “some” or part of a whole.)
Students then represent and solve Add To, Result Unknown and Take From, Result Unknown story problems. Students represent the problems in different ways, by acting them out, drawing, using numbers, or using objects. Connecting cubes and two-color counters should be made accessible in all lesson activities, including cool-downs, for students that want to use them throughout the unit.
Students are also introduced to expressions, a symbolic way to represent addition and subtraction. Initially, the teacher records the process of adding and subtracting using words such as “5 and 3” or “4 take away 1.” Later, students see that “5 and 3” and “4 take away 1” can be expressed by 5+3 and 4–1 , respectively. They learn these expressions are read as “5 plus 3” and “4 minus 1.” Students are not expected to read expressions out loud or to use precise language at this point.
Later in the unit, students connect expressions to pictures and story problems. They find the value of addition and subtraction expressions within 10.
In a future unit, students will compose and decompose numbers up to 10 and solve other types of addition and subtraction problems.
Lesson 1: Count 2 Groups of Objects
Lesson 2: Count 2 Groups of Images
Lesson 3: Count 2 Groups of Scattered Images
Lesson 4: Add with Objects
Lesson 5: Subtract with Objects
Lesson 6: Tell and Act Out Stories
Lesson 7: Use Objects to Represent Stories
Lesson 8: Represent and Solve Story Problems
Lesson 9: Solve Story Problems
Lesson 10: Compare Drawings
Lesson 11: Drawings to Represent Story Problems
Lesson 12: Compare Addition and Subtraction Story Problems
Lesson 13: Create Story Problems
Lesson 14: Expressions and Story Problems
Lesson 15: Expressions and Drawings
Lesson 16: Find the Value of Expressions
Lesson 17: Add 0 and 1
Lesson 18: Tell Story Problems for Expressions
In this unit, students explore different ways to compose and decompose numbers within 10 and to represent the compositions and decompositions.
Previously, students counted and compared groups and images of up to 10 objects. Students solved addition and subtraction story problems and wrote expressions to represent the problems. In this unit, students use those experiences to compose and decompose numbers within 10. (The terms “make” or “break apart” are used with students.)
Special attention is given to composing and decomposing 10, as it is the basis of place value in our number system. To support their reasoning, students use their fingers and a 10-frame—created by putting together two 5-frames. They use these tools to think about pairs of numbers that make 10.
Symbolic notation develops slowly across the units. Students first complete expressions that represent numbers being composed and decomposed. They also practice writing numbers without handwriting lines.
Later, students encounter equations of the form \(5 = 3 + 2\). Teachers read this equation as “5 is 3 plus 2.” Note that the equations are written with the total on the left side of the equal sign and the addends on the right. Aside from representing composition and decomposition, this notation helps students see that the equal sign means that “both sides have the same value,” rather than “the answer comes next.” In a later unit, students will see equations with the addends on the left side.
The work in this unit prepares students to make sense of teen numbers in the next unit and lays the groundwork for students to develop fluency with addition and subtraction facts within 10 in grade 1. (For example, to find the sum of \(9 + 5\), they can decompose 5 into \(1 + 4\) and find \(9 + 1 + 4\) or \(10+ 4\).) Much of the addition and subtraction work in future grades also hinges on the idea of composing and decomposing numbers, 10 in particular.
Lesson 1: Make 2 Parts
Lesson 2: Make and Break Apart Pattern Block Designs
Lesson 3: Snap the Cubes
Lesson 4: Find All the Ways
Lesson 5: Put Together
Lesson 6: Red and Yellow Apples
Lesson 7: Solve Both Addends In Unknown Story Problems
Lesson 8: More than One Way
Lesson 9: Story Problems
Lesson 10: Introduce the 10-Frame
Lesson 11: Equations That Show 10
Lesson 12: How Many Are Missing?
Lesson 13: Make 10
Lesson 14: Towers of 10
Lesson 15: Packing Up Fruit
In this unit, students count and represent collections of objects and images within 20. They apply previously developed counting concepts, such as one-to-one correspondence, keeping track of what has been counted, and conservation of numbers, to larger numbers.
Previously, students counted, composed, and decomposed numbers up to 10. They used counters, connecting cubes, 5-frames, 10-frames, drawings, their fingers, and other tools. They also wrote expressions to record compositions and decompositions.
Here, students use the 10-frame to organize groups of 11–19 objects and images. This tool encourages students to see teen numbers as 10 and some more, emphasizing the \(10+n\) structure of the numbers 11–19. Students use this structure as they represent teen numbers with their fingers, objects, drawings, expressions, and equations. Students see equations with the addends written first, such as \(10 + 6 = 16\). It is important to note that students are not expected to think of 10 ones as a unit called “a ten” or refer to single units as "ones" until Grade 1.
Throughout the unit, students practice tracing and writing numbers 11–20. It is common for students at this stage to write numbers backwards, so the emphasis is on writing a number that is recognizable to others. Reversing the order of the digits of teen numbers is also expected, due to how teen numbers are said in English. Repeatedly seeing the number 1 written first to represent teen numbers helps students recognize the structure of these numbers.
When tracing and writing numbers, students should write on a flat surface while sitting in a chair with feet flat on the floor. Number writing practice can also happen in other parts of the day and can be done using a variety of writing tools (crayons, colored pencils, markers, and so on) for increased engagement. Students can practice creating numbers with dough, tracing numbers in sand, or forming numbers with pipe cleaners.
Lesson 1: Count Larger Collections of Objects
Lesson 2: Keep Track of Objects
Lesson 3: Count Carefully
Lesson 4: Does the Number Change?
Lesson 5: How Many Fingers? How Many Dots?
Lesson 6: Fingers and 10-Frames
Lesson 7: Make Numbers with 10 and Some More (Part 1)
Lesson 8: Make Numbers with 10 and Some More (Part 2)
Lesson 9: Expressions and Equations
Lesson 10: Complete Equations
Lesson 11: Count Images (Part 1)
Lesson 12: Count Images (Part 2)
Lesson 13: Design a Garden
In this unit, students explore solid shapes while reinforcing their knowledge of counting, number writing and comparison, and flat shapes. They compose figures with pattern blocks and continue to count up to 20 objects, write and compare numbers, and solve story problems.
In an earlier unit, students investigated two-dimensional shapes. They named shapes (circle, triangle, rectangle, and square) and described the ways the shapes are different. Students used pattern blocks to build larger shapes and used positional words (above, below, next to, beside) along the way.
Here, students distinguish between flat and solid shapes before focusing on solid shapes. They consider the weights and capacities of solid objects and identify solid shapes around them.
Geoblocks, connecting cubes, and everyday objects are used throughout the unit. Standard geoblock sets do not include cylinders, spheres, and cones. When these shapes are required, “solid shapes” are indicated as required materials. If solid shapes are not available, students can work with everyday items that represent each shape.
The mathematical names cube, cone, sphere, and cylinder are introduced in this unit; however, students are not expected to use the names of solid shapes. Students can and are encouraged to continue to use their own language to describe and identify solid shapes.
3 cones
4 cubes
5 cylinders
How many shapes did you use all together?
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.
Lesson 1: Build Shapes
Lesson 2: More or Fewer Pattern Blocks
Lesson 3: Questions and Stories about Shapes
Lesson 4: Pattern Block Puzzles and Equations
Lesson 5: Story Problems about Shapes
Lesson 6: Make and Break Apart 10 with Pattern Blocks
Lesson 7: Flat and Solid Shapes
Lesson 8: Compare Weights
Lesson 9: Compare Capacities
Lesson 10: Identify and Describe Solid Shapes
Lesson 11: Compare and Sort Solid Shapes
Lesson 12: Build Solid Shapes
Lesson 13: Describe Solid Shapes around Us
Lesson 14: Build with Solid Shapes
Lesson 15: Build and Count with Solid Shapes
Lesson 16: Represent the Classroom with Shapes
In this unit, students apply their learning from the year, revisiting the major work and fluency goals of the grade.
Section A focuses on the concepts of counting and comparing. Section B highlights the presence of math in students' school community. Section C enables students to practice composing and decomposing numbers within 5, as well as adding and subtracting within 5. Section D focuses on composing and decomposing 10.
The sections in this unit are standalone sections, not required to be completed in order. The goal is to offer ample opportunities for students to integrate the knowledge they have gained and to practice skills related to the expected fluencies of the grade.
The content here lays the foundation for grade 1, where students add and subtract fluently within 10 and count and compare larger quantities. Students also learn about "ten" as a unit, which is the basis for understanding place value in the base-ten system.
Lesson 1: Sort, Count, and Compare Groups of Objects
Lesson 2: Count and Compare Collections
Lesson 3: Count to Add and Subtract
Lesson 4: 1 More and 1 Less
Lesson 5: Order Numbers 1–20
Lesson 6: Create Number Books (Part 1)
Lesson 7: Create Number Books (Part 2)
Lesson 8: Find Someone Who, Find Something That
Lesson 9: Where’s the Math?
Lesson 10: Tell Stories about Our School
Lesson 11: Share Story Problems
Lesson 12: Make Dot Images
Lesson 13: Dominoes to 5
Lesson 14: Sort and Color Expressions and Images within 5
Lesson 15: Addition and Subtraction Expressions within 5
Lesson 16: Parts to Make 5
Lesson 17: Make and Break Apart 10
Lesson 18: All the Ways to Make 10
Lesson 19: Find the Number That Makes 10
Lesson 20: More or Fewer than 10?
Lesson 21: Make and Break Apart Numbers 11–19
Pacing Guide
The number of days includes two assessment days per unit. The upper bound of the range includes optional lessons.
Dependency Diagram
In the unit dependency chart, an arrow indicates that a particular unit is designed for students who already know the material in a previous unit. Reversing the order of the units would have a negative effect on mathematical or pedagogical coherence.
The following chart shows unit dependencies across the curriculum for IM Grades 3–8.
Section Dependency Diagrams
In the section dependency charts, an arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.
Big Ideas and Content Connections
IM v.360 organizes each grade level into eight or nine units that each address a major concept and a group of related standards. The unit titles communicate the major concepts that are covered in each grade level.
One way to visualize the content connections is by mapping where each domain of the California Common Core State Standards for Mathematics is covered in IM v.360. Each unit generally addresses several related standards within a primary domain, while also making connections to relevant standards in other supporting domains. This structure supports the vertical alignment of the curriculum as a whole. The domain connections diagrams for each grade band demonstrate that the architecture of the curriculum considers more than simply covering individual standards one by one.
All domain-related information has been coded by color/shape to demonstrate similarities and progressions across grade bands. The key is as follows:
Blue Rhombus:
K only: Counting & Cardinality (CC)
Red Triangle:
K–5: Operations & Algebraic Thinking (OA)
6–8: Expressions and Equations (EE)
9–12: HS Algebra (HSA)
Yellow Rectangle:
K–5: Numbers and Operations in Base Ten (NBT)
6–8: The Number System (NS)
9–12: HS Number and Quantity (HSN)
Orange Pentagon:
K–5: Numbers & Operations—Fractions (NF)
6–7: Ratios & Proportional Relationships (RP)
8: Functions (F)
9–12: HS Functions (HSF)
Purple Hexagon:
K–5: Measurement & Data (MD)
6–8: Statistics & Probability (SP)
9–12: HS Statistics & Probability (HSS)
Green Circle:
All grade levels: Geometry (G/HSG)
Primary Domains
This chart shows the primary domain addressed in each unit. Other supporting domains are not shown here but are shown in the charts below.
Counting and Cardinality
The Counting and Cardinality (CC) domain, while specific to Kindergarten, underlies the Operations and Algebraic Thinking (OA) domain as well as Numbers and Operations in Base Ten (NBT). It is foundational for students’ work in subsequent grades.
K: The CC domain is present in every unit within the Kindergarten course and prepares students for the work they will do throughout Grade 1. These skills are essential for students to grasp concepts that emphasize the NBT and OA domains, such as adding and subtracting within 20 and the understanding of numbers to 99. Here, we’ve highlighted the domain of each unit in IM v.360 Grade 1 that is most affected by the Counting and Cardinality work of Kindergarten.
Operations & Algebraic Thinking
Operations and Algebraic Thinking (OA) is a central domain within each course of IM K–5 v.360.
K–2: In Kindergarten, students begin exploring the OA domain through addition and subtraction in Unit 4, which supports their understanding of composing and decomposing numbers up to 10 in Unit 5. In Grade 1, students build on their understanding by adding and subtracting within 20. Finally, in Grade 2, students explore adding and subtracting within 100. The grade band culminates with students applying their understanding of this domain in Grade 2 Unit 8.
3–5: In Grade 3, students are introduced to multiplication and relating multiplication to division. Students apply this work in Grade 4 by investigating factors and multiples, solving word problems, and exploring multiplicative comparison and measurement. In Grade 5, students use the OA domain in various contexts to find volume, examine place value patterns, and apply operations to decimals.
Numbers & Operations in Base Ten
The Numbers and Operations in Base Ten (NBT) domain focuses on place value and operations ranging from multi-digit whole numbers to decimals up to the thousandths place.
K–2: The NBT domain is largely addressed in most units of Grades 1 and 2. In Kindergarten, students develop a strong understanding of numbers 0–20, which prepares them to work with numbers up to 99 in Grade 1. Here, students build familiarity with the base-ten system before adding within 100. Grade 2 furthers this understanding with a focus on adding and subtracting within 100, and continues moving students into numbers up to 1,000. Students finish Grade 2 with skills to add and subtract within 1,000.
3–5: In Grade 3, students start by working with whole numbers and addition and subtraction within 1,000. In Unit 4, they relate multiplication to division and use their knowledge of the place value system to multiply by multiples of 10. This work continues in Grade 4 as students apply the number system to larger multi-digit numbers in Unit 4 and multiply and divide multi-digit numbers in Unit 6. Grade 5 expands on and concludes these ideas in Units 4 and 5 where students explore place value patterns and decimal operations.
Numbers and Operations—Fractions
The Number and Operations—Fractions (NF) domain only applies to Grades 3–5, but it builds on the work in earlier grades in other domains.
3–5: The NF domain is first emphasized in Grade 3 when students begin to develop an understanding of fractions within the number system in Unit 5. This understanding continues to develop in Grade 4 as they compare fractions in Unit 2. In the next unit, students begin to multiply with fractions and relate fractions to decimals. In Grade 5, they add, subtract, multiply, and divide with fractions starting in Unit 2. This work prepares them to engage with the later Grade 5 concepts, multiplying and dividing fractions and more decimal and fraction operations.
Measurement and Data
In the Measurement and Data (MD) domain, students represent and interpret data, solve problems involving measurement, and work toward understanding concepts of perimeter, area, angle measures, and volume.
K–2: The MD domain is emphasized largely in Grades 1 and 2, while Kindergarten provides the foundational skills that students need in order to successfully develop key concepts. In Kindergarten, students work with classifying and comparing measurable attributes, including length. As they explore this domain in Grade 1, students learn concepts such as length measurements within 120 units and adding, subtracting, and working with data. In Grade 2, students build on that understanding by measuring length, practicing addition and subtraction on the number line, and adding, subtracting, and working with data.
3–5: Grade 3 lays a foundation for understanding geometric measurement with major concepts such as area and multiplication and two-dimensional shapes and perimeter. Grade 4 builds on this domain by exploring angles and angle measurement, and Grade 5 applies this work in Unit 1 as students are asked to find volume. In a similar trajectory, Grade 3 introduces students to different types of measurement, including length, time, liquid volume, and weight in Unit 6. Grade 4 builds on that work with multiplicative comparisons in Unit 5, and Grade 5 introduces conversions of these measures in Unit 6.
Geometry
In the Geometry (G) domain, students work with lines, angles, and shapes. They partition, examine attributes, and classify shapes based on their properties.
K–2: Each course in this grade band devotes an entire unit to the Geometry domain where the bulk of the work is concentrated. In Kindergarten, students specifically explore flat and solid shapes throughout two units. Grade 1 continues to examine shapes with the addition of time. Finally, Grade 2 builds on the previous work in the grade band with a special emphasis on geometry, time, and money.
3–5: Starting in Grade 3, students classify two-dimensional shapes based on their properties and also calculate perimeter. Grade 4 further examines shapes by studying angles in Unit 7 and exploring the properties of two-dimensional shapes in Unit 8. In Grade 5, students begin building the foundation for future work by working with the first quadrant in the coordinate plane in Unit 7.
Big Ideas by Grade Level
Each description of major concepts by grade level contains two tables to demonstrate how the units in IM v.360 map to California’s Big Ideas. The first table is organized by Big Idea and lists each unit that addresses its content. The second table is organized by unit title and lists each Big Idea that it addresses. These two tables share the same information in different formats to demonstrate the close alignment of IM v.360 and California’s Big Ideas. Each unit addresses at least one Big Idea, and each course covers all Big Ideas for the grade level.
In addition to California’s Big Ideas, the second table also showcases the California Common Core State Standards and Standards for Mathematical Practice that are central to each unit. The table lists standards that are addressed during that unit, though there may be additional standards that it builds on or builds toward. Similarly, while students have the opportunity to use all of the Standards for Mathematical Practice throughout each unit, the table highlights those that students are most likely to use. More details on content standards and Standards for Mathematical Practice can be found in the teacher materials for each lesson.
Each major concepts resource contains two exemplar lessons or activities that demonstrate how the curriculum directly supports other aspects of the California Framework. Please note that while language such as Content Connections and Drivers of Investigation may not be used to describe the examples, the lessons and activities have been intentionally chosen to address them across all courses.
The major concepts resources are intended to be viewed alongside the curriculum. Examples are referenced by their title and location in the curriculum rather than including the full text of every activity.
To get the most from the materials:
Navigate to the activity.
Skim the contents of the lesson it is contained within.
Read the full activity.
Read the description detailing the connection between this activity and the rest of the curriculum.
Major Concepts in Kindergarten
IM v.360 Kindergarten focuses on:
representing and comparing whole numbers, initially with sets of objects
understanding and applying addition and subtraction
describing shapes and space
The diagram below links the major concepts in IM v.360 Kindergarten to the domains found in the California Common Core State Standards for Mathematics (CA CCSSM). Each shape represents a domain that is addressed within the major concept. The larger shapes represent the primary domain while the smaller shapes on the periphery represent secondary domains that are addressed. The arrows demonstrate how the major concepts are interconnected and build on each other.
Exemplars:
Unit 2: Numbers 1–10 Lesson 10: Compare Matching Images AccessIM Link
Mathematical Practices: MP1, MP7
CA CCSSM Standards: K.CC.4, K.CC.5
Summary:
This lesson invites students to build their understanding of counting as they answer, “How many?” and “Are
there enough?” questions in the context of real-world situations. In these activities, students count,
represent, and compare whole numbers (1–10) with sets of objects while building toward numbers 0–20.
Students make sense of the world through the relatable and likely situation of setting a table and
comparing the number of students to the number of available items. They make sense of the problem and
persevere in solving it while looking for and making use of structure and strategies.
Unit 4: Understanding Addition and Subtraction Lesson 6: Tell and Act Out Stories Activity 1: What is Happening? AccessIM Link
Mathematical Practice: MP2
CA CCSSM Standard: K.OA.1
Summary:
In this activity, students build their understanding of representing addition and subtraction through
drawings, situations, and expressions while building on major concepts from previous units. Students learn
to mathematize their environment, which influences how they see the world. They reason abstractly and
quantitatively to strengthen their understanding of how mathematical representations can be used to solve
real-world problems.
California’s Big Ideas Within the IM Course
Sort and
Describe Data
How Many?
Bigger
or Equal?
Being Flexible
Within 10
Place and
Position of
Numbers
Model with
Numbers
Shapes in
the World
Making Shapes
from Parts
Units 1–7
Units 1–7
Units 1–7
Units 1–7
Units 1–7
Units 3–7
Unit 3
Unit 7
Unit 3
Unit 7
IM v.360 Kindergarten
Major Concepts
CA CCSSM
Domains*
California’s Big Ideas
CA Standards
MPs
Unit 1:
Math in Our World
CC
G
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Shapes in the world
Making shapes from parts
G.1
G.2
G.3
G.4
G.5
G.6
CC.1
CC.4
CC.5
MP1
MP2
MP3
MP4
MP5
MP6
Unit 2:
Numbers 1–10
CC
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
CC.1
CC.3
CC.4
CC.5
CC.6
CC.7
MP1
MP7
MP8
Unit 3:
Flat Shapes All
around Us
CC
MD G
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Model with numbers
Shapes in the world
Making shapes from parts
CC.1
CC.3
CC.4
CC.5
CC.6
CC.7
G.1
G.2
G.4
G.5
G.6
MD.2
MD.3
MP3
MP4
MP6
Unit 4:
Understanding Addition
and Subtraction
CC OA
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Model with numbers
CC.1
CC.2
CC.3
CC.4
CC.5
OA.1
OA.2
MP2
MP6
Unit 5:
Composing and
Decomposing
Numbers to 10
CC OA
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Model with numbers
CC.1
CC.2
CC.4
CC.5
OA.1
OA.2
OA.3
OA.4
OA.5
MP2
MP7
Unit 6:
Numbers 0–20
CC
OA
NBT
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Model with numbers
CC.1
CC.2
CC.3
CC.4
CC.5
CC.6
OA.1
OA.2
OA.3
OA.4
OA.5
NBT.1
MP7
MP8
Unit 7:
Solid Shapes All
around Us
CC
OA
MD G
Sort and describe data
How many?
Bigger or equal?
Being flexible within 10
Place and position of numbers
Model with numbers
Shapes in the world
Making shapes from parts