The big ideas that define units in InsightMath provide a framework for making connections across the domains and clusters defined by the Common Core State Standards for Mathematics. A description of where and how domains and clusters are connected within each big idea is described in the table below.
Connections Across Domains and Clusters - Grade K
| Unit | Big Idea | Connections Across Domains and Clusters | Major Clusters |
Additional/ Supporting Clusters |
Unit 1 |
Mathematics is a way to think about and describe the world. |
In this unit, students begin to explore what it means to think mathematically. They develop their own schema for how to participate in a mathematics community as they describe various mathematical tools and consider how to use them. Students also build a schema for making comparisons while exploring length (K.MD.A and K.CC.C) and quantity using new comparative vocabulary. They formalize their understanding of number words and numerals as they associate these words and symbols with counting and cardinality (K.CC.A and K.CC.B), setting up the foundations of a schema that will go on to support their understanding of algebraic thinking, the place value system, and their relationship to numbers and number sense. |
K.CC.A K.CC.B K.CC.C |
K.MD.A K.G.A |
Unit 2 |
A number represents a fixed quantity, each being one more than the previous number in the count sequence. |
In this unit, students expand their number representation schema. They move beyond mechanical counting sequences to understanding numbers as quantities that remain constant regardless of arrangement or counting order (K.CC.B). Students develop their understanding that each number in the count sequence represents one more than the previous number, building a foundation for comparing quantities and recognizing magnitude relationships. Students use this understanding to move from making comparisons using matching strategies toward counting strategies, understanding that a number that comes later in the count sequence represents a greater quantity (K.CC.B and K.CC.C). The use of a number path model helps students develop a linear schema of numbers that supports comparisons and understanding of magnitude. |
K.CC.A K.CC.B K.CC.C |
None |
Unit 3 |
Numbers are composed of other numbers. | In this unit, students expand their schema of numbers as they discover the key idea that numbers can be broken into parts. They develop an understanding that a quantity can be viewed both as separate groups and as one total, supporting the Big Idea that numbers are composed of other numbers. They begin by decomposing a set into two categories in various ways (K.MD.B), recognizing that the total remains the same even when the size of the parts is different (K.OA.A). They extend to composing a number in various ways, keeping track of the total as they create the parts. Students begin to use counting on from one part as a more sophisticated counting strategy to counting all items in a set (K.CC.B), an extension of counting on from any number in the count sequence (K.CC.A). This foundational work with parts and totals sets the stage for future work with addition and subtraction. |
K.CC.A K.CC.B K.OA.A |
K.MD.B K.G.A |
Unit 4 |
Addition and subtraction are the mathematics of parts and totals. | In this unit, students parlay their understanding that numbers can be composed of other numbers into seeing how numbers can be put together and taken apart in meaningful ways. This serves as students’ formal introduction to addition and subtraction as actions that change quantities (K.OA.A). At the same time, they see those actions of joining and taking apart as ways to understand parts and totals. As such, they connect addition and subtraction to counting and the count sequence (K.CC.A and K.CC.B). They apply counting strategies such as count all, count on, and count back to add and subtract. They also continue to use tools including the number path, which builds their linear schema of numbers (K.CC.B )and stacks of 10 which begins to build familiarity with 10 pairs. As they connect their physical actions to mathematical symbols, students build foundations for working flexibly with numbers and recognizing patterns in addition and subtraction situations. |
K.CC.A K.CC.B K.CC.C K.OA.A |
None |
Unit 5 |
Objects can be named, sorted, and compared based on particular attributes. |
In this unit, students build and expand their schema for geometric shapes and their attributes. They discover and use mathematical language to describe attributes of shapes (i.e., sides, vertices) and use attributes such as the number of sides to justify the names of two-dimensional shapes (K.G.A), to sort shapes into categories (K.MD.B), and to make comparisons (K.MD.A). Counting the sides of a shape challenges students’ counting schema as they must keep track of the start point and endpoint of their count (K.CC.A). Students recognize and construct various two- and three-dimensional shapes, discovering that size and orientation do not affect the name of a shape (K.G.B). Students also extend their schema of part-total number relationships to part-whole geometric relationships by building composite shapes from simple shapes (K.G.B).
|
K.CC.A |
K.MD.A K.MD.B K.G.A K.G.B |
Unit 6 |
Addition and subtraction can be used to show how numbers can be composed and decomposed in various ways without changing the total. | Students expand their understanding of number relationships by exploring how breaking apart and putting together numbers in various ways can be described by addition and subtraction (K.OA.A). This extends their understanding from unit 3 that a set can be described as parts or a total in various ways without changing the total (K.CC.B), and expands their addition and subtraction schema from action joining and taking away situations to static part-part-total relationships. Their part–part–total schema deepens as they connect concrete models to symbolic notation through number bonds and equations. | K.OA.A | None |
Unit 7 |
The base ten number system relies on identifying and composing groups of 10. | In this unit, students develop their understanding of teen numbers by connecting their counting schema (K.CC.A and K.CC.B) to place value concepts through various representations. They discover that grouping a set into 10 and some more helps to find the total, building foundational understanding of teen numbers and the structure of their numerals (K.NBT.A). Students compose and decompose teen numbers into their place value components and describe the part-part-total relationship with addition, and extension of their work in Units 3 and 6. (K.OA.A). This understanding of the number 10 as special extends from teen numbers to larger numbers as students explore counting by 10s (K.CC.A) and begin to see the broader patterns in our base-ten number system. By the end of the unit, students can flexibly represent numbers using multiple strategies and can understand relationships between numbers in the counting sequence. |
K.CC.A K.CC.B K.OA.A K.NBT.A |
None |
Unit 8 |
Asking questions, and using data to critically answer those questions, help to make sense of the world. | In this unit, students develop an early schema for data organization and interpretation, expanding their understanding of how to make sense of the world through categorization of shapes (K.G.A) and other objects (K.MD.B). They learn that displaying data with graphs and tables provides a powerful way to compare quantities and relationships (K.CC.C and K.MD.B), building upon their existing knowledge of counting (K.CC.A. and K.CC.B). Students also begin to understand how comparisons and operations (K.OA.A) help us to interpret collections and survey data. This foundational work prepares students to see data not just as collections of objects but as structured information that can be used to answer questions and make decisions about their surroundings. |
K.CC.A K.CC.B K.CC.C K.OA.A K.NBT.A
|
K.MD.B K.G.A |
Unit 9 |
Mathematics is a way to think about and describe the world. | In this unit, students’ work with increasingly symbolic representations of numbers as they become fluent in addition and subtraction within 5 (K.OA.A), counting to 100, making number pairs to 10, representing numbers with numerals (K.CC.A). They also compare symbolic numerals, relying on their established schema of the count sequence and how it reflects quantity (K.CC.B and K.CC.C). This unit also provides ample opportunity to see, create, and make connections among various models to represent numbers and operations such as ten frames, number paths, number bonds, and equations to build foundational number sense and skills. |
K.CC.A K.CC.B K.CC.C K.OA.A K.NBT.A |
K.G.A K.G.B |