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 1
| Unit | Big Idea | Connections Across Domains and Clusters | Major Clusters |
Additional/ Supporting Clusters |
Unit 1 |
Addition and subtraction are the mathematics of parts and totals. | In this unit, students expand their addition and subtraction schemas, moving from thinking of these operations as “putting together” and “taking away” to thinking of them as related parts of a total that they can compose and decompose. (1.OA.A) Students decontextualize addition and subtraction by moving from visually and physically joining and separating objects to representing situations with symbols and equations. (1.OA.D) Within this schema, students understand and can identify parts and totals. They use this knowledge to discover the relationship between addition and subtraction as they represent the same situation using both operations. (1.OA.C) Additionally, students utilize an intuitive understanding of the commutative property (1.OA.C) to recognize patterns and build fluency with addition and subtraction problems. (1.OA.C) |
1.OA.A 1.OA.B 1.OA.C 1.OA.D |
None |
Unit 2 Building Approaches to Problem Solving |
Addition and subtraction can help to describe and solve word problems. | In this unit, students enhance their problem-solving schema as they investigate the different ways word problems can be represented and build their capacity for modeling as a means to understand a word problem as well as a means to solve a word problem. (1.OA.A) They move from directly representing situations with manipulatives or visual drawings to using abstract models (1.OA.D) in order to identify what types of values are given (e.g., parts, totals), what relationships are known between those values, and what operations are needed to solve the problem. Along with building those problem-solving skills, this unit also gives students the opportunity to use part–part–total strategies (1.OA.B and 1.OA.C) to model and solve active addition and subtraction problems and utilize these models to solve problems more fluently. (1.OA.C) |
1.OA.A 1.OA.B 1.OA.C 1.OA.D |
None |
Unit 3 Comparing & Measuring Length |
Comparing and measuring length helps to describe and analyze objects and their relationships among other objects. | In this unit, students expand their schema of measurement and spatial reasoning as they formally encounter length as a measurable attribute. Students move from direct comparisons (K.MD.A) to indirect comparisons and finally to quantifying length through iteration of nonstandard units. (1.MD.A) Their understanding of measurement develops from asking comparison questions such as “Which is longer?” to answering “How long?” with increasing precision and efficiency. Students’ schema of using numbers to answer “How Many?” and compare (K.CC.B and K.CC.C) is expanded to using numbers to quantify “How Long?” and compare lengths (1.MD.A), laying the foundational understanding of measurement as a process of comparing a quantity to a unit. This progression lays the foundation for students’ future work with standard measurement units (2.MD.A) and measurement of attributes other than length. (3.MD.A and 3.MD.C) | 1.MD.A | None |
Unit 4 Exploring Place Value Within 100 |
The base-ten place value system provides a structure to represent all numbers symbolically using the same 10 digits. |
This unit introduces students to the place value system as an expansion of their schema around numbers. Students extend the count sequence to 120 (1.NBT.A), examining the way numerals are composed of the same 10 digits. They expand their schema of teen numbers (K.NBT.A) to generalize the structure of greater numbers and their associated numerals (1.NBT.B). Students build a foundation for understanding place value as a base-ten system through manipulatives and other visual models in order to define units of tens and ones before students extend to hundreds. (1.NBT.B) They begin to see numbers as representations of structure, in which the value of each digit is determined by the position of the digit relative to other digits. Students use this understanding to discover place value patterns that are the building blocks for increased number sense and fluency with operations, including the relationships between numbers that are 10 or 1 greater/less than one another (1.NBT.C).
|
1.NBT.A 1.NBT.B 1.NBT.C |
None |
Unit 5 |
Reasoning about equality helps to add and subtract efficiently. | In this unit, students expand their schema of equivalent expressions, which allows them to use more sophisticated strategies for adding and subtracting. Students develop a conceptual sense of how parts can be moved around (with the commutative and associative properties) (1.OA.B) or decomposed and recomposed while maintaining the same total (1.OA.D). They use their understanding of place value structure to develop addition and subtraction strategies that rely on making a ten (1.NBT.B). This allows students to efficiently add and subtract by making a ten, by using near doubles, and by creating other easier equivalent expressions (1.OA.C). These skills build computational fluency—the ability to flexibly choose an efficient strategy for a situation and to find sums and differences quickly. Students apply these addition and subtraction strategies to solve word problems in a variety of situations (1.OA.A) and to solve equations with unknowns in various places (1.OA.D). |
1.OA.A 1.OA.B 1.OA.C 1.OA.D 1.NBT.B |
|
Unit 6 Investigating Data |
Asking questions, and using data to critically answer those questions, help to make sense of the world. | In this unit, students develop their schema for data collection, representation, and analysis (1.MD.C). Their understanding of data collection expands to include both sorting objects and conducting surveys as they learn increasingly efficient ways to collect and display information. Students introduce the formal data investigation process into their data schema as they build from “how do we sort data, collect data, and represent data?” to “what do we do with data?”. Problem solving is approached through the context of data. Comparing the length of bars on bar graphs allows students to find differences and begin solving “how many more” and “how many fewer” questions while reasoning about the meaning in context (1.OA.A). This unit provides students with ample opportunities to engage with the diverse language encountered in word problems. | 1.OA.A | 1.MD.C |
Unit 7 Extending Approaches to Problem Solving |
Addition and subtraction can help to describe and solve word problems. |
In this unit, students’ schema for problem solving through modeling (1.OA.A) and their schema for strategically solving addition and subtraction problems (1.OA.B and 1.OA.C) become intertwined as they consider new types of addition and subtraction word problems—comparison and active addition and subtraction start-unknown problems. They utilize their modeling schema to gain an understanding of what is happening in the story of each new problem type and relate these representations to bar models and equations in order to solve. Students’ schemas of the concept of equality and the relationship between addition and subtraction are also challenged as they find increasingly more strategic and efficient ways to solve equations (1.OA.D), including those representing two-step add-to and take-from word problems and open-ended problems. |
1.OA.A 1.OA.B 1.OA.C 1.OA.D |
1.MD.C |
Unit 8 Extending Place Value Within 100 |
Understanding the value of a two-digit number relies on understanding the value of each digit. | This unit sits in a very crucial position in students’ growing schema of place value as it relates to operations and equality. It serves as a first step for utilizing place value understanding in order to make adding and subtracting more efficient, all while building number sense and fluency. Students’ growing understanding of “ten-ness” as it relates to numbers in the number system will become the building blocks for understanding how place value is connected to the size of numbers and how numbers compare based on the place each digit is located (1.NBT.B). They begin to explore place value strategies for addition and subtraction by identifying which digit is affected when 1 or 10 is added to or subtracted from a two-digit number (1.NBT.C). Solving equations with unknowns in various positions (1.OA.D) that reflect place value decompositions of two-digit numbers also support students’ developing understanding of place value and require students to apply their developed addition and subtraction strategies (1.OA.B and 1.OA.C). |
1.OA.B 1.OA.C 1.OA.D 1.NBT.A 1.NBT.B 1.NBT.C |
None |
Unit 9 Building Place Value Strategies |
Applying place value understanding helps to add and subtract efficiently and use estimation to determine reasonableness. | In this unit, students’ schema for addition and subtraction and their schema for place value become more fully intertwined as they continue to discover the importance of 10 in the number system. Rather than seeing place value changes of tens and ones singularly, students begin to see how place value affects addition and subtraction in a broader sense, beginning with examining the effects of adding or subtracting multiple 10s and 1s, and adding across decades (1.NBT.C). Students use place value understanding (1.NBT.B) to support extension of their existing addition and subtraction strategies (1.OA.B and 1.OA.C). They also extend reasoning skills related to equality (1.OA.D) to compose a ten when necessary to add across a decade. Students’ use of estimation reinforces these schemas by helping students recognize and predict how place value impacts the accuracy and efficiency of addition and subtraction, further strengthening their ability to solve problems. |
1.OA.B 1.OA.C 1.OA.D 1.NBT.B 1.NBT.C |
None |
Unit 10 Composing & Decomposing Shapes |
Names and defining attributes of shapes are determined by how their component parts are put together. | In this unit, students’ schema of shapes progresses from visual recognition (K.G.A) to identifying and reasoning with defining attributes (1.G.A). Students advance geometric understanding by examining how shapes are constructed from their components—sides, vertices, angles, faces, edges—and recognize that these same components can be put together in different ways to create new shapes. As they continue to explore two-dimensional and three-dimensional shapes, students build a stronger understanding of the relationship between them, especially how faces of three-dimensional shapes relate to familiar two-dimensional shapes and how smaller shapes can combine to form larger composite shapes (1.G.1). While there are no direct ties to major clusters in this unit, its placement is meant to build on students’ schema of composing and decomposing numbers to apply similar concepts geometrically. | None | 1.G.A |
Unit 11 Partitioning Shape and Time |
Wholes and parts of wholes can be named by the number of equal-size parts which compose them. | In this unit, students continue to develop their understanding of part-whole relationships as they build schemas for partitioning shapes into equal parts (1.G.A) and for telling time (1.MD.B). Their schema of equality expands from comparing quantities to recognizing equal-sized shares and then applying this understanding to the equal parts of an hour on an analog clock (1.G.A and 1.MD.B). Students’ understanding of halves and fourths deepens as they recognize, create, and analyze these fractional parts across multiple contexts including data contexts (3.MD.C), laying critical groundwork for future work with fractions (3.NF) and elapsed time measurement (3.MD.A). While there are no direct ties to major clusters in this unit, its placement allows students to apply their schemas for equality and part-whole relationships to geometric shapes and time-based data. | None |
1.G.A 1.MD.B 1.MD.C |