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 3
| Unit | Big Idea | Connections Across Domains and Clusters | Major Clusters |
Additional/ Supporting Clusters |
Unit 1 |
Multiplication and division are the mathematics of equal groups.
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Students enter grade 3 with predeveloped schemas for grouping, splitting, and equal groups (2.OA.C). In this unit, students build on their knowledge of numbers and addition and subtraction patterns to develop an understanding of multiplication and division (3.OA.A). Students are introduced to multiplication and division as inverse operations, the commutative property of multiplication (3.OA.B), and patterns inherent in the multiplication table (3.OA.D), and begin to apply these concepts as strategies (3.OA.C) to solve problems and equations (3.OA.A) . Within this unit, students apply their new multiplication and division schemas across multiple contexts, including contexts involving arrays and scaled picture graphs (3.MD.B).
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3.OA.A 3.OA.B 3.OA.C 3.OA.D |
3.MD.B
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Unit 2
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Area is a way to describe and quantify two-dimensional space.
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Students expand their spatial reasoning and measurement schemas as they develop an understanding of area as a way to describe and quantify two-dimensional space (3.MD.C). They progress from direct and indirect comparisons of area to quantitative measurements, discovering that area is an attribute of two-dimensional shapes that can be directly measured with unit squares. As the unit progresses, students see the area of a rectangle as an array of square units and begin to connect area to multiplication (3.OA.A and 3.MD.C). By the end of the unit, students indirectly measure the area of rectangles by multiplying side lengths and use their developing multiplication strategies to find area (3.OA.C).
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3.OA.A 3.OA.C 3.MD.C
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Unit 3 |
Relating known facts and using flexible models and strategies can help to multiply and divide efficiently and fluently.
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Students expand their schemas for multiplication and division by incorporating strategic approaches to solving problems with increasing efficiency and fluency (3.OA.C). Students also apply multiplication and division skills to data situations by working with scaled picture graphs (3.MD.B). Their understanding of operations shifts from concrete counting and repeated addition to more sophisticated strategies that leverage known facts, mathematical patterns (3.OA.D), and properties of operations (3.OA.B). In order to understand and solve word problems and equations, students interpret products and quotients in context appropriate ways by generating models such as number line models, fair sharing models, area models, or bar models (3.OA.A and 3.MD.C). This movement toward flexible and efficient computation aligns with the big idea that relating known facts and using flexible models and strategies can help multiply and divide more fluently. |
3.OA.A 3.OA.B 3.OA.C 3.OA.D 3.MD.C
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3.MD.B
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Unit 4 |
Two-dimensional shapes can be described by many different attributes. Some attributes can be quantified (e.g., perimeter, area), and some define what the shape is called (e.g., quadrilateral).
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In a previous unit, students’ schemas around measurement and shapes were expanded to include area. In this unit, students’ schema of two-dimensional shapes grows to include another measurable attribute, perimeter (3.MD.D), while also developing a deeper understanding of defining attributes that determine shape categories (3.G.A). Students’ understanding of multiplication and division schemas extends as they connect operations to finding area and perimeter (3.NBT.A, 3.OA.B, 3.OA.C, and 3.OA.D), particularly in exploring how area is additive while perimeter follows different patterns (3.MD.C).
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3.OA.B 3.OA.C 3.OA.D 3.MD.C
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3.NBT.A 3.MD.D 3.G.A
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Unit 5 |
Understanding properties and using flexible models and strategies can help to multiply and divide efficiently and fluently.
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Students expand their multiplication and division schemas by incorporating key mathematical properties as tools for efficient computation when solving equations, word problems, and performing data analysis (3.OA.A and 3.MD.B). Their understanding transforms as they discover how the distributive and associative properties can be applied to strategically break apart or group numbers (3.OA.B), making calculations more efficient (3.OA.C and 3.NBT.A) . Building on students’ understanding of area as additive established in the previous unit, area models are used to support conceptual understanding of the distributive property (3.MD.C and 3.OA.B). Expanding their operational schema creates an essential bridge between concrete models and abstract mathematical thinking, helping students develop the flexibility to solve increasingly complex problems more confidently and efficiently.
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3.OA.A 3.OA.B 3.OA.C 3.OA.D 3.MD.C |
3.NBT.A 3.MD.B |
Unit 6 |
The place value system is based on patterns, which makes expressing and working with numbers efficient.
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In this unit, students expand their place value schema by applying it to add, subtract, and estimate within 1,000 efficiently (3.NBT.A). Their understanding of place value deepens as they discover how rounding and estimation provide powerful tools for assessing the reasonableness of answers (3.OA.D). Students connect their existing schema of addition and subtraction strategies to new contexts involving two-step problems and larger numbers, developing flexibility in selecting appropriate strategies based on the specific numbers in a problem.
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3.OA.D | 3.NBT.A |
Unit 7 |
Fractions extend the number system to include numbers that represent equal parts of a whole.
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In this unit, students develop their fractions schema as numerical representations of equal parts of a whole. Building on their prior experiences with partitioning shapes in grades 1 and 2 (2.G.1), students now describe these parts as having equal area (3.MD.C and 3.G.A). They formalize this understanding with fraction notation and integrate fractions into their broader number system schema (3.NF.A). They extend the idea of partitioning shapes to explore fractions on the number line and fractions of sets. Students iterate length models of unit fractions, setting the stage for measurement with fractions of units in Unit 9 (3.MD.B). Students build a robust understanding of fractions through situations that require partitioning strategies, iteration strategies, or a combination of the two. This extends their spatial and numerical reasoning schemas as they discover that fractions can express quantities less than, equal to, or greater than whole numbers. This foundational schema will be critical for developing fraction equivalence and operations in subsequent units and grades.
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3.NF.A 3.MD.C
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3.MD.B 3.G.A |
Unit 8 |
Any number can be represented in an infinite number of different, but equivalent, ways.
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In this unit, students expand their schemas of fractions and equivalence by exploring the concept that any number can be represented in multiple equivalent ways. Students build on their understanding of unit fractions to discover that fractions can be equivalent to each other, to whole numbers, and to mixed numbers (3.NF.A). Students use area models to conceptualize and justify equivalent fractions by equating fractions of equal area (3.MD.C and 3.G.A) Their schema of numbers evolves as they recognize that fractions, like whole numbers, have specific magnitudes that can be compared and ordered on a number line. This growing understanding helps them see the number system as a coherent structure with predictable patterns and relationships, preparing them for future work with fraction operations, decimal equivalents, and proportional reasoning in later grades.
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3.NF.A 3.MD.C |
3.G.A |
Unit 9 |
Measuring the size of an object requires choosing an appropriate attribute, tool, and unit to match the situation.
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Students enter grade 3 with an understanding of length measurement and basic data analysis. In this unit, students are introduced to the concept of continuous quantities. They expand their measurement schema to include increasingly precise measurements with fractions of units (3.NF.A and 3.MD.B), and they develop new schemas for quantifying size using the attributes of volume and mass (3.MD.A). Students apply their skills to interpret and solve a variety of word problems (3.OA.A and 3.OA.D) in measurement contexts using all four operations (3.OA.C).
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3.OA.A 3.OA.C 3.OA.D 3.NF.A 3.MD.A |
3.MD.B |
Unit 10 |
Asking questions and using data to critically answer those questions help to make sense of the world.
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In this unit, problem solving is approached through the context of data (3.OA.A and 3.OA.D) and provides students with ample opportunities to interpret the diverse language encountered in word problems. Students develop their schema for data investigation as they formalize a systematic process for asking questions, collecting and representing data, and analyzing and interpreting results. Students’ understanding of data expands from creating simple representations to using scaled picture graphs and bar graphs to represent larger quantities (3.MD.B), building on their prior work with collecting and organizing data in earlier grades. They make connections between measurement concepts, specifically time and elapsed time (3.MD.A), and data analysis as they consider how timelines and bar graphs can represent the same information in different ways. Students consider how we use fractions of hours to express time and how those fractional hours translate to minutes (3.NF.A). Throughout the unit, students learn to evaluate the strengths of different data representations and how to select the most appropriate display to answer specific questions, preparing them for more complex data analysis in future grades.
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3.OA.A 3.OA.D 3.NF.A 3.MD.A
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3.MD.B |