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 4
| Unit | Big Idea | Connections Across Domains and Clusters | Major Clusters |
Additional/ Supporting Clusters |
Unit 1 |
Multiplication can help to discover, understand, and explain relationships between numbers.
|
Students enter grade 4 with schemas for multiplication as equal groups, arrays, and area models, and an informal understanding of remainders (3.OA.A). In this unit, students deepen their multiplicative reasoning by investigating relationships between factors and multiples (4.OA.B) and exploring patterns in sequences of and involving multiples (4.OA.B and 4.OA.C). By thinking of whole number side lengths of a rectangle as factors of the area, students generate and apply the formula for area of a rectangle (4.MD.A). Their schemas expand to incorporate increasingly sophisticated interpretations of multiplication and division relationships as they model and solve multistep word problems (4.OA.A), including interpreting non-multiples as “a multiple plus some more” as an introduction to remainders before exploring division with remainders in real-world contexts (4.NBT.B).
|
4.OA.A 4.NBT.B |
4.OA.B 4.OA.C 4.MD.A |
Unit 2 |
Multiplication can be used to compare quantities and measurements.
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In this unit, students expand their multiplicative reasoning schema to include comparison (4.OA.A), transforming their understanding of multiplication beyond equal groups into a powerful tool for expressing relationships between quantities. This key advancement allows students to recognize that one quantity can be a multiple of another (e.g., 30 feet is 10 times as long as 3 feet), forming the foundation for proportional reasoning. Students integrate this understanding into their measurement schema as they explore multiplicative relationships within measurement systems to make unit conversions within the U.S. customary system (4.MD.A), establishing conceptual patterns that will support their work with ratios, rates, and algebraic thinking throughout their mathematical journey.
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4.OA.A | 4.MD.A |
Unit 3 |
Understanding the patterns and regularity of the base-ten place value system helps to compare and compute with multidigit numbers.
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In this unit, students expand their schema for place value beyond the thousands to include the millions period (4.NBT.A), recognizing the pattern of repeating periods (4.OA.C) which allows them to effectively work with larger numbers. Students round numbers to any place as a means to understand the magnitude of numbers and to make reasonable estimates (4.NBT.A and 4.MD.A). They deepen their understanding of the base-ten number system by recognizing multiplicative relationships between places where a digit in any position represents 10 times the value of the same digit one position to its right. Students apply place value understanding to examine base-ten patterns in the metric system, describing relationships between units as multiplicative comparisons (4.OA.A) and converting units of measurement (4.MD.A). This expanded place value understanding also becomes the foundation for students to develop efficient strategies for adding and subtracting multidigit numbers (4.NBT.B) including the standard algorithm, connecting their conceptual understanding of place value with procedural fluency.
|
4.OA.A 4.NBT.A 4.NBT.B |
4.OA.C 4.MD.A |
Unit 4 |
Using known facts and place value properties flexibly is helpful to perform multidigit multiplication strategically and efficiently.
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Students enter grade 4 with schemas for multiplication as equal groups, arrays, and area models, along with strategies for multiplying with single-digit factors (3.OA.A and 3.OA.C). In this unit, their schemas for multiplication expand as they extend to multidigit multiplication with increasingly efficient strategies based on place value understanding and properties of operations (4.NBT.B). Students’ understanding of multiplication shifts from procedural repetition to strategic decomposition as they recognize and utilize the patterns of place value when multiplying by powers of 10 (4.NBT.A and 4.NBT.B). This allows them to approach multidigit multiplication with flexibility as they determine when to use partial products, compensation strategies, or other methods based on number relationships. They continue to develop their skills in interpreting, modeling, and solving multiplicative word problems (4.OA.A and 4.MD.A).
|
4.OA.A 4.NBT.A 4.NBT.B |
4.MD.A |
Unit 5 |
Multiplication and division models and strategies can be extended and applied to division problems involving multidigit numbers and remainders.
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Students enter grade 4 with foundational schemas for multiplication and division as operations involving equal groups, arrays, and area (3.OA.A and 3.OA.C). In this unit, students expand their division schema as they develop multiple interpretations of division and more efficient computational strategies for multidigit dividends (4.NBT.B) that rely on using known single-digit multiplication facts to recognize factors in larger numbers (4.NBT.A). They strengthen their understanding of the relationship between multiplication and division as they explore factor pairs and divisibility rules, and now develop strategies to find all factor pairs for a given number (4.OA.B). Students once again explore patterns that rely on multiples (4.OA.C) and solve a variety of word problems (4.OA.A and 4.MD.A) that involve interpreting remainders in context—a key component of a robust division schema that will support future work with fractions, ratios, and algebraic reasoning.
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4.OA.A 4.NBT.A 4.NBT.B |
4.OA.B 4.OA.C 4.MD.A |
Unit 6 |
Thinking flexibly about how fractions, whole numbers, and mixed numbers are composed can help to add and subtract efficiently.
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Students enter grade 4 with an understanding of fractions as iterated unit fractions and basic strategies for comparing fractions with common numerators or denominators (3.NF.A). In this unit, students expand their schema of fraction operations as they learn to flexibly compose and decompose fractions using unit fractions as building blocks and extend this understanding to add and subtract fractions with common denominators (4.NF.B). Their understanding of fractions deepens as they connect various representations—area models, number lines, rulers, and line plots— and solve problems involving fractional measurements (4.MD.A and 4.MD.B). These experiences help build students’ schema that fractions are numbers with which we can perform operations, and strengthen their ability to work with mixed numbers and fractions greater than 1 in meaningful contexts.
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4.NF.B |
4.MD.A 4.MD.B |
Unit 7 |
Any number can be represented in an infinite number of different, but equivalent, ways.
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In this unit, students expand their understanding of fractions by connecting them to decimal representations in our base-ten number system. Students’ schema of equivalence grows as they discover that any number can be represented in an infinite number of different, but equivalent ways, whether as fractions with denominators that are not common (4.NF.A) or as decimals (4.NF.C). Students discover the usefulness of fractions expressed as tenths and hundredths because of our base-ten number system and convert these fractions and decimals to fractions with common denominators in order to add and subtract (4.NF.B and 4.NF.C), a concept they will apply to fractions with other denominators in grade 5 (5.NF.A). Students’ understanding of place value extends beyond whole numbers as they recognize that base-ten patterns continue to the right of the ones place, thus connecting students’ schemas about fractions and place value in the number system (4.NBT.A and 4.NF.C). Problem solving with measurement quantities continues to build students’ schema of continuous quantities, now expanding to understand decimal measurements (4.MD.A).
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4.NBT.A 4.NF.A 4.NF.B 4.NF.C |
4.MD.A |
Unit 8 |
Equal-groups thinking can help when multiplying and comparing quantities involving fractions.
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Students expand their multiplication schema beyond whole numbers to include fractions and mixed numbers. They discover that equal-groups thinking applies to fractional quantities, allowing them to interpret the product of a whole number and a fraction as multiple copies of that fraction (4.NF.B). Through visual models and equations, students connect repeated addition of unit fractions to multiplication, establishing that a non-unit fraction can be expressed as a product of its numerator and a unit fraction. This extension of their multiplication schema provides a foundation for understanding proportional relationships and more complex operations with rational numbers in future grades. Students continue to explore diverse word problem types (4.OA.A and 4.MD.A) involving fractions, using benchmark fractions or equivalent fractions to compare when necessary in context (4.NF.A).
|
4.OA.A 4.NF.A 4.NF.B |
4.MD.A |
Unit 9 |
Properties of two-dimensional shapes are determined by the parts that make up the shape and the relationships between those parts.
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Students enter grade 4 with established schemas for identifying and describing two-dimensional shapes (3.G.A). In this unit, students expand their schema about measurement to include angle size (4.MD.C) and integrate this new measurable attribute of shapes into their classification schema (4.G.A). Their conceptual understanding of measurement grows as they connect angle measurement to fractions of a ray’s rotation about a vertex. In addition, their schema of shape attributes grows to include symmetry as a defining characteristic to analyze and classify figures.
|
None |
4.MD.C 4.G.A |
Unit 10 |
Time can be represented with a variety of models that can help to solve problems and interpret data.
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In this unit, students explore time as an avenue to connect schemas they have built over the course of the year related to measurement, fractions, angles, and data representations. They revisit telling time on an analog clock, now able to relate the angle between its hands (4.MD.C) to the fraction of one rotation (4.NF.A) and interpret the hands’ movements in terms of elapsed time. Students solve time-related word problems (4.MD.A) that challenge them to perform operations with fractions (4.NF.B), interpret multiplicative comparison language (4.OA.A), convert between units of time (4.MD.A and 4.NBT.B), examine repeating time patterns (4.OA.C), and use data displays including line plots (4.MD.B) and timelines.
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4.OA.A 4.NBT.B 4.NF.A 4.NF.B |
4.OA.C 4.MD.A 4.MD.B 4.MD.C |