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 5
| Unit | Big Idea | Connections Across Domains and Clusters | Major Clusters |
Additional/ Supporting Clusters |
Unit 1 |
Multiplying and dividing by powers of ten is the foundation for decimal numbers.
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This unit strengthens students’ understanding of the place value system by discovering how place value relationships extend to any number of places before or after the decimal point (5.NBT.A). Their schema of multiplicative relationships between adjacent place values expands as they recognize that these relationships hold true both for whole numbers and decimal numbers, creating a unified system in which any digit represents ten times the value of the same digit one place to its right and one-tenth the value of the same digit one place to its left (5.NBT.A). Students’ rely on these understandings to explain and apply patterns when multiplying and dividing by powers of 10 (5.NBT.A). They examine the role of base-ten in the metric system and rely on place value shifts to make unit conversions (5.MD.A). In grade 4, students conceptualized addition of decimals by thinking of them as fractions and applying fraction addition strategies (4.NF.C). Now, students develop strategies to add and subtract these numbers using their decimal forms while making connections to fraction addition (5.NF.A and 5.NBT.B). |
5.NBT.A 5.NBT.B 5.NF.A
|
5.MD.A |
Unit 2 |
Multidigit computation can be reduced to repeated processes based on a series of single-digit computations.
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Students enter grade 5 with established schemas for multiplying whole numbers up to four-digit by one-digit and two-digit by two-digit numbers (4.NBT.B). In this unit, students extend their understanding of place value and multiplication by powers of 10 (5.NBT.A) to develop fluency with the standard algorithm for multidigit multiplication (5.NBT.B). They build on the concept that multidigit numbers can be decomposed into place value components (5.NBT.A), allowing students to recognize how complex multiplication can be simplified into a series of single-digit computations systematically organized by place value. |
5.NBT.A 5.NBT.B
|
5.OA.A |
Unit 3 |
Dividing multidigit numbers is a repeated process of estimating partial quotients based on multiples of the divisor.
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In this unit, students extend their multiplication and division schemas to incorporate division with multidigit numbers, including fractional quotients. Students build on their understanding of division in grade 4 (4.NBT.B), where they worked with one-digit divisors, to now include two-digit divisors (5.NBT.B). As in Unit 2, students rely on place value understanding related to powers of 10 (5.NBT.A) to divide multidigit numbers. They begin to connect their fraction schema to their division schema by understanding that division can result in fractional quotients (5.NF.B and 5.NBT.B) and interpret these quotients in context, deciding when a fractional quotient rather than a remainder is appropriate. Through systematic work with partial quotients, students develop increasingly efficient strategies for dividing multidigit numbers, which will provide a foundation for the standard division algorithm and division of decimals in grade 6 (6.NS.B). |
5.NBT.A 5.NBT.B 5.NF.B
|
5.OA.A 5.MD.A |
Unit 4 |
Multiplication can help to discover, understand, and explain three-dimensional space and relationships between numbers.
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Students enter grade 5 with a foundation in measuring area by iterating unit squares and multiplying side lengths to find the area of rectangles (3.MD.C and 4.MD.A), and with a schema of area as additive (3.MD.C). In this unit, students extend these understandings to three-dimensional space as they develop schemas around using multiplication to understand, measure, and reason about volume (5.MD.C). Students use volume of rectangular prisms as an avenue to explore factors and prime and composite numbers, which they formalize through expressions with parentheses (5.OA.A).
|
5.MD.C |
5.OA.A 5.MD.A |
Unit 5 |
Quantities can be added and subtracted when the units are the same size.
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Students enter grade 5 with an understanding that in order to add or subtract measurements, they must be expressed with common units (4.MD.A). In this unit, they build from their grade 4 foundational understanding that any fraction can be expressed as the sum of unit fractions (4.NF. B) as they grapple with how to add and subtract fractions that are not expressed as multiples of the same unit fraction (5.NF.A). Students connect their measurement and fraction schemas to create equivalent fractions in order to add and subtract. Work with fractional measurements and line plots continues to strengthen students’ concept of continuous quantities and data representations (5.MD.B). Throughout the unit, students build fluency in re-expressing fractions, find and utilize strategies for adding and subtracting fractions and mixed numbers efficiently, record their thinking symbolically (5.OA.A), and expand their schema for using estimation to predict sums and differences and to verify the reasonableness of their answers. |
5.NF.A
|
5.OA.A 5.MD.B |
Unit 6 |
Using flexible fraction and multiplication interpretations helps to multiply with fractions.
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In grade 4, students fractions as multiples of unit fractions and performed multiplication of a fraction by a whole number by conceptualizing iterations of the fraction (4.NF.B). In this unit, students expand their multiplication schema to include multiplication as scaling, and use this interpretation to multiply a whole number by a fraction, and a fraction by a fraction (5.NF.B). This important interpretation allows students to predict whether multiplication by a fraction will cause a number to increase or decrease based on the fractions value relative to 1 (5.NF.B). Students continue to build conceptual understanding of continuous quantities by finding the area of rectangles with fractional side lengths, and using area models to represent fraction multiplication in other contexts (5.NF.B).
|
5.NF.B | None |
Unit 7 |
Using multiplication and flexible division interpretations helps to divide with fractions.
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Students expand their fraction operations schema to integrate division with fractions (5.NF.B) as an extension of their existing understanding of multiplication with fractions. By connecting division of fractions to the familiar partitive and quotitive interpretations from whole number division (3.OA.A), students discover that dividing by a fraction within 1 produces a larger quotient, challenging their previous understanding that division always makes things smaller. Throughout the unit, students weave their division and multiplication schemas together as they recognize that, just as with whole number operations, the same situation can often be represented using either operation. This understanding of the inverse nature of multiplication and division will support students to develop fluent strategies to divide with fractions in grade 6 (6.NS.A). Students also spend time in this unit to interpret and model word problems and situations involving fractions to identify the operation(s) involved (5.NF.A and 5.NF.B) and solve problems related to data involving fractional measurements (5.MD.A) .
|
5.NF.A 5.NF.B |
5.MD.B |
Unit 8 |
Extending place value patterns and fraction understanding can help to multiply decimals.
|
Students continue to build their understanding of fractions and decimals as equivalent representations of the same number as they explore multiplication of decimals for the first time, modeling decimal multiplication as they did fractions. As they did with fraction multiplication, students make predictions about the size of the product based on the size of the factors relative to 1 (5.NF.B and 5.NBT.B). They also draw on their schema of how decimals exhibit the same place value relationships as whole numbers and discover that decimal multiplication follows the same fundamental properties as whole number multiplication but with shifts in place value that are predictable and systematic (5.NBT.A and 5.NBT.B). Throughout the unit, students integrate their knowledge of multiplying by powers of 10 with an understanding of tenths and hundredths as fractional parts, developing a coherent mental model for how decimal multiplication affects the magnitude of numbers.
|
5.NBT.A 5.NBT.B 5.NF.B |
5.OA.A |
Unit 9
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Extending place value patterns and fraction understanding can help to divide decimals.
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As in Unit 8, this unit allows students to draw connections between decimals and fractions (5.NF.B) as well as between decimals and whole numbers in order to divide decimals by whole numbers. Students see that decimal division can be modeled in the familiar ways they modeled fraction division (5.NF.B). They also draw on their schema of how decimals exhibit the same place value relationships as whole numbers and discover that decimal division follows the same fundamental properties as whole number multiplication but with shifts in place value that are predictable and systematic (5.NBT.A and 5.NBT.B). Throughout the unit, students integrate their knowledge of dividing by powers of 10 with an understanding of tenths and hundredths as fractional parts, developing a coherent mental model for how decimal division affects the magnitude of numbers.
|
5.NBT.A 5.NBT.B 5.NF.B |
5.OA.A |
Unit 10 |
Creating geometric structures and categories helps to analyze and organize space.
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Students expand their understanding of two-dimensional space by developing systematic ways to organize and analyze geometric relationships. In this unit, students’ schemas for shape classification grow from classifying shapes based on one or two attributes to understanding hierarchical relationships between categories of shapes (5.G.B), while their spatial reasoning schema grows to include the coordinate plane as a tool for representing location in two-dimensions (5.G.A). Like the number line, students extend their use of the coordinate plane from a positional framework to a geometric one which allows numbers and other attributes to be represented as distances from 0. Students generate patterns using two rules, and begin to identify relationships between corresponding terms, seeing that plotting the points on a coordinate plane can be a useful way to identify these relationships (5.OA.B and 5.MD.A). In this way, students begin to make connections between algebraic thinking and geometry that will be further developed in grade 6 and beyond.
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None |
5.OA.B 5.MD.A 5.G.A 5.G.B |