Students extend the operations of addition, subtraction, multiplication, and division to include positive and negative rational numbers, and build fluency with evaluating numerical expressions.
In Unit 2, seventh-grade students extend the operations of addition, subtraction, multiplication, and division to include positive and negative rational numbers. Standards 7.NS.1 and 7.NS.2 represent a culmination in the extension of the four operations to all rational numbers. In this unit, students model addition and subtraction on the number line, and through repeated reasoning and application of properties of operations, they determine efficient rules for computing with rational numbers (MP.8). Students gain the ability to model a greater scope of real-world contexts to include situations involving elevation, temperature changes, debts and credits, and proportional relationships with negative rates of change (MP.4). They also develop greater fluency with evaluating numerical expressions, using the properties of operations to increase their flexibility in approach.
Starting in first grade, students learn about the commutative and associative properties of addition, and the relationship between addition and subtraction. In third grade, students extend their understanding of the properties of operations to include multiplication and the distributive property. Throughout the years, students have applied these properties and relationships between the operations to whole numbers, fractions, and decimals. In seventh grade, all of these skills and concepts come together as students now operate with all rational numbers, including negative numbers.
In several upcoming units, seventh-grade students will rely on their increased number sense and ability to compute with rational numbers, in particular in Unit 3, Numerical and Algebraic Expressions, and in Unit 4, Equations and Inequalities. By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. In eighth grade, students are introduced to irrational numbers, rounding out their understanding of the real number system before learning about complex numbers in high school.
Included in the materials for this unit are some activities that aim to support and build students’ fluency with integer computations, especially mental math. See our Guide to Procedural Skill and Fluency for additional information and strategy and activity suggestions.
Pacing: 22 instructional days (18 lessons, 3 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 7th Grade Scope and Sequence Recommended Adjustments.
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opposite
rational number
distributive property
terminating decimal
absolute value
additive inverse
commutative property
associative property
multiplicative inverse
repeating decimal
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This assessment accompanies Unit 2 and should be given on the suggested assessment day or after completing the unit.
7.NS.A.1
Represent rational numbers on the number line. Define opposites and absolute value.
7.NS.A.1
Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.
7.NS.A.1.A
Describe situations in which opposite quantities combine to make zero.
7.NS.A.1.B
7.NS.A.1.D
Model the addition of integers using a number line.
7.NS.A.1.B
7.NS.A.1.D
Determine efficient ways to add rational numbers with and without the number line.
7.NS.A.1.B
7.NS.A.1.D
Efficiently add and reason about sums of rational numbers.
7.NS.A.1.C
7.NS.A.1.D
Understand subtraction as addition of the opposite value (or additive inverse).
7.NS.A.1.C
Find and represent the distance between two rational numbers as the absolute value of their difference.
7.NS.A.1.C
7.NS.A.1.D
Subtract rational numbers with and without the number line.
7.NS.A.1.D
Add and subtract rational numbers efficiently using properties of operations.
7.NS.A.1
7.NS.A.1.A
7.NS.A.1.B
7.NS.A.1.C
7.NS.A.1.D
Add and subtract rational numbers using a variety of strategies.
7.NS.A.2.A
7.NS.A.2.C
Determine the rules for multiplying signed numbers.
7.NS.A.2.A
7.NS.A.2.C
Multiply signed rational numbers and interpret products in real-world contexts.
7.NS.A.2.B
7.NS.A.2.C
Determine the rules for dividing signed numbers.
7.NS.A.2.B
7.NS.A.2.C
Divide signed rational numbers and interpret quotients in real-world contexts.
7.NS.A.2.D
Convert rational numbers to decimals using long division and equivalent fractions.
7.NS.A.2
7.NS.A.2.C
Multiply and divide with rational numbers using properties of operations.
Key: Major Cluster Supporting Cluster Additional Cluster
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