Students manipulate expressions into different equivalent forms as they expand, factor, add, and subtract numerical and algebraic expressions and face authentic real-world, multi-step problems.
Math
Unit 3
7th Grade
In Unit 3, seventh-grade students bring several prior skills together to manipulate expressions into different equivalent forms. In the preceding unit, students operated and reasoned with positive and negative rational numbers. In this unit, they use these new skills to expand, factor, add, and subtract numerical and algebraic expressions. Students pay particular attention to the structure of expressions in order to better understand what an expression means and how it can be manipulated (Standard for Mathematical Practice 7). Students also face authentic real-world, multi-step problems that require strategic use of rational numbers and estimation where appropriate.
In sixth grade, students learned how the same rules that govern arithmetic also apply to algebraic expressions. They learned to expand and factor expressions using the distributive property, and they combined terms where variables are the same. With new knowledge of the number system, students go from working with expressions like $${5(6x+3y)}$$ in sixth grade to those with rational numbers such as $${-(a+b)-\frac{3}{2}(a-b)}$$ in the seventh grade.
The next seventh-grade unit, Unit 4, Equations and Inequalities, will continue to engage students in working with expressions with rational numbers. In eighth grade, students will work with expressions and equations in both one variable and two variables, solving single linear equations and systems of linear equations. Throughout all of their future work with expressions, students’ ability to look for and make use of the structure in expressions will be as important as their ability to work with them procedurally.
Pacing: 15 instructional days (11 lessons, 3 flex days, 1 assessment day)
For guidance on adjusting the pacing for the 2021-2022 school year, see our 7th Grade Scope and Sequence Recommended Adjustments.
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This assessment accompanies Unit 3 and should be given on the suggested assessment day or after completing the unit.
Unit Launch
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Model | Example |
Rectangular array |
$$\frac{1}{3}(9x-12y-18)=3x-4y-6$$ |
expand an expression
factor an expression
combine like terms
coefficient
commutative property
distributive property
numerical expression
algebraic expression
greatest common factor (gcf)
constant term
order of operations
To see all the vocabulary for Unit 3, view our 7th Grade Vocabulary Glossary.
Topic A: Evaluating Numerical and Algebraic Expressions
Topic B: Generating Equivalent Expressions
Topic C: Solving Multi-Step Problems using Expressions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Operations with Rational Numbers
Unit 4
Equations and Inequalities