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, 7th 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 6th 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 6th grade to those with rational numbers such as $${-(a+b)-\frac{3}{2}(a-b)}$$ in the 7th grade.
The next unit of the 7th grade course, Unit 4, will continue to engage students in working with expressions with rational numbers. In 8th 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)
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The following assessments accompany Unit 3.
Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the Mid-Unit Assessment after lesson 6 .
Use the resources below to assess student understanding of the unit content and action plan for future units.
Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.
Model | Example |
rectangular array |
$$\frac{1}{3}(9x-12y-18)=3x-4y-6$$ |
algebraic expression
combine like terms
coefficient
commutative property
constant term
distributive property
expand an expression
factor an expression
greatest common factor (gcf)
numerical expression
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.
Next
Evaluate numerical expressions with rational numbers using the order of operations.
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