Students venture into the Expressions and Equations domain, using variables to represent unknown or changing quantities, and using properties of operations to investigate equivalent expressions.
Math
Unit 5
6th Grade
In Unit 5, sixth graders venture into the Expressions and Equations domain for the first time, extending on their understanding of arithmetic to see how it applies to algebraic expressions. They start with numerical expressions with exponents, rewriting the expressions into simpler forms until a final value is determined. Students then use variables in expressions to represent quantities that are unknown or quantities that change. Using the properties of operations, students will investigate what makes expressions equivalent to others, a concept that is threaded throughout the middle school Expressions and Equations domain. Throughout this unit, students pay close attention to the structure of expressions, understanding the role of parentheses, the order of operations, and the way expressions are described verbally (MP.7). A note on fluency: Evaluating expressions provides a good opportunity for students to continue developing and to demonstrate fluency with decimal operations. Several problems throughout the unit include decimal values; include additional problems in practice for students as needed.
In elementary school, students used variables to represent unknown quantities, and they evaluated and described numerical expressions without exponents. They used the commutative property to enhance their understanding of multiplication and addition, and they used the distributive property when modeling partial areas. All of these concepts come together and support student understanding in this sixth-grade unit.
Immediately following this unit, sixth graders will start a unit on Equations and Inequalities, where they will use algebra to model and solve real-world problems. They will also revisit percentages using new skills with expressions and equations to efficiently solve percent problems. In seventh and eighth grades, students continue to simplify and solve more complex expressions and equations using the same tools learned in this unit.
Pacing: 16 instructional days (12 lessons, 3 flex days, 1 assessment day)
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The following assessments accompany Unit 5.
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.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
Model | Example |
Tape diagram |
$$4-m$$ $$m-4$$ $$3x+2=x+x+x+2$$ |
Area model |
$$2\times5^2$$ $$2+5^2$$ |
algebraic expression
commutative property
distributive property
equivalent
numerical expression
order of operations
term
variable
To see all the vocabulary for Unit 5, view our 6th Grade Vocabulary Glossary.
Topic A: Numerical Expressions with Exponents
Topic B: Introduction to Algebraic Expressions
Topic C: Equivalent Expressions & Applications
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 4
Rational Numbers
Unit 6
Equations and Inequalities