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.
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)
For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 6th Grade Scope and Sequence Recommended Adjustments.
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
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Tape diagram |
Examples: $$m-4$$ $$4-m$$ $$3x+2=x+x+x+2$$ |
Area model |
Examples: $$2\times5^2$$ $$2+5^2$$ |
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variable
numerical expression
equivalent
term
commutative property
algebraic expression
distributive property
order of operations
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6.EE.A.1
Understand the meaning of exponents.
6.EE.A.1
Evaluate numerical expressions involving whole-number exponents.
6.EE.A.2
6.EE.A.2.C
6.EE.B.6
Use variables to write algebraic expressions.
6.EE.A.2
6.EE.A.2.C
Evaluate algebraic expressions.
6.EE.A.2.A
6.EE.A.2.B
Write expressions for verbal statements and vice versa (Part 1).
6.EE.A.2.A
6.EE.A.2.B
Write expressions for verbal statements and vice versa (Part 2).
6.EE.A.3
6.EE.A.4
Identify equivalent expressions (Part 1).
6.EE.A.3
6.EE.A.4
Identify equivalent expressions (Part 2).
6.EE.A.3
6.EE.A.4
Write equivalent expressions using the distributive property (Part 1).
6.EE.A.3
6.EE.A.4
Write equivalent expressions using the distributive property (Part 2).
6.EE.B.6
Write algebraic expressions for application situations (Part 1).
6.EE.B.6
Write algebraic expressions for application situations (Part 2).
Key: Major Cluster Supporting Cluster Additional Cluster
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