Author:
Mark Freed
Subject:
Mathematics
Material Type:
Teaching/Learning Strategy
Level:
Middle School
Tags:
License:
Creative Commons Attribution
Language:
English

Education Standards

OREGON MATH STANDARDS (2021): [7.AEE]

OREGON MATH STANDARDS (2021): [7.AEE]

Overview

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards. 

Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

2021 Oregon Math Guidance: 7.AEE.A.1

ODE and Oregon Math Project Logo

Cluster: 7.AEE.A - Use properties of operations to generate equivalent expressions.

STANDARD: 7.AEE.A.1

 Standards Statement (2021):

Identify and write equivalent expressions with rational numbers by applying associative, commutative, and distributive properties.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

5.OA.A.2, 6.AEE.A.3

7.AEE.A.2, 8.AEE.C.7, HS.AEE.A.1, HS.AEE.A.2

6.NS.B.4

7.EE.A.1

7.AEE.A Crosswalk

 Standards Guidance:

Teaching Strategies

  • Identify like terms and combine like terms to create equivalent expressions.
  • Apply the distributive property to factor and expand linear expressions.
  • Use numerical substitution to identify equivalent expressions.

Progressions

  • In Grade 7 students start to simplify general linear expressions with rational coefficients. Building on work in Grade 6, where students used conventions about the order of operations to parse, and properties of operations to transform, simple expressions such as 2(3 + 8x) or 10 - 2p, students now encounter linear expressions with more operations and whose transformation may require an understanding of the rules for multiplying negative numbers, such as 7 - 2(3 - 8x).
  • In simplifying this expression students might come up with answers such as
    • 5(3 - 8x), mistakenly detaching the 2 from the indicated multiplication
    • 7 - 2(-5x), through a determination to perform the computation in parentheses first, even though no simplification is possible
    • 7 - 6 - 16x, through an imperfect understanding of the way the distributive law works or of the rules for multiplying negative numbers.
  • Please reference page 8 in the Progression document for additional information.

Examples

  • 4𝑥+2=2(2𝑥+1) and −3(𝑥−5/3)=−3𝑥+5
  • If Massey and Brenda both get paid a wage of $11  per hour, but Massey was paid an additional $55 for overtime, the expression 11(M+B) + 55 may be more clearly interpreted as 11M+55+11B for purposes of understanding Brenda’s pay separated from Massey’s pay.
  • Student Achievement Partners:

2021 Oregon Math Guidance: 7.AEE.A.2

 ODE and Oregon Math Project Logo

Cluster: 7.AEE.A - Use properties of operations to generate equivalent expressions.

STANDARD: 7.AEE.A.2

 Standards Statement (2021):

Understand that rewriting an expression in different forms in a contextual problem can show how quantities are related.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

7.AEE.A.1

HS.AEE.A.1, HS.AEE.A.2

 N/A

7.EE.A.2

7.AEE.A Crosswalk

 Standards Guidance:

Clarifications

  • Building on work in Grade 6, where students used conventions about the order of operations to rewrite simple expressions such as 2(3 + 8x) as 6 +16x and 10p-2 as 2(5p-1), students now encounter linear expressions with more operations that require an understanding of integers, such as 7 - 2(3 - 8x)

Progressions

  • In the example [below], the connection between the expressions and the figure emphasize that they all represent the same number.
  • The connection between the structure of each expression and a method of calculation emphasize the fact that expressions are built up from operations on numbers. (Please reference page 8 in the Progression document).

Examples

  • For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
  • For example, 3 friends each buy a drink for x dollars and popcorn for y dollars.  The total cost could be expressed by “x + x + x +y + y + y”,  “3x +3y” and “3(x+y)”
  • A shirt at a clothing store is on sale for 20% off the regular price, 𝑝. The discount can be expressed as 0.2𝑝. The new price for the shirt can be expressed as 𝑝−0.2𝑝 or 0.8𝑝.
  • A rectangle is twice as long as it is wide. One way to write an expression to find the perimeter would be w + w + 2w + 2w.  Write the expression in two other ways.
  • Write an equivalent expression for 9 – 7(2x + 4).
  • Illustrative Mathematics:
  • Student Achievement Partners:

 

2021 Oregon Math Guidance: 7.AEE.B.3

 ODE and Oregon Math Project Logo

Cluster: 7.AEE.B - Solve mathematical problems in authentic contexts using numerical and algebraic expressions and equations.

STANDARD: 7.AEE.B.3

 Standards Statement (2021):

Write and solve problems in authentic contexts using expressions and equations with positive and negative rational numbers in any form.  Contexts can be limited to those that can be solved with one or two-step linear equations.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.AEE.A.1

8.AEE.A.4

7.NS.A.2, 7.NS.A.3

7.EE.B.3

7.AEE.B Crosswalk

 Standards Guidance:

Clarifications

  • Students should be able to fluently solve equations of the specified forms presented.
  • Students should use the properties of equality to solve for the value of a variable.

Boundaries

  • Continue to build on 6th grade objectives of writing and solving one-step equations from a problem situation to multi-step problem situations. This is also another context for students to practice using rational numbers including: integers, and positive and negative fractions and decimal numbers.

Teaching Strategies

  • Students should be able to represent relationships in various contextual, mathematical situations with equations involving variables and positive and negative rational numbers and explain the meaning of the solution based on the context.
  • Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Progressions

  • As they build a systematic approach to solving equations in one variable, students continue to compare arithmetical and algebraic solutions to word problems. For example they solve the problem
    • The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
      • by subtracting 2 * 6 from 54 and dividing by 2, and also by setting up the equation
      • 2w + 2 * 6 = 54.
  • Please reference page 9 in the Progression document for additional information.

Examples

2021 Oregon Math Guidance: 7.AEE.B.4

 ODE and Oregon Math Project Logo

Cluster: 7.AEE.B - Solve mathematical problems in authentic contexts using numerical and algebraic expressions and equations.

STANDARD: 7.AEE.B.4

 Standards Statement (2021):

Use variables to represent quantities and construct one- and two-step linear inequalities with positive rational numbers to solve authentic problems by reasoning about the quantities.

  Connections:

Preceding Pathway Content (2021)

Subsequent Pathway Content (2021)

Cross Domain Connections (2021)

Common Core (CCSS)

(2010)

6.AEE.B.5, 6.AEE.B.6, 6.AEE.B.7, 6.AEE.C.8

8.AEE.C.7, 8.AEE.C.8, 8.AFN.A.2, HS.AEE.A.1, HS.AEE.D.11, HS.AEE.B.5

7.RP.A.2

7.EE.B.4

7.AEE.B Crosswalk

 Standards Guidance:

Clarification

  • Solve word problems leading to equations of the form 𝑝𝑥+𝑞=𝑟 and (𝑥+𝑞)=𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
  • Solve word problems leading to inequalities of the form 𝑝𝑥+𝑞>𝑟 or 𝑝𝑥+𝑞<𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Teaching Strategies

  • Students should be able to represent relationships in various contextual, mathematical situations with inequalities involving variables and positive and negative rational numbers.
  • Students should be able to fluently solve inequalities of the specified forms.  To achieve fluency, students should be able to choose flexibly among methods and strategies to solve mathematical problems accurately and efficiently.
  • Students should use the properties of inequality to solve for the value of a variable.
  • When identifying a specific value for p, q, and r, any rational number can be used.
  • Students should be able to graph and interpret the solution of an inequality used as a model to explain real-life phenomena.

Examples

  • For example, as a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
  • As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.
  • Illustrative Mathematics:
  • Student Achievement Partners: