Numerical and Algebraic Expressions

Lesson 1

Objective

Evaluate numerical expressions with rational numbers using the order of operations.

Common Core Standards

Core Standards

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  • 7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

  • 7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Foundational Standards

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  • 6.EE.A.2.C

Criteria for Success

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  1. Understand order of operations as a guide to interpreting and evaluating a numerical expression.
  2. Explain how numbers and terms interact together in an expression, especially when parentheses and exponents are involved.
  3. Write successive equivalent expressions that simplify and eventually evaluate a numerical expression.

Tips for Teachers

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  • Lessons 1 and 2 are approaching 7.EE.1 while also engaging students in 7.NS.3. Students review concepts from 6th grade around using the order of operations while also taking the time to analyze and inspect the structure of the expression before solving (MP.7).
  • This blog post on Bill McCallum’s blog, A world without order (of operations) is a valuable read to understand what the order of operations really offers us as a tool.

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Anchor Problems

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Problem 1

Evaluate the following numerical expressions.

$${-2(5+(3)(-2)+4)}$$

$${-2((5+3)(-2+4))}$$

$${-2(5+3(-2+4))}$$

Can the parentheses in any of these expressions be removed without changing the value of the expression?

Guiding Questions

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References

Illustrative Mathematics Watch Out for Parentheses

Watch Out for Parentheses, accessed on Oct. 6, 2017, 2:16 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

Problem 2

An expression is shown below with three expressions that are not equivalent to it. Explain the error(s) that were made in writing each expression, then evaluate the expression.

  $$\frac{6-3(4-8)}{2(1+2)^2}$$  
$$\neq \frac{3(-4)}{2(3)^2}$$ $$\neq \frac{6-3(-4)}{(6)^2}$$ $$\neq \frac{6-12}{(2+4)^2}$$

 

Guiding Questions

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Problem 3

Evaluate:      $${\frac{1}{2}(-3-1)^2-\left ( 10 \div \frac{5}{6} \right )}$$

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Algebra By Example 1.6 Order of Operations
  • Desmos Expressions Mash-UpOptional review of expressions from sixth grade; matching expressions in various formats; requires computers
  • Kuta Software Free Algebra 1 Worksheets Order of OperationsAdapt to include negative numbers, other rational numbers, and exponents

Target Task

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Evaluate the expression below. For each successive expression you write, explain what you did to create an expression equivalent to the expression before.

$${\frac{2-3(4-6)^2}{\frac{1}{2}}}$$

Mastery Response

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