Numerical and Algebraic Expressions

Lesson 2

Math

Unit 5

6th Grade

Lesson 2 of 12

Objective


Evaluate numerical expressions involving whole-number exponents.

Common Core Standards


Core Standards

  • 6.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.

Foundational Standards

  • 5.OA.A.1

Criteria for Success


  1. Understand the role of parentheses in an expression and their impact on how the expression is evaluated (MP.7).
  2. Evaluate numerical expressions with nested parentheses.
  3. Evaluate numerical expressions with exponents.
  4. Distinguish between expressions with exponents inside and outside of parentheses.

Tips for Teachers


  • This blog post "A world without order (of operations)" on Bill McCallum’s blog is a valuable read to understand what the order of operations really offers us as a tool.
  • Students extend their work from 5th grade where they evaluate numerical expressions with parentheses, brackets, or braces to now include expressions with exponents.
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Anchor Problems


Problem 1

Evaluate the following numerical expressions. For each expression, determine if the parentheses can be removed without changing the value of the expression. 

a.   $${2(5+(3)(2)+4)}$$

b.   $${2((5+3)(2+4))}$$

c.   $${2(5+3(2+4))}$$

Guiding Questions

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References

Illustrative Mathematics Watch Out for Parentheses

Watch Out for Parentheses, accessed on Dec. 18, 2017, 2:36 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.

Problem 2

Four expressions are shown below along with four area diagrams. 

Match each expression to a diagram. Then evaluate the expression and find the area of the diagram to demonstrate they are equivalent. 

Expressions:

$$2^{2}+5^{2}$$          $${2\times5^2}$$          $${2+5^2}$$          $${(2+5)^2}$$

Area Diagrams:

Guiding Questions

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Problem 3

Evaluate each numerical expression.

a.   $$2 × \left( 3+4^2 \right)$$

b.   $$2 × (3+4)^2$$

c.   $${[2(3+4)]^2}$$

d.   $${2+3(4+1)^2}$$

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic B > Lesson 6Example 4

Grade 6 Mathematics > Module 4 > Topic B > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


Evaluate the expressions.

a.   $$24\div(2+1)+(11-8)\times2$$

b.   $$3^2\times4-10+(12-3)^2$$

c.   $$(3\times4)^2-10\times(12-3^2)$$

Student Response

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Additional Practice


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

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Lesson 1

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Lesson 3

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Numerical Expressions with Exponents

Topic B: Introduction to Algebraic Expressions

Topic C: Equivalent Expressions & Applications

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