# Numerical and Algebraic Expressions

## Objective

Subtract and simplify expressions.

## 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.

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• 6.EE.A.3

• 6.EE.A.4

• 7.NS.A.1

• 7.NS.A.2

## Criteria for Success

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1. Understand that when an expression is subtracted, every term in the expression is subtracted.
2. Understand that subtracting an expression is the same as distributing a ${-1}$ through the parentheses group, changing the sign of each term.
3. Subtract and simplify expressions.

## Tips for Teachers

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This lesson includes problems such as ${3x - (6 + 8x) }$ but does not include problems such as
${3x - 2(6 + 8x)}$, where a multiple of an expression is being subtracted. This will be covered in Lesson 7 and Lesson 8. The concept of distributing a negative through a parentheses group can be challenging for students, so this lesson focuses on students understanding that when an expression is subtracted, every term in the expression is subtracted, not just the first term.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Consider the numerical expression: ${12-(3+4)}$

The expression is rewritten so it does not include parentheses. Which expression will give the same value as the original expression? Explain your reasoning for each one.

${12-3+4}$                  ${12-3-4}$

### Problem 2

Subtract: ${(3x+5y-4)-(4x+11)}$

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 2Example 1b

Grade 7 Mathematics > Module 3 > Topic A > Lesson 2 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..

### Problem 3

Match each subtraction problem on the left with the equivalent simplified expression on the right.

 A.  $5x-(3x+1)$ 1.  $-8x-1$ B.   $5x-(-3x-1)$ 2.  $-2x+1$ C.   $-5x-(3x+1)$ 3.  $2x-1$ D.   $-5x-(-3x-1)$ 4.  $8x+1$

## 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.

• Include error analysis problems of subtraction problems where not every term in the parentheses was subtracted.
• Include procedural problems where students add and subtract expressions—can be more than two expressions or addition and subtraction combined. (Do not include problems where a multiple of an expression is subtracted, such as ${5x - 2(3x - 8)}$. This will come in Lesson 7.
• Challenge: Expression $A$ is given by $3-x$. Expression $B$ is given by $-x-3$. Write a simplified expression that represents $-A-B-B-A$.

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Two expressions are given below.

Expression A:      ${5q-r}$

Expression B:      ${ -2q+3r-4}$

1. Write a simplified expression that represents A + B.
2. Write a simplified expression that represents A - B.

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