# Numerical and Algebraic Expressions

## Objective

Write and evaluate expressions for mathematical and contextual situations.

## Common Core Standards

### Core Standards

?

• 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.

?

• 6.EE.A.2

## Criteria for Success

?

1. Use substitution to evaluate algebraic expressions for given values.
2. Write algebraic expressions for verbally described expressions or real-world contexts.

## Tips for Teachers

?

This lesson approaches 7.EE.1 while engaging students in 7.NS.3.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

?

### Problem 1

Given the expression: ${(a^2-b)-(2ab)}$

Is the expression greater when ${a=-1}$${b=1}$ or when ${a=1}$${b=-1}$?

### Problem 2

Write an expression for each sequence of operations.

Expression 1: Add $3$ to $x$, subtract the result from $1$, then double what you have.
Expression 2: Add $3$ to $x$, double what you have, then subtract $1$ from the result.

Evaluate each expression for $x=2$.

#### References

Illustrative Mathematics Writing Expressions

Writing Expressions, accessed on Oct. 6, 2017, 2:32 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 3

Three friends went to the movies. Each purchased a medium-sized popcorn for $p$ dollars and a small soft drink for $d$ dollars. The friends paid together with two twenty-dollar bills.

1. Write an expression to represent the amount of money the friends get back in change after paying for their snacks.
2. How much change will the friends get back if the concession stand charges $6.50 for a medium-sized popcorn and$4.00 for a small soft drink?

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 18Exercise 2

Grade 7 Mathematics > Module 2 > Topic C > Lesson 18 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 The Match Foundation, Inc.

## Problem Set

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

?

### Problem 1

Bradley and Louie are roommates at college. At the beginning of the semester, they each paid a security deposit of A dollars. When they move out, their landlord will deduct from this deposit any expenses, B, for any damages and refund the remaining amount. Bradley and Louie will share the expenses equally.

1. Write an expression that represents the amount each roommate will receive from the landlord when they move out.
2. If each roommate paid a deposit of $125 and the landlord deducted$50 total for damages, then how much will each roommate get back?

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 18Exit Ticket

Grade 7 Mathematics > Module 2 > Topic C > Lesson 18 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 2

Evaluative ${2x^3-4\left ( x+4\frac{1}{2} \right )}$ for ${x=-2}$.

?