# Numerical and Algebraic Expressions

## Objective

Write and evaluate expressions for mathematical and contextual situations.

## 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.

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• 6.EE.A.2

## Criteria for Success

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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

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

### Remote Learning Guidance

This lesson reviews prior concepts and extends on 7.NS.A.3; Anchor Problems can be chosen based on what specific concept and/or skill work students need. Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### 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 Fishtank Learning, 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 Fishtank Learning, Inc.

## 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.

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### Problem 1

Four siblings buy a gift for their father on his birthday. Each sibling contributes the same amount of money towards the gift. The gift ends up coming to $63 and after paying for the gift, there is some money left over which the siblings equally split. a. Write an expression to represent the amount of money each sibling will get back after the gift is paid for. b. If each sibling contributed$18 towards the gift, how much money did each sibling get back?

#### Mastery Response

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