# Numerical and Algebraic Expressions

## Objective

Solve multi-step real-world problems with rational numbers.

## Common Core Standards

### Core Standards

?

• 7.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or$2.50, for a new salary of \$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

• 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.

## Criteria for Success

?

1. Develop a strategy to solve real-world problems involving computation with rational numbers.
2. Use properties and order of operations to compute with rational numbers in any form.

## Tips for Teachers

?

Lessons 10 and 11 engage students in solving multi-step real-world problems, drawing on skills from Units 1–3. There is only one Anchor Problem in this lesson that can be introduced as a whole class and then completed by the students in pairs or small groups. For these challenging problems, students would benefit from a mix of peer collaboration time, independent work time, and teacher-led discussion.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

?

Below is a table showing the number of hits and the number of times at bat for two Major League Baseball players during two different seasons:

 Season Derek Jeter David Justice 1995 12 hits in 48 at bats 104 hits in 411 at bats 1996 183 hits in 582 at bats 45 hits in 140 at bats

A player's batting average is the fraction of times at bat when the player gets a hit.

#### References

Illustrative Mathematics Who is the Better Batter?

Who is the Better Batter?, accessed on Oct. 9, 2017, 11:34 a.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 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.

?

The bar-tailed godwit is a bird that makes the longest known nonstop flight during migration. An article described the migration of a bar-tailed godwit from Alaska to New Zealand saying, “She had flown for eight days – nonstop – covering approximately 7,250 miles at an average speed of nearly 30 miles per hour.”

#### References

Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics (6-8 Expressions and Equations)

Progressions for the Common Core State Standards in Mathematics (6-8 Expressions and Equations), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed March 21, 2018, 8:05 p.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Modified by The Match Foundation, Inc.

?