Numerical and Algebraic Expressions

Lesson 10

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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.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from discussion). This could also be done in small groups. Find more guidance on adapting our math curriculum for remote learning here.

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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. 

Who has the better batting average? Justify your answer.

Guiding Questions

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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 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.

Target Task


You have a large sheet of paper that measures $$18\frac{1}{2}$$ inches by $$20$$ inches. You need to cut it into $$6$$ equal-sized rectangles.

a.   Find two different sets of dimensions for the smaller rectangle pieces of paper.

b.   Will the areas of the two rectangles you found in part a be the same? Explain and give the area(s) in square inches.

Mastery Response

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