Operations with Rational Numbers

Lesson 18

Math

Unit 2

7th Grade

Lesson 18 of 18

Objective


Solve problems with rational numbers and all four operations.

Common Core Standards


Core Standards

  • 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. Evaluate expressions with rational numbers and all four operations with efficiency and precision (MP.6).
  2. Use rational numbers and operations to represent real-world contexts.
  3. Make sense of problems and outline strategy and approach to solving real-world problems with rational numbers and four operations (MP.1).

Tips for Teachers


  • In terms of pacing, this lesson may be extended an additional day to ensure students get enough exposure to a variety of contexts, combinations of operations, procedural practice, longer tasks, etc. The Problem Set Guidance includes a variety of tasks and activities that can be used for this objective. 
  • Continue building fluency with mental math and other activities.
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Anchor Problems


Problem 1

Claudio keeps track of how his bank account changes over three weeks. 

Claudio's Bank Account

Week Change in Account Balance
1 -$12.40
2 $28.75
3 -$52.00

a.   At the end of week 3, Claudio has $0 in his bank account. How much did he have at the start of week 1?

b.   What is the average amount of money Claudio had in his account at the end of the week over the three weeks?

Guiding Questions

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Problem 2

Michael’s father bought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal lengths for his shelves.

a.   The saw blade that Michael will use to cut the board will change the length of the board by $$-0.125$$ inches for each cut. How will this affect the total length of the board?

b.   After making his cuts, what will the length of each shelf be to the nearest hundredth of an inch?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2Mid-Module Assessment #5

Grade 7 Mathematics > Module 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, 5:17 p.m..

Problem 3

Evaluate each expression:

a.    $${{-{2\over3}\over{-{8\over9}}} + {1\over5}}$$

b.   $${-0.3(4+(-1.8))-6{1\over2}}$$

Guiding Questions

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Problem Set

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Target Task


The temperatures in Jackman, Maine, are shown in the table below.

Day Monday Tuesday Wednesday Thursday Friday
Temperature (°C) -5 3 -2 0 -8

a.   What is the average temperature in Jackman, Maine, from Monday to Friday?

b.   On Saturday, the weather reporter in Jackman says that the average temperature, from Monday to Saturday, has risen to 0 °C. What is the temperature on Saturday?

Student Response

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Additional Practice


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

  • Include examples where students evaluate algebraic expressions for given values of rational numbers.
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Lesson 17

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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