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Solve Multi-Step Problems with Rational Numbers in Any Form

Multi-step word problems mixing fractions, decimals, and percents ask students to combine operations, judge whether an estimate is reasonable, and solve a matching multiple-choice test-practice set.
Grades
Grade 7, Middle School
File type
PDF
Preparation
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Updated Mar 31, 2022

Subject
Math, Algebra
Topic
multi-step problems, rational numbers
Resource types
Activities
Preparation
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About this resource

What's inside this resource

This resource was developed to meet the requirements of the 7th Grade Expressions & Equations Standards below:

CCSS.MATH.CONTENT.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.


In the classroom

Teaching tips & learning objectives

Learning objectives

  • Convert a value between fraction, decimal, and percent form

  • Estimate the answer to a multi-step rational-number problem using rounding and mental math, then check it against the exact computation

  • Solve a multi-step real-world problem involving positive and negative rational numbers in any form

Teaching tips

  • Work through the converting-formats chart as a warm-up before the estimation and practice problems, since later problems mix fraction, decimal, and percent values

  • Have students record an estimate before calculating the exact answer, then compare the two, following the estimation page's own structure

  • Use the multiple-choice test-practice set as a follow-up check after the open-ended practice problems. Practice checking whether answers are reasonable with this estimate and calculate worksheet.

Skills covered

  • Rational-number form conversion -- students convert values among fraction, decimal, and percent form using a guided chart.

  • Estimation and reasonableness checking -- students round and mentally compute an approximate answer, then verify it against an exact multi-step calculation.

  • Multi-step problem solving with rational numbers -- students combine operations on positive and negative fractions, decimals, and percents to solve real-world word problems.

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Resource details

Concepts & topics

Core concepts

  • rational numbers

  • multi-step problem solving

  • estimation

  • fraction-decimal-percent conversion

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