Solve Multi-Step Problems with Rational Numbers in Any Form

- Grades
- Grade 7, Middle School
- File type
- Preparation
- Print ready
- Subject
- Math, Algebra
- Topic
- multi-step problems, rational numbers
- Resource types
- Activities
- Preparation
- Print ready
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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