Georgia 5.NR.3.5
The Standard
Explain why multiplying a whole number by a fraction greater than one results in a product greater than the whole number, and why multiplying a whole number by a fraction less than one results in a product less than the whole number and multiplying a whole number by a fraction equal to one results in a product equal to the whole number.
Georgia's K-12 Mathematics Standards · Describe fractions and perform operations with fractions to solve relevant, mathematical problems using part-whole strategies and visual models.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare a product with its whole-number factor before calculating. They use number lines, area models, or equal groups to explain how the fraction's size affects the product.
What Mastery Looks Like
- Students correctly predict whether a product will be below, equal to, or above the whole-number factor. They justify each prediction with a model and a clear explanation about the fraction's size.
Common Misconceptions
- Students may think multiplication always makes a number larger. They may judge a fraction by its denominator alone or treat the numerator and denominator as separate multipliers.
How to Assess It
- Ask: Without calculating, compare 12 × 7/6, 12 × 5/8, and 12 × 9/9 with 12. Draw a model for one answer.
Lesson moves
Ways to Teach It
Build six groups of 3/4, 1, and 5/4 with fraction tiles, then compare each total with six.
Write an explanation for this prompt: How can you compare 10 × 7/8 with 10 without calculating?
Sort multiplication cards into three groups: product below, equal to, or above the whole-number factor, then check with a partner.
Compare the total distance from eight laps that are each 3/4 mile, one mile, or 5/4 miles.
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Related Standards
- 3.NR.4.3
Represent fractions, including fractions greater than one, in multiple ways.
- 5.NR.3.4
Model and solve problems involving multiplication of a fraction and a whole number.
- 3.NR.4.1
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- 6.NR.1.2
Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fracti...
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