Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 9
Math
Unit 5
5th Grade
Lesson 9 of 25
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Multiply a fraction by a fraction with subdivisions using tape diagrams and number lines.
The core standards covered in this lesson
5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
The foundational standards covered in this lesson
4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
a. A large box of paper clips weighs $${{1\over5}}$$ kilogram. A small box of paper clips weighs $${{1\over2}}$$ as much as a large box of paper clips. What is the weight, in kilograms, of a small box of paperclips?
b. Valencia has $${{1\over3}}$$ hour until bedtime. She uses $${{3\over4}}$$ of that time to read a bedtime story. How much time, in hours, does Valencia spend reading a bedtime story?
c. EXTENSION: How much time, in minutes, does Valencia spend reading a bedtime story?
a. Zack had $${{2\over3}}$$ of the lawn left to cut. After lunch, he cut $${{3\over4}}$$ of the grass he had left. How much of the whole lawn did Zack cut after lunch?
b. Alisa had $${{5\over6}}$$ a liter of juice in a bottle. She drank $${{1\over2}}$$ of the juice that was in the bottle. How many liters of juice did she drink?
Drinking Juice, accessed on April 24, 2018, 1:36 p.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.
Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.
Folding Strips of Paper, accessed on April 24, 2018, 1:36 p.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.
Solve. Show or explain your work.
a. $${{1\over2}}$$ of $${{1\over4}}$$
b. $${{2\over3}}$$ of $${{1\over3}}$$
c. $${{3\over4} \times {2\over5}}$$
d. $${{{1\over2}}} \times {3\over4}$$
Problem Set
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a. $${{2\over3}}$$ of $${{1\over4}}$$
b. $${{5\over6} \times {3\over4}}$$
Ladonna spent $$1\over4$$ of the time it took her to do her homework on her math homework and $$1\over2$$ of the rest of the time on her history homework. What fraction of the time Ladonna spent doing her homework did she spend on her history homework?
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The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
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Lesson 8
Lesson 10
Topic A: Fractions as Division
Relate equal shares of objects to division expressions and visual representations of fractions.
5.NF.B.3
Write division expressions that represent fractions and vice versa.
Solve division problems when the quotient is a fraction or mixed number, including cases with larger values.
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Topic B: Multiplying a Fraction by a Whole Number
Multiply a fraction by a whole number where the product is a whole number.
5.NF.B.4.A 5.NF.B.6
Multiply a fraction by a whole number where the product is a whole number or a fraction.
Relate multiplication of a fraction by a whole number to multiplication of a whole number by a fraction and use this to develop a general method to multiply any fraction by any whole number (or vice versa).
5.NF.B.4.A 5.NF.B.5
Solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers.
5.NF.B.4 5.NF.B.6 5.OA.A.2
Topic C: Multiplying a Fraction by a Fraction
Multiply a fraction by a fraction without subdivisions using tape diagrams and number lines.
5.NF.B.4 5.NF.B.5 5.NF.B.6
Multiply a fraction by a fraction with more complicated subdivisions using an area model.
Develop a general method to multiply a fraction by a fraction.
Solve real-world problems involving multiplication of fractions with fractions and create real-world contexts for expressions involving multiplication of fractions with fractions.
Topic D: Multiplying with Mixed Numbers
Multiply mixed numbers by whole numbers.
Multiply mixed numbers by fractions.
Multiply mixed numbers by mixed numbers.
Develop a general method to multiply with mixed numbers.
Solve real-world problems involving multiplication with mixed numbers and create real-world contexts for expressions involving multiplication with mixed numbers.
Interpret multiplication as scaling.
5.NF.B.5 5.NF.B.5.A 5.NF.B.5.B
Topic E: Dividing with Fractions
Divide a unit fraction by a whole number.
5.NF.B.7.A 5.NF.B.7.C
Divide a whole number by a unit fraction.
5.NF.B.7.B 5.NF.B.7.C
Solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions.
5.NF.B.7.C 5.OA.A.2
Topic F: Fraction Expressions and Real-World Problems
Solve real-world problems involving multiplication and division with fractions.
5.NF.B.3 5.NF.B.6 5.NF.B.7
Write and evaluate numerical expressions involving operations with fractions.
5.NF.B.3 5.NF.B.4 5.NF.B.5 5.NF.B.6 5.NF.B.7 5.OA.A.1 5.OA.A.2
Topic G: Line Plots
Create line plots.
5.MD.B.2
Solve problems involving information presented in a line plot (dot plot).
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