Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 5
Math
Unit 5
5th Grade
Lesson 5 of 25
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Multiply a fraction by a whole number where the product is a whole number or a fraction.
The core standards covered in this lesson
5.NF.B.4.A — Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
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. Rosie has 15 yards of fabric. She uses $${{2\over3 }}$$ of it to make a dress. How much fabric, in yards, does she use to make the dress?
b. Rosie also bought 11 feet of ribbon. She uses $${{1\over2}}$$ of it to make a bow for her dress. How much ribbon, in feet, does she use to make the bow?
Grade 5 Mathematics > Module 4 > Topic C > Lesson 7 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, 5:15 p.m..
a. How would you write “5 groups of 12” as a mathematical expression? How does that inform how you would write “$${{1\over4}}$$ group of 12” as a mathematical expression?
b. Use your observation from Part (a) to solve the following:
a. Frederick says $$\frac16 \times 18 = 18 \div 6$$. Do you agree or disagree? Justify your thinking.
b. How would you modify Frederick’s equation to represent $$\frac56 \times 18$$?
Problem Set
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Solve. Show or explain your work.
a. $${{3\over4} \times 32}$$
b. $${{2\over5} \times 8}$$
On Monday, Mrs. Johnson went on a walk that was $$4$$ miles long. On Tuesday, she goes on a walk that is $${{2\over3}}$$ as long as her walk on Monday. How long was Mrs. Johnson’s walk on Tuesday?
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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 4
Lesson 6
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
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 subdivisions using tape diagrams and number lines.
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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