Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 6
Math
Unit 5
5th Grade
Lesson 6 of 24
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Lesson Notes
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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).
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.5 — Interpret multiplication as scaling (resizing), by:
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
Suggestions for teachers to help them teach this lesson
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
For each expression, explain how the model below represents the expression.
a. $$\frac{2}{3}\times3$$
b. $$3\times \frac{2}{3}$$
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a. Solve. Draw a model if it is helpful.
b. Soheil says that to multiply a whole number by a fraction or a fraction by a whole number, he’d multiply the whole number and the numerator and use the same denominator. Do you agree with Soheil? Explain your reasoning.
When solving $$10 \times \frac35$$, Guy computed like so:
$$10 \times \frac35 = \frac{10\times3}{5} = \frac{\overset{2}{\cancel{10}}\times3}{\underset{1}{\cancel{5}}} = \frac{2\times3}{1} = 6$$
He said, “I simplified my fraction before multiplying which made it easier!"
a. Explain why Guy's strategy works.
b. Use Guy's strategy to find the value of the other expressions in Part (a) in Anchor Task 2 above. Decide whether your answers are equivalent.
Before solving, predict whether each product will be less than, equal to, or greater than $${12}$$. Then solve.
a. $${5\over8} \times {12}$$
b. $${9\over8} \times {12}$$
c. $${8\over8} \times {12}$$
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Solve. Show or explain your work.
a. $${{3\over5}\times20}$$
b. $${10\times{5\over4}}$$
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.
Extra Practice Problems
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
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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.
Topic A: Fractions as Division
Relate equal shares of objects to division expressions and visual representations of fractions.
Standards
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 unit fraction by a whole number.
5.NF.B.4.A5.NF.B.6
Multiply a non-unit fraction by a whole number.
5.NF.B.4.A5.NF.B.5
5.NF.B.45.NF.B.65.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.45.NF.B.55.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.55.NF.B.5.A5.NF.B.5.B
Topic E: Dividing with Fractions
Divide a unit fraction by a whole number.
5.NF.B.7.A5.NF.B.7.C
Divide a whole number by a unit fraction.
5.NF.B.7.B5.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.C5.OA.A.2
Topic F: Fraction Real-World Problems and Line Plots
Solve real-world problems involving multiplication and division with fractions.
5.NF.B.35.NF.B.65.NF.B.7
Create line plots.
5.MD.B.2
Solve problems involving information presented in a line plot (dot plot).
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