Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 14
Math
Unit 5
5th Grade
Lesson 14 of 24
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Lesson Notes
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Multiply mixed numbers by fractions.
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
3.MD.C.7 — Relate area to the operations of multiplication and addition.
4.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
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
25-30 minutes
a. A construction worker is tiling a backsplash. The backsplash is $${4{{{1\over2}}}}$$ tiles long and $${{1\over2}}$$ tile tall. How many tiles are needed in total for the whole backsplash? Give an exact answer that includes the fractions of a tile she will need.
b. A runway measures $${10{1\over3}}$$ yards long and $${{3\over4}}$$ yards wide. What is the area, in square yards, of the runway?
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a. Kendra is making $${{1\over2}}$$ of a recipe. The full recipe calls for $${3 {1\over4}}$$ cups of flour. How many cups of flour should Kendra use?
b. Claire walked $${2{2\over5}}$$ miles. Jason walked $${{2\over3}}$$ as far as Claire. How many miles did Jason walk?
Half of a Recipe, accessed on April 25, 2018, 1:28 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.
Math Spring Operational 2015 Grade 5 End of Year Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Dec. 5, 2017, 3:47 p.m..
Solve. Show or explain your work.
a. $${{2\over3} \times 4{1\over4}}$$
b. $${3{2\over5} \times {1\over2}}$$
c. $${{5\over4} \times 3{1\over3}}$$
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
a. $${{2\over3} \times 9{1\over6}}$$
b. $${5{1\over2} \times {3\over4}}$$
Penelope buys a pumpkin that weighs $${6 {1\over4}}$$ kilograms. Penelope’s sister buys a pumpkin that weighs half as much. What is the weight of Penelope’s sister’s pumpkin?
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.
Next
Multiply mixed numbers by mixed 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.
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.A5.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.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.
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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