Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 7
Math
Unit 5
5th Grade
Lesson 7 of 25
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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.
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.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.
5.OA.A.2 — Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
The foundational standards covered in this lesson
3.OA.A.1 — Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
3.OA.A.2 — Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
3.OA.D.8 — Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
4.OA.A.1 — Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.A.2 — Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson connects the work of solving real-world problems involving multiplication of fractions and mixed numbers (5.NF.6) with writing and interpreting numerical expressions (5.OA.A), connecting content across domains.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Some of the problems below can be solved by multiplying $$\tfrac{3}{5}\times15$$, while others need a different operation. For each one, explain whether or not it can be solved by multiplying these two numbers. If they cannot be solved by multiplying, tell what operation is appropriate. In all cases, solve the problem (if possible) and include appropriate units in the answer.
a. There are 15 people at a party. $$\tfrac{3}{5}$$ of them are boys. How many people at the party are boys?
b. Wesley ran 15 miles on Monday and $$\tfrac{3}{5}$$ mile on Tuesday. How many miles did Wesley run?
c. If each person at a party eats $$\tfrac{3}{5}$$ of a pound of roast beef and there are 15 people at the party, how many pounds of roast beef are needed?
d. Nathaniel has 15 cups of soup split into 5 equal-sized portions. He’ll serve three of the portions for dinner tonight. What is the total amount of soup, in cups, that Nathaniel will serve tonight?
e. 15 students in the fifth grade want to play soccer. $$\tfrac{3}{5}$$ of the students in fifth grade want to play basketball. How many students want to play either soccer or basketball?
f. Helena is carpeting a long corridor. It is $$\tfrac{3}{5}$$ yards wide and 15 yards long. How much carpeting, in square yards, does Helena need?
g. Lisbeth has $$\tfrac{3}{5}$$ of a pound of chocolate that she wants to share evenly with 15 people. How much chocolate will everyone get?
h. Dawa has 15 pencils in her pencil case. Theo has $$\tfrac{3}{5}$$ as many pencils in his pencil case as Dawa does. How many pencils does Theo have?
i. Tiffany has $15. She spends $$\tfrac{3}{5}$$ of her money on a teddy bear. How much money does she have left?
To Multiply or Not to Multiply, accessed on April 24, 2018, 1:06 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.
a. Write a story context that can be solved by multiplying $$8\times \frac{3}{4}$$.
b. Write a story context that can be solved by multiplying $${{2\over3} \times 4}$$.
Progressions for the Common Core State Standards in Mathematics (Numbers and Operations - Fractions, 3-5), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed April 16, 2018, 11:23 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.
Brit is buying a cake and a pie for an upcoming birthday party. The cake costs $32 and the pie costs $$\frac58$$ as much as the cake.
a. Write an expression that represents the total cost of the cake and pie.
b. Find the total cost of the cake and pie.
Problem Set
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In a bakery, $$1\over4$$ of the cookies for sale are gingersnaps and $$2\over3$$ are chocolate chip. There are 24 cookies for sale. How many cookies are neither gingersnaps nor chocolate chip?
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Lesson 6
Lesson 8
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
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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