Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 12
Math
Unit 5
5th Grade
Lesson 12 of 25
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Solve real-world problems involving multiplication of fractions with fractions and create real-world contexts for expressions involving multiplication of fractions with 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.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 $$\tfrac{1}{8}\times\tfrac{2}{5}$$, while others need a different operation. Select the ones that can be solved by multiplying these two numbers. For the remaining, tell what operation is appropriate. In all cases, solve the problem (if possible) and include appropriate units in the answer.
a. Two-fifths of the students in Anya’s fifth-grade class are girls. One-eighth of the girls wear glasses. What fraction of Anya’s class consists of girls who wear glasses?
b. A farm is in the shape of a rectangle $$\tfrac{1}{8}$$ of a mile long and $$\tfrac{2}{5}$$ of a mile wide. What is the area of the farm?
c. There is $$\tfrac{2}{5}$$ of a pizza left. If Jamie eats another $$\tfrac{1}{8}$$ of the original whole pizza, what fraction of the original pizza is left over?
d. $$\tfrac{1}{8}$$ of kids in a class are boys. Of those boys, $$\tfrac{2}{5}$$ have red hair. What fraction of the class is red-haired boys?
e. Only $$\tfrac{1}{20}$$ of the guests at the party wore both red and green. If $$\tfrac{1}{8}$$ of the guests wore red, what fraction of the guests who wore red also wore green?
f. Alex was planting a garden. He planted $$\tfrac{2}{5}$$ of the garden with potatoes and $$\tfrac{1}{8}$$ of the garden with lettuce. What fraction of the garden is planted with potatoes or lettuce?
g. At the start of the trip, the gas tank on the car was $$\tfrac{2}{5}$$ full. If the trip used $$\tfrac{1}{8}$$ of the remaining gas, what fraction of a tank of gas is left at the end of the trip?
h. On Monday, $$\tfrac{1}{8}$$ of the students in Mr. Brown’s class were absent from school. The nurse told Mr. Brown that $$\tfrac{2}{5}$$ of those students who were absent had the flu. What fraction of the absent students had the flu?
i. Of the children at a daycare, $$\tfrac{1}{8}$$ are boys and $$\tfrac{2}{5}$$ of the boys are under 1 year old. How many boys at the daycare are under 1 year old?
j. Jason lives $$\tfrac{2}{5}$$ of a mile from school. Grace lives $$\tfrac{1}{8}$$ as far from school as Jason does. How far, in miles, does Grace live from school?
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.
Write a story context that can be solved by multiplying $${{3\over8}\times{4\over5}}$$.
One section of a beach has a total of 180 people. Of these 180 people, $$\frac{4}{9}$$ are wearing a hat and $$\frac{2}{5}$$ of the people wearing hats are also wearing sunglasses. How many people in that section of beach are wearing both a hat and sunglasses?
a. Write an expression to determine how many people in that section of the beach are wearing both a hat and sunglasses.
b. Find the number of people in that section of the beach that are wearing both a hat and sunglasses.
c. Find the number of people in that section of the beach that are wearing a hat but not wearing sunglasses.
Math Spring 2017 Grade 5 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed May 23, 2018, 11:29 a.m..
Problem Set
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All of the cars in a parking lot are either silver, white, or blue. Three-quarters of the cars in the school parking lot are silver. There are $$\frac15$$ as many white cars as there are silver cars. The rest of the cars are blue. What fraction of all the cars in the parking lot are blue?
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Lesson 11
Lesson 13
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 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.
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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