Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 10
Math
Unit 5
5th Grade
Lesson 10 of 25
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Multiply a fraction by a fraction with more complicated subdivisions using an area model.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
The area model on the right is problematic because “the red shading extended horizontally over the entire [whole, which] implies that the whole for [one third is the same as the whole for one-fourth]-the entire whole” (emphasis mine) (Webel, Krupa, and McManus, “Using Representations of Fraction Multiplication,” NCTM Journal Teaching Children Mathematics). When students are computing $$\frac{1}{3}\times \frac{1}{4}$$, they are finding one third of one fourth, and thus the unit for one third is one fourth, so shading should correspond to this distinction.
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
a. Jan has $${{1\over3}}$$ of a pan of brownies. She sends $${{1\over4}}$$ of the brownies to school with her children. What fraction of a pan of brownies does Jan send to school?
b. Jan has $${{7\over8}}$$ of a pan of brownies. She sends $${{1\over2}}$$ of the brownies to school with her children. What fraction of a pan of brownies does Jan send to school?
c. Jan has $${{3\over4}}$$ of a pan of brownies. She sends $${{5\over8}}$$ of the brownies to school with her children. What fraction of a pan of brownies does Jan send to school?
Grade 5 Mathematics > Module 4 > Topic E > Lesson 15 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..
Grade 5 Mathematics > Module 4 > Topic E > Lesson 14 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..
Grade 5 Mathematics > Module 4 > Topic E > Lesson 13 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. There are two design proposals for a new rectangular park in town.
Which design (1 or 2) will have a bigger soccer field? Explain your answer. Draw a diagram that can be used to compare the size of the soccer field in the two designs. Label the values $${{{{{{{{1\over2}}}}}}}}$$ and $${{{{{{{{{{3\over4}}}}}}}}}}$$ on the diagram.
b. Presley and Julia are cutting $$1$$ ft. square poster board to make a sign for the new park. Presley cut her poster so that the length of the top and bottom are $${{{{{{{{1\over2}}}}}}}}$$ ft. and the length of the sides are $${{{{{{{{{{3\over4}}}}}}}}}}$$ ft. Julia cut her poster so that the lengths of the top and bottom are $${{{{{{{{{{3\over4}}}}}}}}}}$$ ft. and the length of the sides are $${{{{{{{{1\over2}}}}}}}}$$ ft.
Draw a diagram of each poster board. Label the values on the diagram.
How are their poster boards similar and different? Justify your reasoning.
New Park, accessed on April 24, 2018, 1:51 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.
Solve. Show or explain your work.
a. $${{1\over6} }$$ of $${{1\over4}}$$
b. $${{{1\over4}}} \times {5\over6}$$
c. $${{3\over4}\times{5\over8}}$$
d. $${{2\over5} \times {7\over8}}$$
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
a. $${{2\over3} }$$ of $${{4\over5}}$$
b. $${{4\over9}}\times \frac{5}{8}$$
A farmer’s land measures $${{7\over8}}$$ of a mile long and $${{4\over5}}$$ of a mile wide. What is the area, in square miles, of the farmer’s land?
An example response to the Target Task at the level of detail expected of the students.
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 9
Lesson 11
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.
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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