Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 8
Math
Unit 5
5th Grade
Lesson 8 of 25
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Multiply a fraction by a fraction without subdivisions using tape diagrams and number lines.
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
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
This lesson exclusively looks at fraction multiplication problems in which the units or fractional parts do not need to be subdivided or partitioned further. For example, “students who solve [the problem $$\frac13$$ of $$\frac34$$] with a picture or using a number line do not need to subdivide the unit fractions that comprise 34 to find $$\frac13$$ of $$\frac34$$ since it is naturally composed of 3 pieces” (Illustrative Mathematics).
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
The distance between Rosa’s house and her school is $${{3\over4}}$$ mile. She ran $${{1\over3}}$$ of the way to school. How many miles did she run?
Running to School, accessed on Sept. 28, 2017, 2:09 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. You have $${{4\over5}}$$ of a loaf of bread. If you use $${{3\over4}}$$ of the bread that is left of the loaf to make sandwiches, how much of a whole loaf did you use?
b. $${{6\over10}}$$ of the first-grade students are girls. $${{2\over3}}$$ of the first-grade girls have brown eyes. What fraction of first-grade students are girls with brown eyes?
Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.
Solve. Show or explain your work.
a. $${{{{1\over2}}}}$$ of $${{2\over3}}$$
b. $${{{{1\over2}}}}$$ of $${{4\over9}}$$
c. $${{3\over5}}$$ $$\times$$ $${{5\over8}}$$
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
$${{1\over3}}$$ of $${{3\over8}}$$
In a park, $$5\over6$$ of the space is filled with sports fields. If soccer fields account for $$2\over5$$ of the space for sports fields, what fraction of the park is soccer fields?
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.
Extra Practice Problems
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Lesson 7
Lesson 9
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
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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