Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 15
Math
Unit 5
5th Grade
Lesson 15 of 25
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Multiply mixed numbers by mixed 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.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.)
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
a. Chavone is tiling her kitchen floor. The floor is $${4{1\over2}}$$ tiles long and $${6{1\over4}}$$ tiles wide. How many tiles are needed in total for the whole kitchen? Give an exact answer that includes the fractions of a tile she will need.
b. Chavone is also putting in a new countertop. It measures $${2{1\over4}}$$ feet wide and $${10{3\over4}}$$ feet long. What is the area, in square feet, of the countertop?
Chavone's Bathroom Tiles, accessed on April 25, 2018, 2:54 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. A glass can hold $${1{1\over2}}$$ cups of water. Ms. Needham drinks $${4{1\over3}}$$ glasses of water on Monday. How much water, in cups, did Mrs. Needham drink?
b. Wildflower Hiking Trail is $${3{3\over8}}$$ miles long. Oak Tree Hiking Trail is $${2{1\over2}}$$ times as long as Wildflower Hiking Trail. How long, in miles, is Oak Tree Hiking Trail?
Solve. Show or explain your work.
a. $$6\frac{1}{2} \times 4\frac{2}{3}$$
b. $$4\frac{3}{4} \times 2\frac{1}{9}$$
Problem Set
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a. $${4 {1\over6} \times 9 {3\over4}}$$
b. $${3 {2\over3} \times 4 {4\over5}}$$
Naira wants to buy a new desk for her bedroom. The desktop of one she is looking at is $$5\tfrac{2}{3}$$ long and $$2\tfrac{1}{2}$$ feet wide. What is the area of the desktop?
An example response to the Target Task at the level of detail expected of the students.
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Lesson 14
Lesson 16
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.
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.
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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