Curriculum / Math / 5th Grade / Unit 5: Multiplication and Division of Fractions / Lesson 11
Math
Unit 5
5th Grade
Lesson 11 of 25
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Develop a general method to multiply a fraction by a fraction.
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
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Below is a model of the fraction $${{{{4\over5}}}}$$.
Explain how to find $${{6\over7}}$$ of $${{{{4\over5}}}}$$. Try not to make additional drawings on the model above.
Van de Walle, John A. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013.
a. Solve. Draw a diagram if it is helpful.
b. Connor says that to multiply a fraction by a fraction, he’d multiply the numerators of the factors together to find the numerator of the product and multiply the denominators of the factors together to find the denominator of the product. Do you agree with Connor? Explain your reasoning.
When solving $$\frac{1}{12} \times \frac89$$, Almira computed like so:
$$\frac{1}{12}\times\frac{8}{9}=\frac{1\times \overset{2}{\cancel{8}}}{\underset{3}{\cancel{12}}\times9} = \frac{2}{27}$$
She said, "I simplified my fraction before multiplying which made it easier!"
a. Explain what Almira did in your own words.
b. Use Almira’s strategy to solve Parts (iii) and (iv) in Anchor Task 2. Determine whether your answers are equivalent.
Before solving, predict whether each product will be less than, equal to, or greater than $${{2\over7}}$$. Then solve.
a. $${3\over10}\times{{{2\over7}}}$$
b. $${14\over10}\times{{{2\over7}}}$$
c. $${10\over10}\times {{{2\over7}}}$$
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
Solve. Show or explain your work.
a. $${{2\over3} \times {5\over6}}$$
b. $${{4\over9} \times { 3\over 8}}$$
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 10
Lesson 12
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.
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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