Curriculum / Math / 4th Grade / Unit 5: Fraction Operations / Lesson 17
Math
Unit 5
4th Grade
Lesson 17 of 21
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Multiply a whole number by a mixed number.
The core standards covered in this lesson
4.NF.B.4.B — Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
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
a. Draw a model to represent each of the following. Then find the product.
b. What do you notice about Part (a)? What do you wonder?
a. Here is Kellen’s strategy for finding the value of $$3\times2\tfrac14$$: “I know I can write $$2\tfrac14$$ as $$2+\tfrac14$$, so I can compute $$3\times2\tfrac14=(3\times2) + \left(3\times\tfrac14\right)$$. Since $$3\times2=6$$ and $$3\times\tfrac14=\tfrac34$$, then $$3\times2\tfrac14=6+\tfrac34=6\tfrac34$$.” Does Kellen’s strategy for finding the product of a whole number and a mixed number work? Show or explain your thinking.
b. Estimate the following products. Then solve.
Juliette decided to solve $$3\times2\frac14$$ in a different way from Kellen’s strategy:
$${3\times2{1\over4} =3\times\left(2+\frac{1}{4}\right)=3\times{9\over4}}$$
a. Does Juliette’s strategy work? Will it yield the same product as Kellen's strategy?
b. Solve the computations from Part (b) of Anchor Task 2 using this method. Are your products the same regardless of which method you use?
c. Which method do you prefer? Why?
Problem Set
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Solve. Show or explain your work.
a. $${4 \times 3{7\over8}}$$
b. $${2\times 6{2\over5}}$$
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Lesson 16
Lesson 18
Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1
Decompose fractions as a sum of unit fractions and as a multiple of a unit fraction.
4.NF.B.3.B 4.NF.B.4.A
Decompose fractions as a sum of fractions with the same denominator in more than one way.
Add and subtract fractions within 1 with the same units.
4.NF.B.3.A 4.NF.B.3.C
Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.
4.NF.B.3.D
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Topic B: Building, Adding, and Subtracting Fractions Less Than 2
Decompose non-unit fractions less than 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.
Add and subtract fractions that require regrouping where the total is less than 2.
Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.
Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2
Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.
4.NF.B.3.B
Convert fractions greater than 1 to mixed numbers.
4.NF.B.3.B 4.NF.B.3.C
Convert mixed numbers to fractions greater than 1.
Compare and order fractions greater than 1 using various methods.
4.NF.B.3.C
Add fractions and mixed numbers where the total is greater than or equal to 2.
Subtract fractions and mixed numbers where the total is greater than or equal to 2.
Add and subtract mixed numbers using a variety of mental strategies.
Solve word problems involving addition and subtraction of fractions.
Topic D: Multiplication of Fractions
Multiply a whole number by a fraction.
4.NF.B.4.B
Solve word problems involving multiplication of fractions.
4.NF.B.4.C
Solve word problems involving addition, subtraction, and multiplication of fractions.
4.NF.B.3.D 4.NF.B.4.C
Topic E: Line Plots
Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.
4.MD.B.4
Solve problems using information presented in line plots.
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