Curriculum / Math / 4th Grade / Unit 5: Fraction Operations / Lesson 5
Math
Unit 5
4th Grade
Lesson 5 of 21
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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.
The core standards covered in this lesson
4.NF.B.3.B — Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
4.NF.B.4.A — Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
The foundational standards covered in this lesson
3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.
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Lin’s family recipe for cookies also calls for $$\frac64$$ cups chopped nuts. Write an addition equation and a multiplication equation to show how she can use the $$\frac14$$-cup measure to measure the amount of chopped nuts.
Grade 4 Unit 3 Lesson 7 Activity 1 ("Activity 1: Barley Soup"), accessed on March 18, 2022, 10:07 a.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. On each number line, draw two “jumps” to show how to use thirds to make a sum of $$\frac53$$. Then, write an equation to represent each combination of jumps.
b. Noah draws the following number line and writes: $$\frac53 = \frac33 + \frac23$$ and $$\frac53= 1+\frac23$$. Which equation is correct? Explain your reasoning.
c. Write $$\frac64$$ as a sum of a whole number and a fraction. Use a number line if it would help you.
Math Grade 4 Unit 3 Lesson 8 Activity 1, accessed on March 18, 2022, 10:17 a.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. On each number line, draw “jumps” to show how to use eighths to make a sum of $$1\frac38$$. Then, write an equation to represent each combination of jumps.
b. Explain why $${1{3\over8}}={11\over8}$$ using a number line or words.
Problem Set
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Decompose the following fractions (i) as a sum of unit fractions, (ii) as a multiple of a unit fraction, and (iii) in at least one other way.
a. $${{7\over6}}$$
b. $${1{3\over4}}$$
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Lesson 4
Lesson 6
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
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
Multiply a whole number by a mixed number.
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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