Curriculum / Math / 4th Grade / Unit 5: Fraction Operations / Lesson 2
Math
Unit 5
4th Grade
Lesson 2 of 21
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Lesson Notes
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Decompose fractions as a sum of fractions with the same denominator in more than one way.
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.
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
25-30 minutes
Lin later found a $$\frac34$$-cup measuring cup. Show how she could use the $$\frac34$$ and $$\frac14$$ measuring cups to measure the right amount of each ingredient below.
a. $$\frac34$$ cups sugar
b. 1 cup butter
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Grade 4 Unit 3 Lesson 7 Activity 1, accessed on March 17, 2022, 3:49 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.
On each number line, draw two “jumps” to show how to use sixths to make a sum of $$\frac66$$. Then, write an equation to represent each combination of jumps.
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. Use different combinations of tenths to make a sum of $$\frac{9}{10}$$.
b. Write different ways to use fifths to make a total of $$\frac 55$$. How many can you think of? Write an equation for each combination.
c. Is it possible to write any fraction with a denominator of 8 as a sum of other eighths? Explain or show your reasoning.
Grade 4 Unit 3 Lesson 7 Activity 2, accessed on March 17, 2022, 3:56 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.
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Decompose the following fraction in three different ways. Record the decompositions with equations.
$${{7\over8}}$$
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
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
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Add and subtract fractions within 1 with the same units.
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.
Standards
4.NF.B.3.B4.NF.B.4.A
4.NF.B.3.A4.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.B4.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.D4.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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