Curriculum / Math / 4th Grade / Unit 5: Fraction Operations / Lesson 1
Math
Unit 5
4th Grade
Lesson 1 of 21
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Decompose fractions as a sum of unit fractions and as a multiple of 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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Lin is learning to make cookies using a family recipe. She has only one measuring cup that measures $$\frac1 4$$ cup. Show how Lin could use the cup to measure the amount of each ingredient below.
a. $$\frac 3 4$$ cups sugar
b. 1 cup butter
Grade 4 Unit 3 Lesson 7 Activity 1, accessed on March 17, 2022, 10:23 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.
Decompose the fraction represented below into a sum of unit fractions and a multiple of that unit fraction. Record the decompositions with equations.
Decompose the following fractions into a sum of unit fractions and a multiple of that unit fraction, recording each with an equation.
a. $$\frac{4}{5}$$
b. $$\frac{3}{3}$$
Problem Set
Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Decompose the following fraction as a sum of unit fractions as well as a multiple of unit fractions. Record the decompositions with equations.
$$\frac69$$
An example response to the Target Task at the level of detail expected of the students.
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.
Before the Problem Set, you could have students play around with manipulatives to decompose fractions into a sum of unit fractions or non-unit fractions, similar to Joe Schwartz’s blog post “Building Towers”. Just make sure students are building fractions less than or equal to 1. If you don’t have fraction towers or even fraction tiles, you can create them from paper.
Extra Practice Problems
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Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Lesson 2
Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1
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
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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