Curriculum / Math / 4th Grade / Unit 5: Fraction Operations / Lesson 6
Math
Unit 5
4th Grade
Lesson 6 of 21
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Add and subtract fractions that require regrouping where the total is less than 2.
The core standards covered in this lesson
4.NF.B.3.A — Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
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. Estimate whether the following sums will be more or less than 1.
i. $${{3\over4}+{2\over4}}$$
ii. $${{5\over6}+{3\over6}}$$
b. Solve for the actual sums in Part (a) above.
Cary computes $$\frac{9}{10} + \frac4{10}$$ using a different strategy. Here is her reasoning:
“First I broke $$\frac4{10}$$ into $$\frac1{10}$$ and $$\frac3{10}$$. Then I added $$\frac9{10}$$ and $$\frac1{10}$$ to get to 1, then added the other $$\frac3{10}$$ to get $$1\frac3{10}$$.
So $$\frac{9}{10} + \frac4{10} = 1\frac3{10}$$."
a. Is Cary’s calculation correct? Explain.
b. Will Cary’s strategy always work? If not, give an example of a calculation for which Cary can’t use this strategy.
c. Use Cary’s strategy to find $$\frac45+\frac35$$.
a. Estimate whether the following differences will be more or less than 1.
i. $${1{1\over3}-{2\over3}}$$
ii. $${1{3\over8}-{5\over8}}$$
b. Solve for the actual differences in Part (a) above.
Corrado computes $$1\frac15 - \frac25$$ using a different strategy. Here is his reasoning:
“First I broke $$\frac25$$ into $$\frac15$$ and $$\frac15$$. Then I subtracted $$\frac15$$ from $$1\frac15$$ to get to 1, then subtracted the other $$\frac15$$ to get $$\frac45$$.
So $$1\frac15 - \frac25 = \frac45$$."
a. Is Corrado’s calculation correct? Explain.
b. Will Corrado’s strategy always work? If not, give an example of a calculation for which Corrado can’t use this strategy.
c. Use Corrado’s strategy to find $$1\frac2{12}-\frac5{12}$$.
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
What is $$\frac{11}{12}+\frac{5}{12}$$?
Solve. Show or explain your work.
$$1\frac{3}{8} - \frac{6}{8}=$$ _________
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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
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Lesson 5
Lesson 7
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 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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