Fraction Operations

Lesson 13

Math

Unit 5

4th Grade

Lesson 13 of 21

Objective


Subtract fractions and mixed numbers where the total is greater than or equal to 2.

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Subtract a fraction or a mixed number from a mixed number using a variety of methods, such as:
    1. Subtracting like units where possible first, then regrouping to subtract if necessary,
    2. Converting the mixed numbers to fractions greater than one and subtracting like units, or
    3. Regrouping 1 whole in the minuend and then subtracting like units.
  2. (Optional) Simplify solutions by rewriting them using the largest possible unit.
  3. Estimate the difference of a mixed number and a fraction or two mixed numbers and assess the reasonableness of answers based on estimates (MP.1).

Tips for Teachers


  • You may choose to give students much more time with these concepts, perhaps spanning the lesson over two days. You could do this by having Anchor Tasks 1 and 2 on the first day and Anchor Task 3 on the second day. The Problem Set and Homework can be split accordingly.
  • Similar to previous lessons in the unit, since it is possible to overemphasize the importance of simplifying fractions, the corresponding criteria for success and guiding questions in the Anchor Tasks in Lessons 12–15 are optional. Note, however, that Target Task #1 asks students to identify the correct answer in more than one form, one of which is simplified.
  • Before the Problem Set, you could have students play a modified version of “Rolling Fractions” found on p. 63 of the Georgia Standards of Excellence Curriculum Frameworks: Mathematics GSE Fourth Grade Unit 4: Operations with Fractions. Students can play one round with the rules as such, then change them so that the objective is to create the smallest possible (positive) difference (which should provide students with more practice involving regrouping in order to subtract). You may also modify it by giving students more denominators to choose from in #1 of the directions (e.g., include all denominators students are expected to work with in Grade 4, including 2, 3, 4, 5, 6, 8, 10, and 12).
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Anchor Tasks


Problem 1

Estimate the following differences. Then solve.

a.   $$2\frac45 - \frac15$$

b.   $$4\frac36-\frac36$$

c.   $$3\frac23-1\frac13$$

d.   $$4\frac34-2\frac14$$

Guiding Questions

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Problem 2

a.   Here are three ways to solve $$4-3\frac16$$:

$$\begin{align} 4-3\frac{1}{6} &=1-\frac{1}{6} \\ &=\frac{5}{6} \end{align}$$

$$\begin{align} 4-3\frac{1}{6} &= \frac{24}{6}-\frac{19}{6} \\ &=\frac{5}{6}\end{align}$$

$$\begin{align} 4-3\frac{1}{6}&=3\frac{6}{6}-3\frac{1}{6} \\ &= \frac{5}{6} \end{align}$$

Explain how each strategy works. 

b.   Use any strategy to compute the following:

  1. $$2-\frac34$$
  2. $$3-\frac98$$
  3. $$6-1\frac25$$
  4. $$7-5\frac9{10}$$

Guiding Questions

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Problem 3

Estimate the following differences. Then solve.

a.    $$8\frac38 - \frac68$$

b.    $$6\frac4{10} - 2\frac7{10}$$

c.   $$11\frac3{12}-9\frac{11}{12}$$

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • What two values did you come up with in #2? How many possible answers are there? What do all of those answers have in common? 
  • What were the two ways you solved #4? Can you think of yet another way to solve? 
  • What strategies did you use for #7? Did you use the same strategies as your classmates? 
  • What error did the Stan make in #8? What is the correct sum? What error did Lila make? What is the correct difference? 
  • How is 7 tens 3 ones - 9 ones like 7 ones 3 tenths - 9 tenths? How is it different? 
  • If you were unsure of any answer on this Problem Set, what could you do to see if your answer is reasonable? Would drawing a picture or estimating the difference be helpful?

Target Task


Problem 1

What is the value of $$10\frac16-\frac56$$? Select the two correct answers. 

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Problem 2

Solve. Show or explain your work.

a.   $$6\frac9{10}-3\frac7{10}$$

b.   $$8\frac15-2\frac35$$

Student Response

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Additional Practice


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

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 12

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Lesson 14

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Topic D: Multiplication of Fractions

Topic E: Line Plots

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