Fraction Operations

Lesson 14

Objective

Subtract a fraction from a mixed number.

Materials and Resources

Common Core Standards

Core Standards

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  • 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

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  1. Estimate the difference of a mixed number and a fraction, determining whether that estimate will be greater than or less than the actual difference.
  2. Subtract a fraction from a mixed number using a variety of strategies, such as:
    1. Converting the mixed numbers to a fraction greater than one and subtracting like units,
    2. Subtracting the fraction from the fractional part of the mixed number, regrouping a whole if necessary, or
    3. Using simplifying strategies, such as going down over a whole or counting up over a whole.
  3. Assess the reasonableness of answers based on estimates (MP.1).

Tips for Teachers

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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. You should modify it by having students subtract a fraction from a mixed number and not a mixed number from a mixed number. 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

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Problem 1

  1. Solve. 
    1. 4 hundreds 2 tens – 1 ten = ___________
    2. 4 dogs 2 puppies – 1 puppy = ___________
    3. 4 ones 2 thirds – 1 third = ___________
  2. What do you notice about the problems in #1? What do you wonder?

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic F > Lesson 32Concept Development

Grade 4 Mathematics > Module 5 > Topic F > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Solve.

a.   $${2{4\over5}-{1\over5}}$$

b.   $${5{7\over10}-{3\over10}}$$

c.   $${4{3\over6}-{3\over6}}$$

Guiding Questions

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Problem 3

Solve.

a.  $${4-{1\over6}}$$

b.  $${4{3\over6}-{4\over6}}$$

c.  $${8{5\over12}-{8\over12}}$$

Guiding Questions

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Discussion of Problem Set

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  • What were the two ways you solved #2? Can you think of yet another way to solve? 
  • Why are both George and Oscar right in #4? 
  • 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

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Problem 1

What is the value of $$8\frac{3}{8}-\frac{5}{8}$$?

A.  $$\frac{29}{4}$$

B.  $$\frac{31}{4}$$

C.  $$\frac{33}{4}$$

D.  $$\frac{35}{4}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic F > Lesson 32Concept Development

Grade 4 Mathematics > Module 5 > Topic F > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Solve. Show or explain your work.

$$10\frac{5}{6}-\frac{4}{6}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic F > Lesson 32Concept Development

Grade 4 Mathematics > Module 5 > Topic F > Lesson 32 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

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