Fraction Operations

Lesson 15

Objective

Subtract a mixed number from a mixed number.

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 two mixed numbers, determining whether that estimate will be greater than or less than the actual difference.
  2. Subtract two mixed numbers using a variety of strategies, such as:
    1. Converting the mixed numbers to fractions greater than 1 and subtracting like units,
    2. Subtracting the corresponding whole number and fractional parts of both the minuend and subtrahend, regrouping a whole if necessary, or
    3. Using mental 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).

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Tasks 2 and 3 (benefit from worked examples). You could consolidate these as one Anchor Task using Anchor Task 2 Part (a) and (c) and Anchor Task 3 Parts (b) and (c) (or even just Part (c)). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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Problem 1

  1. Solve. 
    1. 3 thousands 5 tens – 1 thousand 2 tens = ___________
    2. 3 dogs 5 puppies – 1 orange 2 puppies = ___________
    3. 3 ones 5 eighths – 1 one 2 eighths = ___________
  2. What do you notice about the problems in #1? What do you wonder?

Guiding Questions

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Problem 2

Solve.

a.   $${3{2\over3}-1{1\over3}}$$

b.   $$4\frac{3}{4}-2\frac{1}{4}$$

c.   $${6{7\over10}-2{7\over10}}$$

Guiding Questions

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Problem 3

Solve.

a.   $${5-1{2\over5}}$$

b.   $${6{7\over10}-2{8\over10}}$$

c.   $${9{2\over6}-3{5\over6}}$$

Guiding Questions

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Problem 4

Solve.

a.   $${4{3\over8}-3{6\over8}}$$

b.   $${11{3\over12}-9{11\over12}}$$

Guiding Questions

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Problem Set & Homework

Discussion of Problem Set

  • Can you accurately subtract mixed numbers by subtracting the fraction first, or must you always subtract the whole numbers first? 
  • When subtracting mixed numbers, what is the advantage of subtracting the whole numbers first? 
  • Which strategy do you prefer to use? What are the advantages and disadvantages of that strategy?
  • How can subtracting a mixed number from a mixed number be similar to subtracting a fraction from a mixed number? 
  • 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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Solve. Show or explain your work.

1.   $${4{2\over3}-2{1\over3}}$$

2.   $${12{5\over8}-11{7\over8}}$$

References

Mastery Response

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Additional Practice

Unit Practice

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