Fraction Operations

Lesson 12

Objective

Add a mixed number and a fraction.

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 sum of a mixed number and a fraction, determining whether that estimate will be greater than or less than the actual sum. 
  2. Add a mixed number and a fraction using a variety of strategies, such as:
    1. Converting the mixed number to a fraction greater than 1 and adding like units,
    2. Adding the fractional part of the mixed number to the other addend that is a fraction, regrouping a whole if necessary, or
    3. Using simplifying strategies, such as making a whole. 
  3. Assess the reasonableness of answers based on estimates (MP.1).

Tips for Teachers

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  • Similar to previous lessons in the unit, since it is possible to overemphasize the importance of simplifying fractions, the corresponding criteria for success and questions in the Anchor Tasks in Lessons 12–16 are optional. If you want the focus for today to solely be on adding a mixed number and a fraction, you may decide to cut this aspect of the lesson, but be sure to touch on the idea at some point in the unit.
  • Throughout Lessons 12–16, “calculations with mixed numbers provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 12).
  • 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 find the sum and not the difference, and having students add a mixed number and a fraction and not two mixed numbers. 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 3 tens + 2 tens = ___________
    2. 4 dollars 3 cents + 2 cents = ___________
    3. 4 ones 3 sixths + 2 sixths = ___________
  2. What do you notice about the problems in #1? What do you wonder?

Guiding Questions

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Problem 2

Solve.

a.   $${2{1\over5}+{3\over5}}$$

b.   $${7{3\over10}+{5\over10}}$$

Guiding Questions

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Problem 3

Solve.

a.   $${3{7\over8}+{1\over8}}$$

b.   $${3{7\over8}+{3\over8}}$$

c.   $${{5\over12}+{10{10\over12}}}$$

Guiding Questions

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Discussion of Problem Set

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  • Explain how you solved #1(d). 
  • What two strategies did you use to solve #2?
  • What advice would you give to D’ante in #3? Why is it a bad idea to record values the way he did? 
  • Explain the challenge in solving #6(d). What strategy did you use? 
  • 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 sum be helpful? 

Target Task

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Solve. Show or explain your work.

1.   $${3{2\over6}+{3\over6}}$$

2.   $${6{9\over10}+{3\over10}}$$

Mastery Response

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