Lesson 12 | Fraction Operations | 4th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Number and Operations—Fractions

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

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Add a mixed number and a fraction or two mixed numbers using a variety of methods, such as:
1. Converting the mixed numbers to fractions greater than 1 and adding like units, or
2. Adding the corresponding whole number and fractional parts of both addends, regrouping a whole if necessary.
(Optional) Simplify solutions by rewriting them using the largest possible unit.
Estimate the sum 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

Suggestions for teachers to help them teach this lesson

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 12–15 are optional. If you want the focus for today to solely be on adding fractions and mixed numbers, 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 12–15, “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

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. Solve.

4 hundreds 3 tens + 2 tens = ___________
4 dollars 3 cents + 2 cents = ___________
4 ones 3 sixths + 2 sixths = ___________

b. What do you notice about the problems in Part (a)? What do you wonder?

c. Use your observations from Part (b) to solve 3 ones 1 fourth + 5 ones 2 fourths.

Guiding Questions

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Problem 2

Estimate the following sums. Then solve.

a. $${2{1\over5}+{3\over5}}$$

b. $$1\frac14+2\frac24$$

c. $$4\frac1{10} + 5\frac4{10}$$

Guiding Questions

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Problem 3

Estimate the following sums. Then solve.

a. $${3{7\over8}+{1\over8}}$$

b. $$\frac5{12} + 10\frac{10}{12}$$

c. $$2\frac{5}{8}+1\frac{3}{8}$$

d. $$4\frac7{12}+ 16\frac9{12}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Explain how you solved #2(d).
What two strategies did you use to solve #3?
What advice would you give to D’ante in #4? Why is it a bad idea to record values the way he did?
Was anyone able to answer #5 without actually adding any values together on paper? How?
What error did the student make in #7? What can help you to avoid that mistake?
What strategies did you use for #8? Did you use the same strategies as your classmates?
What two values did you come up with in #9? How many possible answers are there? What do all of those answers have in common?
How is 4 tens 7 ones + 6 tens 9 ones similar to 4 ones 7 twelfths + 6 ones 9 twelfths? 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 sum be helpful?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

What is the value of $$\frac25+4\frac15$$? Select the two correct answers.

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Problem 2

Solve. Show or explain your work.

a. $$3\frac26+\frac56$$

b. $$1\frac58+4\frac78$$

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

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 11

Lesson 13

Lesson Map

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.

4.NF.B.3.B 4.NF.B.4.A

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

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.

4.NF.B.3.B 4.NF.B.4.A

Add and subtract fractions that require regrouping where the total is less than 2.

4.NF.B.3.A 4.NF.B.3.C

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

4.NF.B.3.A 4.NF.B.3.C

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.

4.NF.B.3.B 4.NF.B.3.C

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.

4.NF.B.3.C

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

4.NF.B.3.C

Add and subtract mixed numbers using a variety of mental strategies.

4.NF.B.3.C

Solve word problems involving addition and subtraction of fractions.

4.NF.B.3.D

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.

4.NF.B.4.B

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.

4.MD.B.4

Fraction Operations

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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