Lesson 11 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

Add and subtract more than two fractions.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Number and Operations—Fractions

5.NF.A.1 — Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Foundational Standards

The foundational standards covered in this lesson

4.NF.A.1

Number and Operations—Fractions

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.A.2

Number and Operations—Fractions

4.NF.A.2 — Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.B.3

Number and Operations—Fractions

4.NF.B.3 — Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Criteria for Success

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

Find a common unit for more than two fractions, ideally (but not necessarily) by finding the least common denominator.
Add more than two fractions with unlike denominators.
Subtract more than two fractions with unlike denominators.
Use the properties of addition and subtraction to make a multi-term computation easier (e.g., to add $${{{{1\over3}}}+{3\over5}+{{{2\over3}}}}$$, first add $${{1\over3}}$$ and $${{2\over3}}$$ to make $$1$$, making the computation easier) (MP.7).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson provides an opportunity to refer back to the order of operations, particularly that addition and subtraction should be performed simultaneously from left to right.
If you are worried about pacing, you can cut Anchor Task #1 since it doesn’t provide necessary skills or concepts needed to understand the objective that aren’t addressed in the more straightforward computational problems below it. However, it is an engaging way to introduce the idea of adding more than two fractions, which is why it is included.
Note that on the Problem Set, Problem 6 is a partner game that requires two dice. Because of the difficulty of previous problems on the problem set, it’s not especially likely that students will get to this task, but make sure to have the materials ready in case any students do.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

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

Problem 1

Ancient Egyptians used unit fractions, such as $${{1\over2}}$$ and $${{1\over3}}$$, to represent all fractions. For example, they might write the number $${{{{2\over3}}}}$$ as $${{{1\over2}}}+{1\over6}$$.

We often think of $${{{{2\over3}}}}$$ as $${{{1\over3}}}+{{{1\over3}}}$$, but the ancient Egyptians would not write it this way because they didn’t use the same unit fraction twice.

a. Write each of the following Egyptian fractions as a single fraction:

$${{{1\over2}}}+{{{1\over3}}}$$
$${{{1\over2}}}+{{{1\over3}}}+{1\over5}$$
$${{1\over4}+{1\over5}+{1\over12}}$$

b. How might the ancient Egyptians have written the fraction we write as $${{3\over4}}$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Egyptian Fractions

Egyptian Fractions, accessed on Feb. 8, 2018, 12:52 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

Solve. Show or explain your work.

a. $$\frac{2}{3} + \frac{1}{4} + \frac{1}{2}$$

b. $$\frac{2}{3} + \frac{1}{5} + \frac{1}{3} + 1 \frac{4}{5}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic C > Lesson 9 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 9 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 Fishtank Learning, Inc.

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 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 Fishtank Learning, Inc.

Problem 3

Solve. Show or explain your work.

a. $$8 \frac{11}{12} - \frac{14}{3} - \frac{9}{4} $$

b. $$5 \frac{7}{8} - \frac{1}{2} - \frac{7}{8} - 1 \frac{1}{2} $$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Modified by Fishtank Learning, Inc.

Problem 4

Solve. Show or explain your work.

a. $$6 \frac{3}{4} + \frac{3}{5} - 5 \frac{1}{2}$$

b. $$2 \frac{5}{6} - \frac{1}{3} + 5 \frac{1}{6} $$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 5 Mathematics > Module 3 > Topic D > Lesson 14 — Concept Development

Modified by Fishtank Learning, Inc.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

Look at #3. How did you solve?
Look at #5. Was Lucy’s method correct? Can she use it to measure out $${{1\over12}}$$of a cup? What other amounts of water can she measure?
Look at #6. What equation did you come up with? Is there more than one correct answer?

Target Task

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

Problem 1

Solve.

$${{2\over3}+{7\over8}-{1\over6}}$$

Problem 2

Solve.

$${{4\over5}-{2\over3}+1{7\over10}}$$

Student Response

An example response to the Target Task at the level of detail expected of the students.

Create a free account or sign in to view Student Response

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

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 10

Lesson 12

Lesson Map

Topic A: Addition and Subtraction of Fractions

Recognize and generate equivalent fractions.

5.NF.A

Add fractions with like denominators.

5.NF.A

Subtract fractions with like denominators.

5.NF.A

Add fractions with unlike denominators whose sum is less than 1.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 1 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is less than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is greater than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions greater than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.

5.NF.A.2

Add and subtract more than two fractions.

5.NF.A.1

Solve two- and multi-step word problems involving addition and subtraction of fractions.

5.NF.A.2

Topic B: Addition and Subtraction of Decimals

Add decimals.

5.NBT.B.7

Subtract decimals.

5.NBT.B.7

Solve two- and multi-step word problems involving addition and subtraction of decimals.

5.NBT.B.7

Addition and Subtraction of Fractions/Decimals

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Number and Operations—Fractions

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem 4

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy