Lesson 8 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

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

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.)
5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Number and Operations—Fractions

5.NF.A.2 — Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

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 common units for fractions with unlike denominators by finding equivalent fractions using multiplication or division.
Understand that there is more than one possibility for the common unit used, and use that to optionally find the least common denominator.
Add two fractions, including mixed numbers, with unlike denominators that require regrouping whose sum is greater than 2, simplifying and writing the sum as a mixed number, if applicable.
Assess the reasonableness of an answer using number sense and estimation (MP.1).
Solve one-step word problems involving the addition of two fractions with unlike denominators whose sum is more than 2 (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

“Calculations with mixed numbers provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 13). In general, given the Grade 4 instruction on this content, it’s unlikely that students will rewrite mixed numbers as “improper” fractions and add but instead will add like units and then regroup where necessary. For the problems that require regrouping, you should at least go through this strategy of adding like units and regrouping when necessary since this is a universal strategy. Students may also use computation-specific strategies, which are listed below.
For some problems in this lesson, students may use the computation-specific strategy of making a whole, e.g., $$2\frac{8}{10}+1\frac{5}{10}=3\frac{8}{10}+ \frac{5}{10}=3\frac{8}{10}+\frac{2}{10}+\frac{3}{10}=4+\frac{3}{10}=4\frac{3}{10}$$.

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

a. Estimate which two whole numbers each of the following sums will be in between.

$${2{1\over5}+1{1\over2}}$$
$${2{4\over5}+1{1\over2}}$$

b. Solve for the actual sums in Part (a) above.

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 10 — Concept Development

Grade 5 Mathematics > Module 3 > Topic C > Lesson 10 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 2

a. Estimate the following sums. Determine whether the actual sum will be more or less than the estimated sum. Be prepared to explain your reasoning.

$${3{5\over7}+6{2\over3}}$$
$${3{1\over4}+4{7\over8}}$$
$${15{1\over6}+8{7\over10}}$$

b. Solve for the actual sums in Part (a) above. Are your answers reasonable? Why or why not?

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 10 — Concept Development

Modified by Fishtank Learning, Inc.

Problem 3

It takes Wei $$2\frac{7}{10}$$ hours to clean her home. It takes Bernard $$1\frac{3}{4}$$ more hours to clean his home than it takes Wei. How long does it take Bernard to clean his home?

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 10 — 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 #2. What was wrong with options A through C? How could you change them to be correct?
Look at #5. What two ways did you solve? Are there other ways you could have solved? Could you have used the strategy of making 1? Why or why not?
Look at #6. How did you solve? Did anyone make a whole with two of their addends?
Look at #6. What is the sum of your two fractions? Was anyone able to come up with a larger sum? What if you used fractions greater than 1 for the fractional part of each mixed number? Why do you think it is that we don’t usually write numbers in that way?

Target Task

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

Problem 1

Solve. Show or explain your work.

$${2{5\over8}+4{2\over3}}$$

Problem 2

Sang needs $$3\tfrac{1}{2}$$ feet of string to make a necklace and $$2\tfrac{1}{4}$$ feet of string left. How much string, in feet, did Sang have before making the necklace?

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 7

Lesson 9

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

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 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