Standard

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.)

Student Language:

"I can add and subtract fractions with unlike denominators and mixed numbers."

Explanation

About the Math, Learning Targets, and Rigor

This standard builds on the work in fourth grade where students add fractions with like denominators. In fifth grade, the example provided in the standard has students find a common denominator by finding the product of both denominators. For 1/3 + 1/6 , a common denominator is 18, which is the product of 3 and 6. This process should be introduced using visual fraction models (area models, number lines, etc.) to build understanding before moving into the standard algorithm.

Students should apply their understanding of equivalent fractions developed in fourth grade and their ability to rewrite fractions in an equivalent form to find common denominators. They should know that multiplying the denominators will always give a common denominator but may not result in the smallest denominator.

Mental computations and estimation strategies should be used to determine the reasonableness of answers. Students need to prove or disprove whether an answer provided for a problem is reasonable.

Resources

Videos

• Instructional Video (1:10 - 7:49)
• Khan Academy
  • Scroll to 5.NF.1, click on skill, find videos on left side of each skill
• Learn Zillion
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 5th grade at bottom, then 5.NF.1
• Common Core Sheets

Released Assessment Questions

PARCC

Common Core State Standards

5.NF.1-1

Add two fractions with unlike denominators, or subtract two fractions with unlike denominators, 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.)

• Tasks have no context.
• Tasks ask for the answer or ask for an intermediate step that shows evidence of using equivalent fractions as a strategy.
• Tasks do not include mixed numbers.
• Tasks may involve fractions greater than 1 (including fractions equal to whole numbers).
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.

5.NF.1-2

Add three fractions with no two denominators equal by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum of fractions with like denominators. For example, 1/2 + 1/3 + 1/4 = (3/6 + 2/6) + 1/4 = 5/6 + 1/4 = 10/12 + 3/12 = 13/12 or alternatively 1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12.

• Tasks have no context.
• Tasks ask for the answer or ask for an intermediate step that shows evidence of using equivalent fractions as a strategy.
• Tasks do not include mixed numbers.
• Tasks may involve fractions greater than 1.
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.

5.NF.1-3

Compute the result of adding two fractions and subtracting a third, where no two denominators are equal, 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, 1/2 + 1/3 – 1/4 or 7/8 – 1/3 + 1/2.

• Tasks have no context.
• Tasks ask for the answer or ask for an intermediate step that shows evidence of using equivalent fractions as a strategy.
• Subtraction may be either the first or second operation. The fraction being subtracted must be less than both the other two.

Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.

5.NF.1-4

Add two mixed numbers with unlike denominators, expressing the result as a mixed number, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum with like denominators. For example, 3 1/2 + 2 2/3 = (3 + 2) + (1/2 + 2/3) = 5 + (3/6 + 4/6) = 5 + 7/6 = 5 + 1 + 1/6 = 6 1/6.

• Tasks have no context.
• Tasks ask for the answer or ask for an intermediate step that shows evidence of using equivalent fractions as a strategy.
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.

5.NF.1-5

Subtract two mixed numbers with unlike denominators, expressing the result as a mixed number, by replacing given fractions with equivalent fractions in such a way as to produce an equivalent difference with like denominators.

• Tasks have no context.
• Tasks ask for the answer or ask for an intermediate step that shows evidence of using equivalent fractions as a strategy.
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.

Performance Indicators: 5.NF.1-1, 5.NF.1-2, 5.NF.1-3, 5.NF.1-4, 5.NF.1-5

Level 5: Exceeds Expectations

Adds and subtracts three or more fractions and adds and subtracts two mixed numbers with unlike denominators in such a way as to produce an equivalent sum or difference with like denominators.

Level 4: Meets Expectations

Adds and subtracts two fractions or mixed numbers with unlike denominators in such a way as to produce an equivalent sum or difference with like denominators.

Critiquing/Reasoning Standards

5.C.7-3

Distinguish correct explanation/reasoning from that which is flawed, and – if there is a flaw in the argument – present corrected reasoning. (For example, some flawed ‘student’ reasoning is presented and the task is to correct and improve it.)

(Content Scope: Knowledge and skills articulated in 5.NF.1)

Performance Indicators: 5.C.7-3

Level 5: Exceeds Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• analyzing and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• evaluating explanation/reasoning if there is a flaw in the argument
• presenting and defending corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• an efficient and logical progression of steps with appropriate justification
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s
• responses, approaches and reasoning, and providing a counter-example where applicable

Level 4: Meets Expectations

In connection with the content knowledge, skills, and abilities described in Sub-claim A, the student clearly constructs and communicates a well-organized and complete response by:

• analyzing and defending solutions to multi-step problems in the form of valid chains of reasoning, using symbols such as equal signs appropriately
• distinguishing correct explanation/reasoning from that which is flawed
• identifying and describing the flaw in reasoning or describing errors in solutions to multi-step problems
• presenting corrected reasoning

Response may include:

• a logical approach based on a conjecture and/or stated assumptions, utilizing mathematical connections (when appropriate)
• a logical progression of steps
• precision of calculation
• correct use of grade-level vocabulary, symbols and labels
• justification of a conclusion
• evaluation of whether an argument or conclusion is generalizable
• evaluating, interpreting and critiquing the validity of other’s responses, approaches and reasoning