Standard

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.

Student Language:

"I can solve word problems that involve fractions."

Explanation

About the Math, Learning Targets, and Rigor

This standard refers to solving word problems involving fractions with unlike denominators. It also refers to number sense, which means students’ understanding of fractions as numbers that lie between whole numbers on a number line. Number sense in fractions also includes moving between decimals and fractions to find equivalents, also being able to use reasoning such as 7/8 is greater than 3/4 because 7/8 is missing only 1/8 and 3/4 is missing 1/4 so 7/8 is closer to a whole.

Example:

Jerry was making two different types of cookies. One recipe needed 3/4 cup of sugar and the other needed 2/3 cup of sugar. How much sugar did he need to make both recipes?

Mental estimation

• A student may say that Jerry needs more than 1 cup of sugar but less than 2 cups. An explanation may compare both fractions to 1 2 and state that both are larger than 1 2 so the total must be more than 1. In addition, both fractions are slightly less than 1 so the sum cannot be more than 2.

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.2, click on skill, find videos on left side of each skill
• Learn Zillion

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 5th grade at bottom, then 5.NF.2
• Common Core Sheets

Released Assessment Questions

PARCC

Common Core State Standards

5.NF.2-1

Solve word problems involving addition and subtraction of fractions referring to the same whole, in cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem.

• The situation types are those shown in Table 2, p. 9 of the OA Progression document, sampled equally.
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.
• Tasks may involve fractions greater than one, including mixed numbers

STUDENT SAMPLE RESPONSE

5.NF.2-2

Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers to word problems involving addition and subtraction of fractions referring to the same whole in cases of unlike denominators. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

• The situation types are those shown in Table 2, p. 9 of the OA Progression document, sampled equally.
• Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.
• Tasks may involve fractions greater than one, including mixed numbers

STUDENT SAMPLE RESPONSE

Performance Indicators: 5.NF.2-1, 5.NF.2-2, 5.NF.A.Int.1

Level 5: Exceeds Expectations

Describes a model to represent word problems involving addition and subtraction of fractions and mixed numbers referring to the same whole in cases of unlike denominators by using visual fraction models or equations.

Assesses and justifies reasonableness using benchmark fractions and number sense of fractions.

Level 4: Meets Expectations

Solves word problems involving addition and subtraction of fractions and mixed numbers referring to the same whole in cases of unlike denominators by using visual fraction models or equations.

Integrated Standards

5.NF.A.Int.1

Solve word problems involving knowledge and skills articulated in 5.NF.A. (5.NF.1, 5.NF.2)

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

Critiquing/Reasoning Standards

5.C.4-1

Base arithmetic explanations/reasoning on concrete referents such as diagrams (whether provided in the prompt or constructed by the student in her response), connecting the diagrams to a written (symbolic) method.

(Content Scope: Knowledge and skills articulated in 5.NF.2)

5.C.5-1

Base explanations/reasoning on a number line diagram (whether provided in the prompt or constructed by the student in her response).

(Content Scope: Knowledge and skills articulated in 5.NF.2)

5.C.7-2

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.2)

Performance Indicators: 5.C.4-1, 5.C.5-1

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 based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which 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 counterexample 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 based on operations using concrete referents such as diagrams--including number lines (whether provided in the prompt or constructed by the student) and connecting the diagrams to a written (symbolic) method, which 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.

Performance Indicators: 5.C.7-2

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

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