Standard

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

(NOTE: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

Explanation

About the Math, Learning Targets, & Rigor

This standard continues the work of equivalent fractions by having students change fractions with a 10 in the denominator into equivalent fractions that have a 100 in the denominator. In order to prepare for work with decimals (4.NF.6 and 4.NF.7), experiences that allow students to shade decimal grids (10x10 grids) support this work.

Student experiences should focus on working with grids rather than algorithms. Students can also use base ten blocks and other place value models to explore the relationship between fractions with denominators of 10 and denominators of 100.

This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth grade.

Resources

Videos

• Teaching Video (12:40-14:00)
• Khan Academy (scroll to find 4.NF.5 - click on a skill)
  • Videos (on left side in each skill)
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

• Module 6, Topic B, Lesson 5: Model the equivalence of tenths and hundredths using the area model and number disks.
• Module 6, Topic B, Lesson 6: Use the area model and number line to represent mixed numbers with units of ones, tenths, and hundredths in fraction and decimal forms.
• Module 6, Topic D, Lesson 12: Apply understanding of fraction equivalence to add tenths and hundredths.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.NF.5
• Common Core Sheets

Released Assessment Questions

PARCC

Common Core State Standards

4.NF.5

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

• Tasks do not have a context.

STUDENT SAMPLE RESPONSE

Performance Indicators: 4.NF.5 & 4.NF.Int.2

Level 5: Exceeds Expectations

• Compares decimals to hundredths; uses decimal notations for fractions with denominators 10 or 100. Compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators, comparing to a benchmark fraction and generating equivalent fractions.
• Recognizes that decimals and fractions must refer to the same whole in order to compare.
• Shows results using symbols.
• Demonstrates the use of conceptual understanding of fractional equivalence and ordering when solving simple word problems requiring fraction comparison.
• Converts a simple fraction to a denominator of 10 or 100 and writes as a decimal (e.g.,1/2 = 5/10 = .5, ¼ = 25/100 = 0.25, 1/20 = 5/100 = 0.05).
• Adds fractions with denominators of 10 and 100.

Level 4: Meets Expectations

• Given a visual model and/or manipulatives, compares decimals to hundredths:
  • Expresses a fraction with denominator 10 as an equivalent fraction with denominator 100.
  • Uses decimal notation for fractions with denominators 10 or 100.
  • Compares fractions, with like or unlike numerators and denominators, by creating equivalent fractions with common denominators and comparing to a benchmark fraction.
• Recognizes that decimals and fractions must refer to the same whole in order to compare.
• Shows results using symbols.
• Solves simple word problems requiring fraction comparison.

Integrated Standards

4.NF.Int.2

Solve one-step addition word problems.

(Content Scope: 4.NF.5, 4.NF.6 only)

• Tasks are one of two kinds: Add To with result unknown, or Put Together with result unknown.
• See Table 2, p. 9 of the OA Progression document; these situations are sampled equally.

Critiquing & Reasoning Standards

4.C.4-5

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 4.NF.C)

• Tasks have “thin context” or no context.
• Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

4.C.5-5

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 4.NF.C)

• Tasks have “thin context” or no context.
• Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Performance Indicators: 4.C.4-5

"Concrete diagrams"

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: 4.C.5-5

"Distinguish correct explanation/reasoning from that which is flawed"

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:

• presenting 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 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 by:

• presenting 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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