Embedded Files
Standard
Standard
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.
Explanation
Explanation
Students will begin to notice connections between the models and fractions in the way both the parts and wholes are counted and begin to generate a rule for writing equivalent fractions.
The models should be represented in drawings. Students should also use benchmark fractions such as 1/2 to compare two fractions and explain their reasoning. The result of the comparisons should be recorded using ˃, ˂ and = symbols.
Videos
Videos
- Teaching Video (1:08-3:58)
- Khan Academy (scroll to find 4.NF.1 - click on a skill)
- Videos (on left side in each skill)
- Learn Zillion
- Virtual Nerd
EngageNY Lessons
EngageNY Lessons
- Module 5, Topic B, Lesson 7: Use the area model and multiplication to show the equivalence of two fractions.
- Module 5, Topic B, Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
- Module 5, Topic B, Lesson 9: Use the area model and division to show the equivalence of two fractions.
- Module 5, Topic B, Lesson 10: Use the area model and division to show the equivalence of two fractions.
- Module 5, Topic B, Lesson 11: Explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division.
Extra Practice
Extra Practice
- North Carolina Tasks
- Illustrative Math Tasks
- Howard County Tasks
- Click on 4th grade at bottom, then 4.NF.1
- Common Core Sheets
PARCC
PARCC
Common Core State Standards
Common Core State Standards
Use the principle a/b = (nxa)/(nxb) to recognize and generate equivalent fractions.
- The explanation aspect of 4.NF.1 is not assessed here.
- Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- Tasks may include fractions that equal whole numbers. Whole numbers are limited to 0 through 5.
Performance Indicators: 4.NF.1-2 & 4.NF.A.Int.1
Performance Indicators: 4.NF.1-2 & 4.NF.A.Int.1
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
Integrated Standards
Apply conceptual understanding of fraction equivalence and ordering to solve simple word problems requiring fraction comparison.
(Content Scope: 4.NF.A)
- Tasks have “thin context.”
- Tasks do not require adding, subtracting, multiplying, or dividing fractions.
- Prompts do not provide visual fraction models; students may at their discretion draw visual fraction models as a strategy.
- Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- Tasks may include fractions that equal whole numbers. Whole numbers are limited to 0 through 5.
Critiquing & Reasoning Standards
Critiquing & Reasoning Standards
4.C.4-1
4.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 4.NF.A)
- Tasks have “thin context” or no context.
- Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
4.C.5-2
4.C.5-2
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 4.NF.1 only)
- Tasks have “thin context” or no context.
- Tasks are limited to denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- Tasks may include fractions that equal whole numbers. Whole numbers are limited to 0 through 5.
4.C.7-1
4.C.7-1
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 4.NF.1)
- Fractions equivalent to whole numbers are limited to 0 through 5.
Performance Indicators: 4.C.4-1 & 4.C.7-1
Performance Indicators: 4.C.4-1 & 4.C.7-1
"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.5-2
Performance Indicators: 4.C.5-2
"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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