Embedded Files
Standard
Standard
Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
Student Language:
"I can think of multiplication as the scaling of a number (similar to a scale on a map.)"
Explanation
Explanation
About the Math, Learning Targets, and Rigor
5.NF.5a
This standard calls for students to examine the magnitude of products in terms of the relationship between two types of problems.
5.NF.5b
This standard asks students to examine how numbers change when we multiply by fractions. Students should have ample opportunities to examine both cases in the standard: a) when multiplying by a fraction greater than 1, the number increases and b) when multiplying by a fraction less the one, the number decreases.
2 2/3 x 8 must be more than 8 because 2 groups of 8 is 16. Also 2 2/3 is almost 3 groups of 8. So the answer must be close to, but less than 24.
Resources
Resources
Videos
Videos
- Khan Academy
- Scroll to 5.NF.5, click on skill, find videos on left side of each skill
- Learn Zillion
EngageNY Lessons
EngageNY Lessons
Extra Practice
Extra Practice
- North Carolina Tasks
- Illustrative Math Tasks
- Howard County Tasks
- Click on 5th grade at bottom, then 5.NF.5
- Common Core Sheets
PARCC
PARCC
Common Core State Standards
Common Core State Standards
5.NF.5a
5.NF.5a
Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- Insofar as possible, tasks are designed to be completed without performing the indicated multiplication.
- Products involve at least one factor that is a fraction or mixed number.
STUDENT SAMPLE RESPONSE
Performance Indicators: 5.NF.5a
Performance Indicators: 5.NF.5a
Level 5: Exceeds Expectations
Interprets multiplication scaling by comparing the size of the product to the size of one factor on the basis of the size of the second factor without performing the indicated multiplication, focusing on one factor being a fraction greater than or less than one.
Level 4: Meets Expectations
Interprets multiplication scaling by comparing the size of a product to the size of one factor on the basis of the size of the second factor without performing the indicated multiplication where one factor is a fraction less than one.
Critiquing/Reasoning Standards
Critiquing/Reasoning Standards
5.C.7-1
5.C.7-1
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.5b)
Performance Indicators: 5.C.7-1
Performance Indicators: 5.C.7-1
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 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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