Download Using the Associative Property of Multiplication

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 40357
Using the Associative Property of Multiplication
Students are asked to find the product of three numbers and are observed to see if they use the Associative Property to find the product more
easily.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, Associative Property, multiplication, division
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_UsingTheAssociativePropertyOfMultiplication_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task may be implemented individually or with a small group.
1. The teacher provides the student with the attached Using the Associative Property of Multiplication worksheet and asks the student to solve both problems. The teacher
should ask the student to show two different ways to work each problem.
2. After the student determines the product for each expression, the teacher should ask the student to explain which way was easier and why.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand how to multiply an expression that includes three numbers.
Examples of Student Work at this Level
The student adds the three numbers together instead of multiplying (i.e., the student adds 6 + 2 + 4).
The student only multiples the first two of the three numbers together and is then unsure how to continue.
The student multiplies 6 × 2 and 2 × 4 and is then unsure how to continue.
Questions Eliciting Thinking
page 1 of 3 What does this symbol mean? Should I add, subtract, multiply, or divide? What numbers should I multiply?
If I have 2 + 3 + 4, do I only add 2 + 3 together and then 3 + 4 together? Or, do I need to add all three together? So, then how do you think I should multiply 6 x 2 x 4?
Instructional Implications
Work with the student on determining the correct operation to perform based on the operational symbol.
Model how to multiply three factors in more than one way (e.g. compute (8 × 2) × 5 and 8 × (2 × 5)). Ask the student which way he or she would use to solve the
problem.
Moving Forward
Misconception/Error
The student multiplies the numbers in the given order only and is unable to use the Associative Property to find an alternate way to complete the multiplication.
Examples of Student Work at this Level
In the first problem, the student multiplies 6 × 2 getting 12 and then multiples 12 × 4 to get the final product. Even with prompting, the student is unable to consider
multiplying in the order 6 × (2 × 4) = 6 × 8 = 48.
In the second problem, the student first multiplies 7 × 3 getting 21 and then multiples 21 × 3 to get the final product. Even with prompting, the student is unable to
consider multiplying in the order 7 × (3 × 3) = 7 × 9 = 63.
Questions Eliciting Thinking
You multiplied 7 × 3 first and found the product is 21. Then, you multiplied 21 × 3 by drawing a picture. Is there another way we could multiply? Can we group the
numbers another way?
Is there a way to group the numbers together to help us find the product?
Instructional Implications
Model using the Associative Property when multiplying three numbers and evaluating whether or not one way may be more efficient than the other.
Give the student a word problem which requires multiplying three numbers. Model writing an expression to match the word problem and then solving the problem by using
the Associative Property. Then, give the student another problem and have the student multiply using the Associative Property.
When given three numbers, a, b, and c to multiply, guide the student to explicitly consider if multiplying (a x b) x c is any more efficient than multiplying a x (b x c).
Almost There
Misconception/Error
The student does not clearly explain his or her strategy and cannot explain why the Associative Property helps in finding the product of three factors.
Examples of Student Work at this Level
The student draws parenthesis to show the numbers multiplied first but is unable to clearly explain his or her strategy or reasoning.
Note: Students need not refer to the Associative Property by name, but their explanations should demonstrate an understanding of this property.
Questions Eliciting Thinking
Why did you multiply these two numbers together first?
Is there another way to group the numbers together to help us find the product?
Instructional Implications
Model multiplying three factors using the Associative Property and explaining your strategy and reasoning. Then, give the student a similar problem and have the student
solve and explain his or her strategy.
Provide opportunities for the student to explain his or her thinking to the class.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student uses the Associative Property to multiply the three numbers. He or she is able to clearly explain his or her strategy.
Questions Eliciting Thinking
Why did you multiply these two numbers first?
Will it always be a good strategy to multiply the second two numbers first?
Instructional Implications
Give the student a variety of three-factor problems, some for which using the Associative Property simplifies the computation, and ask the student to determine which
problems become easier by using the Associative Property. Ask the student to justify his or her responses.
page 2 of 3 When showing work, encourage the student to use parentheses to indicate which pair of factors is multiplied first.
Consider using the MFAS task, Does It Work for Division?, (3.OA.2.5).
Work with the student on solving multiplication and division problems by using the relationship between multiplication and division.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Using the Associative Property of Multiplication worksheet
Pencil
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.3.OA.2.5:
Description
Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24
is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or
by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16,
one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
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