Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58630
Multiplying Using An Array or Area Model
Students are asked to multiply a four-digit number by a one-digit number and two, two-digit numbers using an array or area model.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, array model, area model, multiplication, place value, decompose, multiply, product
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_MultiplyingUsingAnArrayOrAreaModel_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually or in small groups.
1. The teacher provides the student with Multiplying Using An Array or Area Model worksheet and reads the directions aloud.
2. If the student begins the multiplication using the standard algorithm, the teacher should ask, “Can you multiply these numbers using an array or area model?”
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand how to multiply two numbers using an array or area model.
Examples of Student Work at this Level
The student:
Attempts to use place value but makes significant errors and is unable to complete the problem.
page 1 of 4 Starts to draw a rectangle and decompose the numbers by place value but is unable to do so correctly even with prompting.
Correctly uses place value to create an area model for the first problem and shows an understanding of how to use an area model to determine the product. However,
he or she makes errors when multiplying by each place value. The student is unsuccessful in his or her attempt to use an area model to determine the product of the
second problem.
Attempts to use the standard algorithm but makes significant errors.
Questions Eliciting Thinking
Do you know what it means to use place value to multiply?
Have you ever used an array or area model to multiply? What does one look like?
What is the value of each digit in 4,835? Can you use that to multiply 4,835 x 6 in an easier way?
Instructional Implications
Use place value blocks to model for the student how to multiply a two-digit number by a one-digit number. Provide opportunities for the student to practice finding
products using the place value blocks.
Model how to use arrays to multiply numbers and allow the student to practice using this model. Once the student has an understanding of how an array works then
introduce the area model as a more efficient way to multiply using place value. Have the student initially practice multiplying two-digit numbers by one-digit numbers using an
area model. Then transition the student to multiplying two, two-digit factors.
Moving Forward
Misconception/Error
The student is unable to correctly use an area or array model when the factors are both two-digit numbers.
Examples of Student Work at this Level
The student draws an area model and multiplies 4,000 x 6 = 24,000, 800 x 6 = 4,800, 30 x 6 = 180, and 5 x 6 = 30 and adds the products to get 29,010, but is unable to
use the same strategy to multiply 83 x 25.
Questions Eliciting Thinking
What are the values of each digit in 83? 25? How can you use that to help you multiply these two numbers?
How could an area model help you keep track of the partial products?
What does the area model show? How can you show me this problem using this model?
I see you multiplied 80 x 20 and 3 x 5 to find the product of 83 x 25. Did you make sure you have all the parts?
Can you draw a picture to represent what you did?
Instructional Implications
Model for the student how to use an area model to identify and multiply all four partial products when multiplying two, two-digit numbers.
page 2 of 4 Model for the student how to multiply two-digit by two-digit numbers using a partial products strategy. Provide additional opportunities for the student to practice using
both a partial products strategy and area models.
Almost There
Misconception/Error
The student requires some teacher prompting or makes a computational error when multiplying two, two-digit numbers.
Examples of Student Work at this Level
The student:
Correctly multiplies the four-digit number by the one-digit number. However, he or she needs prompting to identify and multiply all four partial products when using an
array or area model to determine the product of a two-digit by a two-digit number.
Uses an array or area model to multiply all parts of the problem, but makes an error in computation.
Questions Eliciting Thinking
How did you decompose the 83? How could that help you with the 25?
How can we keep track of all of the partial products we are finding to be sure we have not missed any?
Good mathematicians always check their work. Can you go back and make sure you multiplied everything correctly?
Instructional Implications
Provide additional opportunities for the student to work with a partner to multiply two, two-digit numbers using an array or area model. Have the students compare answers
and reconcile any differences.
Encourage the student to compare the use of an array or area model to the standard algorithm to analyze how the strategies are similar and how they are different.
Encourage the student to check his or her work for computational errors.
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 correctly uses an array or area model to determine the product of 4,835 x 6 is 29,010 and the product of 83 x 25 is 2,075.
Questions Eliciting Thinking
What does each rectangle represent in the area model?
How could you use an area model to represent 385 x 25?
Instructional Implications
Encourage the student to compare a partial products strategy to the use of an array or area model to analyze how these strategies are similar and how they are different.
Encourage the student to use a partial products strategy to multiply a three-digit number by a two-digit number and explain why there are six partial products instead of
four. Continue to provide opportunities to multiply larger numbers.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
page 3 of 4 Multiplying Using An Array or Area Model worksheet
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.4.NBT.2.5:
Description
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using
strategies based on place value and the properties of operations. Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard, they combine prior understanding of multiplication with
deepening understanding of the base-ten system of units to express the product of two multi-digit numbers as
another multi-digit number. This work will continue in grade 5 and culminate in fluency with the standard algorithms
in grade 6.
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