How Much Greater Is The Product?
Resource ID#: 55675
Primary Type: Formative Assessment
This document was generated on CPALMS - www.cpalms.org
Students are asked to model an expression that is a multiple of a sum and to compare the expression to the sum.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, sum, product, expression, compare
Instructional Component Type(s): Formative
Assessment
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_HowMuchGreaterIsTheProduct_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually or in small groups.
1. The teacher shows the student seven linked cubes of one color and four linked cubes of a different color. The teacher models adding seven and four by connecting the
links and says, “When I put these two groups together, it shows 7 + 4. The teacher then shows the student the 11 linking cubes arranged in one row as shown below.
Next, the teacher says to the student, “Can you draw a picture to model 3 x (7 + 4) now that you have seen a representation of 7 + 4?” The teacher may use the
attached How Much Greater is the Product worksheet for the student to record his or her drawing.
2. After the student draws a representation of 3 x (7 + 4), the teacher asks, “Can you show me 7 + 4 in your picture? Where is the “times three” in your picture?”
3. Finally the teacher asks, “How much greater is the product 3 x (7 + 4) than 7 + 4?” The teacher may refer to the initial set of cubes or to the student’s representation
when asking this question.
TASK RUBRIC
Getting Started
Misconception/Error
The student’s representation does not clearly show 3 x (7 + 4).
Examples of Student Work at this Level
page 1 of 3 The student’s representation is lacking detail and he or she cannot explain how it shows 3 x (7 + 4).
The student believes that 3 x (7 + 4) is represented by a group of 7 + 4 and then three more groups of 7 + 4 as shown in the video. This representation shows 4 x (7 +
4).
Questions Eliciting Thinking
Where do you see 7 + 4 in your picture?
Remember when we modeled 7 + 4 with the cubes? How could you show that in your picture?
What does it mean to multiply a number?
How could we make your representation more clear?
Instructional Implications
Give the student simple expressions that include only one operation and have the student represent the expressions with drawings. Have the student practice explaining
where in his or her representations operations are shown. Transition the student to multi-operational expressions some of which include parentheses.
Consider using MFAS task With and Without Parenthesis (5.OA.1.1) to check for understanding of the order of operations.
Moving Forward
Misconception/Error
The student is unable to explain how his or her representation models the expression and to determine how much greater the product is.
Examples of Student Work at this Level
The student’s representation is clear, but he or she cannot clearly justify it. Additionally, the student does not know how much larger the product 3 x (7 + 4) is than 7 + 4.
Questions Eliciting Thinking
Can you show me 7 + 4 in your representation?
Where do we see the “multiply by three”?
If we multiply by three, what happens to the product? How much larger is it?
Instructional Implications
Encourage the student to explain and justify his or her representation to a partner or the class. Allow others to give feedback on how to make the explanation clearer.
Provide opportunities for the student to draw other representations of expressions involving more than one operation including some that require parentheses.
Almost There
Misconception/Error
The student cannot determine how much greater the product is.
Examples of Student Work at this Level
The student’s drawing appropriately shows 3 x (7 + 4). However, he or she cannot determine that 3 x (7 + 4) is three times greater than 7 + 4 without calculating each
quantity.
Questions Eliciting Thinking
Where do we see the “multiply by three”?
What happens when we multiply a number by another number? How much larger is the product than the number that got multiplied?
What if we multiply by any number? How much larger will the product be?
Instructional Implications
Give the student hints about a number and have him or her work backwards to find it. From those clues, the student can create equations, using parentheses appropriately.
For example, “I am thinking of a number and if I add 7 and then double it, I’ll get 24.” This should be represented as (x + 7) x 2 = 24.
Got It
Misconception/Error
page 2 of 3 The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student draws an appropriate representation of 3 x (7 + 4) and explains how his or her picture shows each part of the expression. The student also explains that 3 x (7
+ 4) is three times greater than 7 + 4 without calculating.
Questions Eliciting Thinking
Can you create an expression of your own that includes addition and multiplication and then make a representation to model it?
Instructional Implications
Encourage the student to write his or her own expressions that include several operations and parentheses and then to draw representations to model them.
Guide the student in writing equations to match verbal descriptions as seen in the MFAS task Write The Equation (5.OA.1.2).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
How Much Greater is the Product worksheet
Linking cubes (seven of one color and four of a different color)
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.5.OA.1.2:
Description
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating
them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 ×
(18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
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