Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56122
Making Necklaces
The student is asked to solve a multiplicative comparison word problem comparing 6 inches of string to 24 inches of string.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, multiplication, compare, comparison, equation
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_MakingNecklaces_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Making Necklaces worksheet and reads the problem aloud.
A mom and daughter were making necklaces. The daughter used six inches of string for her necklace; the mom’s necklace was 24 inches long. How does the length of
the mom’s necklace compare to the length of her daughter’s necklace?
2. Give the student time to complete the problem and ask questions, if necessary.
3. If the student uses a strategy involving addition or subtraction, ask the student if he or she could use multiplication to solve the problem.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not use an effective strategy to solve the problem.
Examples of Student Work at this Level
The student finds the difference or the sum of the numbers given in the problem and writes an equation such as 24 – 6 = 18 or 24 + 6 = 30 to represent the problem.
page 1 of 4 The student uses various incorrect operations to solve the problem, for example: 24 x 6 = 144, 6 + 24 = 30, 6 – 24 = 18 and cannot correct with prompting.
Questions Eliciting Thinking
What in the problem made you decide to add or subtract?
Can you explain what is happening in the word problem?
How could you model the problem?
What does each number represent in the problem?
Why did you write 24 x 6? What in the problem told you to solve it that way?
If the mom’s necklace is 24 inches and the daughter’s necklace is 6 inches how can you compare the lengths? Can you use multiplication to compare the lengths?
How many times longer is the mom’s necklace than the daughter’s?
Instructional Implications
Guide the student to visualize what is happening in the problem and to draw a model or diagram to represent his or her thinking. Provide opportunities for the student to
read word problems, consider what the problems are asking, and draw a representation of each problem which can be used to solve the problem.
Consider using the MFAS task, Writing An Equation To Match A Word Problem (4.OA.1.1)
Moving Forward
Misconception/Error
The student solves the problem correctly using repeated addition or subtraction but despite teacher prompting is unable to explain the connection to multiplication or
division.
Examples of Student Work at this Level
The student solves the problem by writing 24 – 6 = 18, 18 – 6 = 12, 12 – 6 = 6, and 6 – 6 = 0 or 6 + 6 = 12, 12 + 6 = 18, and 18 + 6 = 24 and correctly determines
the answer is four but does not understand what the four represents.
Questions Eliciting Thinking
Can you explain to me how you solved the problem? How did you know to solve the problem that way?
Could you have solved the problem another way? How about a more efficient way? Could multiplication or division help you?
What are you trying to find in this problem?
How could you model that story problem using a bar diagram? Can you explain to me what you have drawn?
How many times longer is the mom’s necklace than the daughter’s?
Instructional Implications
Encourage the student to solve multiplicative comparison problems by drawing diagrams or illustrations. Help the student interpret his or her diagram or illustration in terms of
multiplication. Guide the student to write a multiplication equation to represent his or her illustration or diagram.
Work with the student on interpreting repeated addition as multiplication, i.e., 6 + 6 + 6 + 6 = 4 x 6 = 24 or repeated subtraction as division, i.e., 24 – 6 = 18, 18 – 6 =
12, 12 – 6 = 6, and 6 – 6 = 0 is 24 ÷ 6 = 4. Encourage the student to write repeated addition problems as multiplications and repeated subtractions as divisions.
Represent multiplicative comparison word problems for the student using bar diagrams. Provide opportunities for the student to write equations that model multiplicative
comparison problem types (multiplication, measurement division, and partitive division). Help the student use the relationship between multiplication and division to solve
these types of problems.
Almost There
Misconception/Error
The student is able to solve the problem correctly but needs much prompting to do so.
page 2 of 4 Examples of Student Work at this Level
The student initially solves the problem using addition or subtraction but with prompting is able to transition to multiplication or division.
Questions Eliciting Thinking
If the mom’s necklace is 24 inches and the daughter’s necklace is 6 inches how can you compare the lengths?
Can you use multiplication to compare the lengths?
You have subtracted to find the difference. Can you use multiplication to compare the necklaces?
How many times longer is the mom’s necklace than the daughter’s necklace?
Instructional Implications
Have the student work in groups writing multiplicative comparison word problems and trading problems to solve. Encourage students to compare strategies and answers and
to reconcile any differences.
Consider using the MFAS task Dogs as Pets (4.OA.1.2).
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 a strategy based on multiplication or division to solve the problem. The student says that the answer is four and can clearly say that the mom’s necklace is
four times longer than the daughter’s necklace.
Questions Eliciting Thinking
Can you write an equation to represent the word problem? How do you represent an unknown in an equation?
Could you solve the problem using a different equation?
Instructional Implications
Challenge the student to write two different equations to model the word problem. Have the student explore and share efficient methods for solving comparative word
problems.
Provide the student with multiplication equations and have the student create his or her own multiplicative comparison word problems. Then have the student partner with
another student to solve each other’s problems.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Making Necklaces worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
page 3 of 4 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.OA.1.2:
Description
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with
a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive
comparison.
page 4 of 4