Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 40388
Changing Division Equations into Multiplication Equations
Students consider a division fact that they are likely to know and are asked to turn it into a multiplication fact. If successful, they are asked to
rewrite a basic division fact that they are not likely to know and which has a symbol for the unknown number.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, division, multiplication, inverse
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_Changing Division Equations into Multiplication Equations_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually or with a small group. Prior to implementing the task, the teacher should prepare a set of Changing Division Equations into
Multiplication Equations cards for each student.
1. The teacher shows the student the equation 8 ÷ 4 = 2 and then asks the student to use his or her cards to create another equation with the same numbers but using
the × card instead of the ÷ card. The teacher should ask the student to be sure that his or her equation is true. If not, the teacher should provide feedback and
assistance and allow the student to make changes.
2. Next, the teacher shows the student the equation 54 ÷ 9 = ? and again asks the student to use his or her cards to create another equation with the same numbers but
using the × card instead of the ÷ card.
3. The teacher should ask the student if he or she knows what number can replace the blank in the new equation to make it a true statement. If the student does not
know, the teacher may tell the student the answer.
4. Finally, the teacher should ask the student what number can replace the blank in the original division equation to make it a true statement. The teacher should prompt
the student to explain and justify his or her response.
TASK RUBRIC
Getting Started
Misconception/Error
page 1 of 3 The student does not demonstrate knowledge of division as an unknown factor multiplication problem.
Examples of Student Work at this Level
The student has difficulty converting the first division equation into a multiplication equation, and eventually has to be shown how to do it.
Questions Eliciting Thinking
You know that simply putting × in the place of ÷ does not give a true equation because 8 × 4 ? 2. So, could you rearrange the order of the numbers 8, 4, and 2? Do you
know that 8, 4, and 2 are members of a multiplication and division fact family? Do you know what that means?
Instructional Implications
Have the student work on related multiplication and division facts with smaller factors such as those within 20. When the student begins to understand the inverse
relationship between multiplication and division, give the student a division equation, such as 168 ÷ 14 = 14, and ask the student to rewrite it as a multiplication equation.
Use a multiplication table to reinforce the relationship between multiplication and division. Show the student how to find the product in the body of the table of numbers
selected from the first column and top row. Likewise, show the student how to use the table to find the quotient of a number from the body of the table and a number
selected from the first column or top row.
Moving Forward
Misconception/Error
The student is unable to rewrite a division equation as a multiplication equation when one of the quantities in unknown.
Examples of Student Work at this Level
The student turns the first division equation into a multiplication equation and verifies in some manner that the resulting equation is true. However, the student cannot turn
the second division equation into a multiplication equation even with prompting.
Questions Eliciting Thinking
Let"s return to the first problem and examine what you did. Can you use the same strategy for the second problem?
Suppose I told you that the answer to the second problem is six. Replace the symbol for the unknown with a six. Does that help you solve the problem?
Instructional Implications
Use a multiplication table to reinforce the relationship between multiplication and division. Show the student how to find the product in the body of the table of numbers
selected from the first column and top row. Likewise, show the student how to use the table to find the quotient of a number from the body of the table and a number
selected from the first column or top row.
Give the student a multiplication equation, such as 6 × 7 = 42, and have him or her rewrite it as a division equation. In the same manner, ask the student to rewrite given
division equations. Once the student can confidently rewrite equations in which all quantities are known, ask the student to rewrite equations that contain unknowns.
Almost There
Misconception/Error
The student can rewrite the division problem as a multiplication problem but struggles to explain the relationship between multiplication and division.
Examples of Student Work at this Level
The student can rewrite each equation and understands that the solution of 54 ÷ 9 = ? is six but struggles to explain why both 54 ÷ 9 = ? and 9×? = 54 have the same
solution.
Questions Eliciting Thinking
How did using multiplication help you?
What if the problem was 12 ÷ 2 = ?? What multiplication problem could you use to help you? Will that always work?
Why does multiplication help? Can you give me a different related multiplication and division problem?
Can you explain why you can solve division problems by multiplying? What about the equation 8 ÷ 2 = 4? Why do we get eight as an answer when we multiply the two and
the four?
Instructional Implications
Model explaining the relationship between multiplication and division in the context of a specific problem. For example, if there are four groups of six marbles, then there are
24 marbles (4 × 6 = 24). Likewise, if 24 marbles are divided into four equal groups, then each group would have to contain six marbles (24 ÷ 6 = 4).
Use the relationship between addition and subtraction to introduce the concept of inverse operations. Then, present multiplication and division as another example of
page 2 of 3 inverse operations. Have the student write related multiplication and division equations.
Encourage the student to explain the relationship between multiplication and division to other students in the class.
Consider using the MFAS task Alien Math (3.OA.1.3).
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 can readily turn a division equation into an equivalent multiplication equation even if there is an unknown factor. The student easily solves problems one and
two and can justify and explain his or her work.
Questions Eliciting Thinking
Can you use this same procedure if the division equation goes beyond the basic facts? For example, could you rewrite 93 ÷ 3 as a multiplication problem, and find the
answer through multiplication?
What if the division problem has two unknowns such as a ÷ 5 = b? Can you rewrite this equation in multiplication form?
Instructional Implications
Pose more difficult division problems, such as 60 ÷ 5 or 93 ÷ 3, and ask the student to rewrite them as unknown factor problems and solve them.
Expose the student to division problems with remainders using word problems. Encourage the student to interpret the meaning of the remainder in the context of the
problem.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Changing Division Equations into Multiplication Equations cards.
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.2.6:
Description
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32
when multiplied by 8.
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