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MF.SN.3 Challenge MF-025-A12-V04

Multiply and divide signed numbers and interpret sign patterns correctly.

Recognize equivalent signed multiplication and division models

Problem

Identify exactly \(\text{all}~\text{representations}\) that preserve the division relationship \((-21)~\div~7\). Include representations with \(-21\) as the total and \(7\) as the number of equal groups, along with the matching inverse equation. Report the complete set of labels.

Target: \((-21)~\div~7\)

Representations:
A. a total of \(-21\) shared equally among \(7~\text{groups}\)
B. the number that makes \(7~\times~?~=~-21\)
C. \((-7)(3)\)
D. \(21~\div~(-7)\)
E. A loss of \(21~\text{points}\) shared equally across \(7~\text{rounds}\) means \(-3~\text{points}~\text{each}~\text{round}\)
F. \(7~\text{groups}~\text{of}~-3\)
G. \(-21~+~7\)
H. \(21~\div~7\)

Target-and-options organizer for signed division with a negative total. The target box shows (-21) divided by 7 and reminds students to keep total negative 21 and 7 equal groups or use the inverse equation. Eight labeled option cards mix equal-sharing descriptions, inverse equations, multiplication facts, addition, and sign distractors. Open full size
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Four variants of this problem type
Curriculum context
Standard
MF.SN.3
Category
Signed Numbers
Domain
Operations
Objective
Multiply and divide signed numbers and interpret sign patterns correctly.
Problem type
Recognize equivalent signed multiplication and division models