Maryland Math 3.NOS.C.5
The Standard
Explain and use the inverse relationship between multiplication and division to determine the unknown whole number in a multiplication or division equation involving three whole numbers (e.g., find 32 ÷ 8 by thinking of unknown-factor problem and finding the number that equals 32 when multiplied by 8).
Maryland College and Career Ready Standards for Mathematics (2025) · UNDERSTAND PROPERTIES OF MULTIPLICATION AND THE RELATIONSHIP BETWEEN MULTIPLICATION DIVISION.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find a missing number in a multiplication or division equation. They use a related fact to find the number and explain why it works.
What Mastery Looks Like
- Given 42 ÷ ? = 7, a student writes 7 × ? = 42 and finds 6. They check that 42 ÷ 6 = 7.
Common Misconceptions
- Some students put 8 in the blank in 32 ÷ ? = 8 because they copy the number they see. Others write 32 × 8 = ? when trying to check their answer.
How to Assess It
- On an exit ticket, ask: Solve 42 ÷ ? = 7. Write a multiplication fact that proves your answer.
Lesson moves
Ways to Teach It
Give pairs 24 counters to make groups of 6, then have them write 24 ÷ 6 = ? and 6 × ? = 24.
Ask students to explain in writing how 7 × 5 = 35 helps them solve 35 ÷ ? = 7.
Give partners cards marked 6, 7, and 42, and have them build equations with one blank for the other person to solve.
Ask students to pack 30 pencils into 5 equal cups, then write a multiplication fact to find how many pencils go in each cup.
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Printable 3.NOS.C.5 Worksheet
A ready-to-print activity worksheet aligned to 3.NOS.C.5, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 4.NOS.C.7.d
Use the inverse relationship between multiplication and division (e.g., think of 4 × ? = 28 to solve 28 ÷ 4 = ?) to multiply and divide.
- 3.NOS.E.9.d
Use the inverse relationship between multiplication and division (e.g., think of 4 × ? = 28 to solve 28 ÷ 4 = ?) to multiply and divide.
- 6.NOS.B.2.b
Use strategies (e.g., partial quotients, inverse relationship between multiplication and division) to divide.
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