Maryland Math 3.NOS.E.9
Standard Cluster
Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotients less than or equal to 10). Skip count (2s, 5s, 10s) and apply properties of operations (0s, 1s) to derive foundational facts. Derive unknown facts from known facts using double facts (e.g., to solve 4 × 3, double 3 to get 6 and double 6 to get 12) to multiply and divide. Use properties of operations (e.g., to solve 8 × 7, think of (5 × 7) + (3 × 7)) to multiply. Use the inverse relationship between multiplication and division (e.g., think of 4 × ? = 28 to solve 28 ÷ 4 = ?) to multiply and divide.
Maryland College and Career Ready Standards for Mathematics (2025) · MULTIPLY AND DIVIDE WITHIN 100.
Cluster contents
Standards in This Cluster
3.NOS.E.9 is a cluster heading. These are the individual standards under it.
- 3.NOS.E.9.a
Skip count (2s, 5s, 10s) and apply properties of operations (0s, 1s) to derive foundational facts.
- 3.NOS.E.9.b
Derive unknown facts from known facts using double facts (e.g., to solve 4 × 3, double 3 to get 6 and double 6 to get 12) to multiply and divide.
- 3.NOS.E.9.c
Use properties of operations (e.g., to solve 8 × 7, think of (5 × 7) + (3 × 7)) to multiply.
- 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.
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students recall multiplication and division facts with numbers through 10 or work them out quickly. They skip-count by 2s, 5s, and 10s, use zero and one facts, double known facts, split groups, and use multiplication to solve division.
What Mastery Looks Like
- A student can find 8 × 7 by adding 5 × 7 and 3 × 7. They use 8 × 7 = 56 to solve 56 ÷ 8 = 7. They answer 0 × 7 and 1 × 7 without counting.
Common Misconceptions
- Some students answer 7 for 0 × 7 or 1 for 1 × 7. When splitting 8 × 7, they may add 5 × 7 and 3 instead of 3 × 7. They may not see that 8 × 7 = 56 helps them solve 56 ÷ 8.
How to Assess It
- Exit ticket: Find 8 × 7 using 5 × 7, then use your answer to solve 56 ÷ 8. Show each step.
Lesson moves
Ways to Teach It
Build 2 rows of 3 counters, double the rows to find 4 × 3, then double again to find 8 × 3.
Ask partners, “How can 5 × 7 help you find 8 × 7?” Have them draw and explain the extra groups.
Play fact-family match with cards for 6 × 4, 24 ÷ 6, and 24 ÷ 4; partners match and solve them.
Put 30 pencils into 5 cups equally; ask how many go in each cup, then check with multiplication.
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Printable 3.NOS.E.9 Worksheet
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Related Standards
- 2.NOS.B.6
Recall or quickly derive addition and subtraction facts within 20.
- 6.NOS.B.2.b
Use strategies (e.g., partial quotients, inverse relationship between multiplication and division) to divide.
- 4.NOS.C.7
Recall or quickly derive multiplication and division facts within 100 (e.g., factors less than or equal to 10 and quotients less than are equal to 10).
- 1.NOS.D.9
Recall or quickly derive addition and subtraction facts within 20.
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