Maryland Math 3.NOS.C.4
The Standard
Identify and apply the Commutative Property of Multiplication, Associative Property of Multiplication, and Distributive Property of Multiplication as strategies to multiply.
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 change the order or grouping of factors to make multiplication easier. They also split a factor into two parts, multiply each part, and add the results.
What Mastery Looks Like
- A student can show 4 × 6 = 6 × 4 by rotating an array. They can rewrite (2 × 3) × 4 as 2 × (3 × 4), and solve 7 × 6 as (7 × 4) + (7 × 2).
Common Misconceptions
- Students may think changing the order or grouping of factors changes the product. When splitting a factor, they may multiply only one part or forget to add the two products.
How to Assess It
- Give an exit ticket: Rewrite 8 × 3 by switching factors, (2 × 3) × 4 by changing the grouping, and 7 × 6 by splitting 6 into 4 + 2. Find each product.
Lesson moves
Ways to Teach It
Build a 4 by 6 counter array, rotate it, then split it into 4 by 2 and 4 by 4 arrays.
Ask: Why do (2 × 3) × 4 and 2 × (3 × 4) give the same answer? Draw groups to explain.
Play property match with cards showing 5 × 8, 8 × 5, 5 × (6 + 2), and (5 × 6) + (5 × 2).
Use a 6 by 8 classroom seating chart to count seats by splitting each row into 5 seats and 3 seats.
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Printable 3.NOS.C.4 Worksheet
A ready-to-print activity worksheet aligned to 3.NOS.C.4, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 4.NOS.B.5.b
Use strategies based on place value (e.g., partial products) to multiply.
- 5.NOS.B.7.d
Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.
- 5.NOS.D.13.b
Apply and extend whole number multiplication strategies (e.g. area model, partial products).
- 1.NOS.C.7
Apply the Commutative Property of Addition and Associative Property of Addition as a strategy to add.
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