Montana Math MT.3.OA.5
The Standard
Apply the commutative property of multiplication, associative property of multiplication, and distributive property of multiplication over addition on whole numbers as strategies to multiply.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students change the order or grouping of factors to use facts they know. They split an array into parts, multiply each part, and add the results.
What Mastery Looks Like
- A student can solve 6 × 7 as 6 × 5 + 6 × 2 = 42. They can show that (3 × 4) × 2 and 3 × (4 × 2) both equal 24. They can use 4 × 6 = 6 × 4 to recall a fact.
Common Misconceptions
- Students may write 3 × (4 + 2) as 3 × 4 + 2, forgetting to multiply the 2. Some confuse changing factor order with changing grouping, or think swapping numbers works for subtraction too.
How to Assess It
- Exit ticket: Use switched factors to find 4 × 7, show two groupings for 3 × 4 × 2, and split 6 × (5 + 2) into partial products.
Lesson moves
Ways to Teach It
Build a 3-by-7 array with tiles, split it into 3-by-5 and 3-by-2 sections, and write the matching equation.
Ask partners to sketch how 4 × 6 and 6 × 4 can describe the same tiles, then explain their sketches.
Give pairs cards with three factors; have them find two groupings for each card and check the products.
Show a seating chart with 5 rows of 8 chairs; split each row into 5 and 3 to count the chairs.
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Printable MT.3.OA.5 Worksheet
A ready-to-print activity worksheet aligned to MT.3.OA.5, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- MT.K.OA.1
Represent addition and subtraction in multiple ways.
- MT.2.NBT.9
Understand and make connections between different strategies for addition and subtraction.
- MT.4.NBT.5
Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, flexibly using strategies based on place value and the...
- MT.K.OA.6
Recognize the characteristics of the commutative property in addition.
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