Worked Example 1
Distributive Property
Find 6 × 34 using the distributive property.
- 1Break 34 into 30 + 4: 6 × 34 = 6 × (30 + 4)
- 2Multiply each part: (6 × 30) + (6 × 4) = 180 + 24
- 3180 + 24 = 204
Answer: 204
Florida Grade 3 Math · Algebraic Reasoning
MA.3.AR.1.1: Properties of Multiplication
What this Grade 3 benchmark means, worked examples, common mistakes, and a free printable worksheet.
Created by a Florida mom · Published by Tropical Learning LLC
What Is Benchmark MA.3.AR.1.1?
Students use the properties of multiplication to make products easier, and they name the properties. The distributive property breaks a two-digit number apart: 4 × 72 = 4 × (70 + 2) = (4 × 70) + (4 × 2) = 288.
The commutative property says the order doesn't matter (3 × 8 = 8 × 3). The associative property says the grouping doesn't matter: (2 × 5) × 7 = 2 × (5 × 7). Students use parentheses to show the grouping.
Official benchmarkApply the distributive property to multiply a one-digit number and two-digit number. Apply properties of multiplication to find a product of one-digit whole numbers.
On the FAST test: part of the Grade 3 reporting category Number Sense and Multiplicative Reasoning, which is about 23–29% of the test.
Worked Examples
Worked Example 2
Commutative and Associative Properties
Find 2 × 7 × 5 in an easy way.
- 1Change the order (commutative property): 2 × 7 × 5 = 2 × 5 × 7
- 2Group the friendly numbers (associative property): (2 × 5) × 7
- 3(2 × 5) × 7 = 10 × 7 = 70
Answer: 70
Common Mistakes to Watch For
Multiplying only one part
Wrong:3 × 46 = (3 × 40) + 6 = 126
Multiply both parts by 3: (3 × 40) + (3 × 6) = 120 + 18 = 138.
Mixing up the property names
Wrong:3 × 8 = 8 × 3 is the associative property.
Changing the order is the commutative property. Changing the grouping with parentheses is the associative property.
Helpful Math Tip
Use an area model: draw a rectangle for 6 × 34, split it into a 6 × 30 part and a 6 × 4 part, and add the two areas.
Related Grade 3 Skills
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