Properties of Multiplication — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
In Grade 3, (2 x 3) x 4 equals 2 x (3 x 5) by the associative property.
Corrected: In Grade 3, (2 x 3) x 4 equals 2 x (3 x 4) by the associative property.
Grade 3 associative property regroups the same factors 2, 3, and 4 without changing them.
2. Fix the sentence:
The Grade 3 associative property lets you change the order of the factors in 4 x 5 x 2.
Corrected: The Grade 3 associative property lets you change the grouping of the factors in 4 x 5 x 2.
Only the commutative property changes order; associative changes how factors are grouped in Grade 3.
3. Fix the sentence:
In Grade 3, (3 x 2) x 5 gives a different product than 3 x (2 x 5).
Corrected: In Grade 3, (3 x 2) x 5 gives the same product as 3 x (2 x 5).
Both groupings equal 30, so the associative property holds in Grade 3.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. In Grade 3, (2 x 4) x 3 = 2 x (4 x 3).
Associative property regroups 2, 4, and 3 without changing any factor.
2. A Grade 3 student finds 5 x 2 x 3 by first computing (5 x 2) = 10 and then multiplying by 3.
(5 x 2) x 3 = 10 x 3 = 30, showing associative grouping in Grade 3.
3. In Grade 3, 2 x (3 x 4) equals 2 x 12, which equals 24.
2 x (3 x 4) = 2 x 12 = 24 in Grade 3 associative practice.
4. Grade 3 students see (4 x 2) x 5 = 4 x (2 x 5) by the associative property.
Associative property regroups 4, 2, and 5 to keep the same Grade 3 product.
Part C: True or False?
Read each statement. Circle True or False.
1. In Grade 3, (3 x 4) x 2 equals 3 x (4 x 2) because of the associative property.
True False
Both sides equal 24, confirming associativity for Grade 3.
2. The Grade 3 associative property changes the order of the factors.
True False
Changing order is the commutative property; associative only moves parentheses in Grade 3.
3. A Grade 3 student can group 2 x 5 first in 2 x 5 x 7 to make the math easier.
True False
(2 x 5) x 7 = 10 x 7 = 70, a helpful Grade 3 associative strategy.