Imagine Schools Math Challenge Worksheet With Answer Key - 4th Grade, 2014 Page 9
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33Project #7
Domain: Number and Operations in Base Ten
Standards:
4.NBT.5 Multiply a whole number of up to four digits by a one‐digit whole number, and multiply two
two‐digit numbers, using strategies based on place value and the properties of operations. Illustrate
and explain the calculation by using equations, rectangular arrays, and/or area models.
Directions:
th
1. Read the following definitions to remind you of concepts you should have learned during your 4
grade math class.
Associative Property
The property which states that for all real numbers a, b, and c,
their product is always the same, regardless of their grouping:
.
.
.
.
(a
b)
c = a
(b
c)
Example:
.
.
.
.
(5
6)
7 = 5
(6
7)
Distributive Property
The property which states that multiplying a sum by a number gives the same result
as multiplying each addend by the number and then adding the products
a(b + c) = a X b + a X c
Examples:
3(4 + 5) = 3 X 4 + 3 X 5
3(a + b) = 3a + 3b
2. Then solve the following three problems and state which property you used to do so. Show all of
your work.
1. 25 x 28=
2. 102
3. 425 divided by 12
x 14
3. Finally, create one real world problem to show you understand the associative property and one
word problem to show you understand the distributive property.
Two examples for the associative property:
Partial products method—14 x 16 = 100 (multiply 10 x 10) + 40 (multiply 10 x 4) + multiply 6 x 10
+ (multiply 6 x 4)
Multiple addition method—14 x 16 = 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16 + 16
+16 + 16 + 16 + 16
Two examples for the distributive property:
Share 25 books among 4 girls. (6 with a remainder of 1)
Share 25 bananas among 4 girls (6 ¼).
Page 9
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