Download Document

1. Jon completed the problem below for a test. Did Jon complete the
problem correctly? If not, solve the problem correctly and describe
in words why his work was incorrect.
6² - (3 x 2) + 4
6² - (6) + 4
12 - 6 + 4
12-10
2
No, Jon did not complete the problem correctly. He should have
solved the problem like this:
6² - (3 x 2) + 4
6²-(6) + 4
36-6+4
30+4
34
His first mistake was saying that 6² is 12, when it is really 6x6 which
is 36. Next in his third step he should have subtracted before he
added. Adding and subtracting are really part of the same step in
order of operations and when you have both of them you need to do
whichever comes first left to right. Jon did not get the correct
answer because he did not follow the order of operations.
2. Amy is in charge or ordering new computers for her classroom. If
each computer costs $1256.33 and Amy needs to order 5 computers,
about how much money will Amy need?
Amy says she will need about $5,000.00 for her new computers.
She shows her work:
$1256.33 rounds to $1000.00 and 1000.00 times 5 = $5,000.00
Did Amy round correctly for this situation? Defend you
answers using words and examples.
I do not think Amy rounded correctly for this situation. In this situation
Amy underestimated when she should have overestimated. By rounding
$1256.33 to $1000.00 she will end up being short on money and not have
enough to buy all five computers she needs. In many situations that deal
with money it is better to have an estimate higher than what you actually
need instead of lower. Amy should have rounded 1256.33 to 1300.00. When
you take 1300.00 times 5 you would get $6500.00. [ 5(13) = 5(10+3) = (5x10)
+ (5x3) = 50 + 15 = 65 add the two zeros for 6500 ]
3. Identify each number property below. List characteristics for each
property and explain how you knew it was that property.
(commutative, associative, distributive)
8 + (x + 7) = (8 + x) + 7 – Associative Property of addition– I know this
because only the grouping of the numbers change. The order of the numbers
stay the same and the parenthesis are the only thing that change. This
property can apply to both multiplication and addition. It follows the
format: A + (B + C) = (A + B) + C.
5 (7 + 8) = 5(7) + 5(8) – Distributive – I know this because by definition the
distributive property tells me that I multiply a number by a sum. Here I
multiply 5 times 7 + 8 (sum). This is the only property I have learned about
that has two operations in one, multiplication and addition. This problem
follows the format of: A(B+C) = (AB) + (AC)
3 x 4 x 6 = 3 x 6 x 4 – Commutative Property - This is the commutative
property of multiplication. I know this because the only thing different on
opposite sides of the equal sign is the ordering of the numbers. The
commutative property tells me that I can change the ordering of numbers in
addition and multiplication and it won’t change my answer. It follows the
format: A x B x C = B x C x A.