Lower Elementary
Question: Jessica wants to give 7 silly bands to each of her 6 closest friends. She already has 13 silly bands. How many more does she need?
Answer: 29 silly bands
Note: In order for Jessica to give 7 silly bands to 6 of her closest friends, she needs to have (7 x 6) 42 silly bands. Since she only has 13 right now she needs (42 – 13) 29 more.
Upper Elementary
Question: Jeff invited his entire class of 32 kids to his birthday party. 3/4 of the kids in his class replied to say they would attend the birthday party. If he wants each classmate to have 1/4 of a pizza. How many pizzas will he need to order?
Answer: 6
Note: First we find out how many kids are going to attend Jeff”s birthday party. The entire class has 32 kids. If 3/4 of the class decides to come to the party then that is (3/4 of 32) 24 kids who are going to attend the party. If each of the 24 kids is to have 1/4 of a pizza that means he will need (1/4 x 24) 6 pizzas.
An alternative for finding 1/4 x 24 besides direct multiplication, would be to find 1/4 of 24. 1/4 is a half of a half. Half of 24 is 12 and half of 12 is 6.
Middle School
Question: Rina bought a shirt that was on sale for 20% off. Rina paid $28 for the shirt. What was the original price of the shirt?
Answer: $35
Note: Ignore sales tax in this problem.
A solution for this problem would be to use the percent discount equation:
(original price – new price)/original price = percent discount. We know that the new price is $28 and that the percent discount is 20%.
Let x = original price, then
(x – 28)/x = 20/100. We can now solve this proportion.
100(x – 28) = 20x
100x – 2800 = 20x
80x = 2800
x = 35
Another solution for this problem would be to note that, if the shirt was on sale for 20% off then Rina paid 80% of the original price. That means $28 is 80% of the original price.
That means 80% of _____ = 28.
From this point either the equation 0.8x = 28 can be used and solving for x we find x = $35.
Or we can not that 80% is 4/5. So 4/5 of a number is 28. That means that 4 equal parts makes 28. That means that there are 7 in each part. So 5 parts would be 35.
Algebra and Up
Question: It takes h hours for Painter A to paint an entire house. If it takes Painter B 3/4 as long as Painter A to paint 
the same house, how long will it take for them to paint the house together?
(*Hint – Solve for the time in terms of h.)
Answer: 3h/7 hours
Note: This is an algebra “work” problem. The way to solve this problem is using the following principles.
1) “The whole equals the sum of its parts,” and
2) “If it takes T amount of time to a whole job, then in x amount of time, T/x of the whole job can be done.”
Let the total time for Painters A and B working together equal T.
Using the second principle, the amount of the whole just that can be done by Painter A is T/h.
Since Painter B takes 3/4 as long to do the job as Painter A he can do T / (3/4h) = 4T/3h of the job.
Using the first principle we take the sum of the parts that each painter can do to form 1 whole job.
T/h + 4T/3h = 1
First, multiply the equation through by the least common denominator of h and 3h, which is 3h.
3h(T/h + 4T/3h = 1)
3T + 4T = 3h
7T = 3h
T = 3h/7
