Lower Elementary:
Question: How many legs do 2 dogs, 3 birds, and 4 fish have altogether?
Answer: 14 legs
Solution: Dogs have 4 legs. 4 doubled is 8. Birds have 2 legs. 3 doubled is 6. Fish have no legs. Add them together; you get 8 + 6 + 0 = 14.
Upper Elementary
Question: Michael ate 8/9 of a pie. Sue ate 4/5 of a pie. Who ate more pie?
Answer: Michael
Solution: Computation:
Find the common denominator (or same name) for each fraction. The smallest number that 9 and 5 both go into is 45. 8/9 = 40/45 and 4/5 = 36/45. Michael ate 40/45 of a pie and Sue ate 36/45 of a pie. So Michael ate more pie.
Number Sense:
Compare how much of the pie each did not eat. Michael did not eat 1/9 of a pie. Sue did not eat 1/5 of a pie. 1/5 is larger than 1/9, which means Sue has more pie left over. So Michael ate more pie.
Middle School:
Question: Jessica spent a total of $200 on her doll collection. 30% was spent on accessories like cars and furniture, 25% was spent on the doll house, and the rest was spent on toy dolls. How much money did Jessica spend on toy dolls?
Answer: $90
Solution: Method 1: one part is equal to the total minus the sum of the other parts. So we need to find how much each part of the collection costs. Accessories are $60 (percent means for each hundred, so 30% of 200 is 30 + 30 = 60). The doll house is $50 (25% of 200 is 25 + 25 = 50). So far, Jessica spent $60 + $50 = $110. To see how much the toy dolls cost, subtract the amount she spent on the house and accessories from the total. $200 – $110 = $90
Method 2: Find the percent of the collection that was spent on toy dolls.
The total percent spent on accessories and the house is:
30% + 25 % = 55%.
Subtract that from 100% to get the percent spent on toy dolls.
100% – 55% = 45%.
45% of the $200 was spent on toy dolls. 45% of 200 is 90 (percent means for each hundred, so 45% of 200 is 45 + 45 = 90), so Jessica spent $90 on toy dolls.
Algebra and Up:
Question: One pint of paint can cover 25 square feet. How many pints of paint are needed to paint the outside of an opened top rectangular box with a length of 10 feet, a width of 5 feet, and a height of 5 feet?
Answer: 8 pints of paint
Solution: First we need to find the surface area of the box. The surface area is the area of all the sides. The formula for a rectangular box is SA = 2×length×width + 2×length×height + 2×width×height. However, this is an opened top box, so that means the top does not count towards the surface area. So now our formula becomes SA = length×width + 2×length×height + 2×width×height. Plugging it in we get:
SA = (10)(5) + 2(10)(5) + 2(5)(5) = 50 + 100 + 50 = 200 square feet.
Each pint of paint can cover 25 square feet, so divide be 25 to get the number of pints needed. 200 ÷ 25 = 8 pints of paint are needed.
