Lower Elementary
Question: Jesse ran 6 laps around the school yard. If Scott ran 3 laps more than Jesse, how many total laps did Scott and Jesse run together?
Answer: 15 laps
Solution: Scott ran 3 more laps that Jesse. Because Jesse ran 6 laps, Scott ran 9 laps (3 more than 6). Adding the laps that Jesse ran to the laps Scott ran, gives 15 laps (9 laps + 6 laps).
Upper Elementary
Question: A certain type of hummingbird can flap its wings 70 times per second. How many times does the hummingbird flap its wings in five minutes?
Answer: 21,000 times
Solution: This hummingbird flaps its wings 70 times per second. That means it flaps it wings 4200 per minute (70 × 60). In 5 minutes it flaps its wings 5 times 4200 or 21,000 times.
Middle School
Question: If the earth were the size of a basketball, how tall would the 1250-foot tall Empire State building be? The earth has diameter of 42,000,000 feet and a basketball’s diameter is 0.8 feet.
Answer: About 2.4×10-5 feet
Solution: This problem is best solved using proportional thinking.
42,000,000/1250 = 0.8/x
Cross-multiply and solve for x.
42,000,000x = 1250(0.8)
42,000,000x = 1000
x = 1000/42,000,000 ≈ 0.000024 = 2.4×10-5 feet
Algebra and Up
Question: A 25 pound bag of sand is 20% red. The rest of the sand is white. How much red sand must be added to make a mixture that is 25% red?
Answer: 1â…” pounds
Solution: 20% of a 25 pound is 5 pounds. There are 5 pounds of red sand and 20 pounds of white sand. The amount of white sand doesn’t change. The final mixture is supposed to be 25% red sand which means it will be 75% white sand. So one way to find the solution is the answer the question 75% of what number is 20?
Let t be the total amount of sand after adding the red sand.
0.75t = 20
t = 26â…”
Because we originally had 25 pounds of sand, the difference between the original amount and the new amount is 1â…” pounds (26â…” – 25).
Algebraically we can use proportions to solve this problem.
Let r equal the amount of red sand added,
5+r/25+r = .25 = ¼
The ratio of the new amount of red (5+r) to the new total amount (25+r) is 25% or ¼.
Cross-multiply and solve for r.
4(5 + r) = 25 + r
20 + 4r = 25 + r
3r = 5
r = 5/3 = 1â…” pounds
