**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