Lower Elementary
Question: Every hour Jackie drove 40 miles. How many miles did Jackie have driven in 2 and a half hours?
Answer: 100 miles
Note: In the first hour Jackie drove 40 miles. In the second hour she drove another 40 miles. And the last half hour she drove half of 40 miles or 20 miles.
So,
40 miles + 40 miles + 20 miles = 100 miles
Upper Elementary
Question: A 4 gigabyte iPod nano can store 1000 songs. How many songs can an 80 gigabyte iPod store?
Answer: 20,000 songs
Note: A 4gb iPod nano can store 1,000 songs, so a 40gb (4 x 10) iPod can store 10,000 songs (1,000 x 10). Doubling 40gb to 80gb we also double 10,000 songs to 20,000 songs.
4gb = 1,000
4gb x 10 = 1,000 x 10
40gb = 10,000
Double 40gb = Double 10,000
80gb = 20,000
Middle School
Question: Hannah started the day with $15. She then collected 583 aluminum cans and took them to a recycling center where she gets 63¢ per pound. If 33 cans equal a pound, how much money did Hannah have after she recycled the cans?
Answer: $26.13
Note: Hannah has 583 aluminum cans where 33 cans equal a pound. By dividing 583 by 33 we find how many pounds of aluminum cans Hannah has.
583 ÷ 33 = 17 2/3 pounds
Because the recycling center pays 63¢ per pound, we multiply 17 2/3 by $0.63.
17 2/3 â— $0.63 = $11.13
Hannah started with $15.00 and after recycling she now has $11.13 more.
$15.00 + $11.13 = $26.13
Algebra and Up
Question: The Richter scale is used to measure the magnitude of an earthquake. It is based on a logarithmic function with a base of 10, such that the Magnitude = Log10(Amplitude). If the 2010 Chilean earthquake had a magnitude of 8.8 and the magnitude of the 2010 Haitian earthquake was 7.0, how much greater was the amplitude in the Chilean earthquake than that of the Haitian earthquake?
Answer: 63 times greater
Note: In order to solve for the amplitude, we need to rewrite the logarithmic equation into exponential equation.
Letting the variables m and a stand for magnitude and amplitude respectively,
m = Log10a
Rewriting this in exponential form:
a = 10m
Now plug in the given magnitude for both earthquakes, solve, and compare.
Chile:
aC = 108.8 ≈ 630957344
Haiti:
aH = 107.0 = 10000000
aC/aH ≈ 63 times greater
