Lower Elementary
Question: The Earth is part of the Milky Way galaxy, which contains about 200 billion stars. The Sun is a yellow star in the Milky Way. In the Milky Way galaxy, a fifth of the stars are yellow stars like the Sun. How many yellow stars are there in the Milky Way?
Answer: 40 billion yellow stars
Note: : Although the number 200 billion seems like a large number, however we can simplify this problem by seeing that billion is the name and we only need to find 1/5 of 200. To find 1/5 of 200 break 200 into five equal groups.
200 ÷ 5 = 40
and
40 + 40 + 40 + 40 + 40 = 200
Because we can break 200 into five equal groups of 40, we know that a fifth of 200 is 40.
That means that 200 billion stars broken into five equal groups has 40 billion stars in each group.

Upper Elementary
Question: It takes about 365 days for the Earth to circle around the Sun. If Mercury takes about a quarter of the time it takes the Earth to circle the Sun, how many days does it take Mercury to circle the Sun?
Answer: 91¼ days
Note: A quarter is equal to a half of a half. Taking half of a half of 365 days will give us how many days it takes Mercury to circle the Sun.
Half of 365 = 182½
Half of 182½ = 91¼

Middle School:
Question: Betelgeuse, a star located in the Orion constellation, is 1000 times larger than the Sun. If we shrunk the Earth to have the same diameter of a golf ball, the diameter of Betelgeuse would be the length of 6 Empire State Buildings stacked on top of one another. If a golf ball has a diameter of 1.68 inches and the Empire State Building is 1,472 feet tall, how many times larger is the diameter of Betelgeuse than the diameter of the Earth?
Answer: 63,084 times larger
Note: The extra fact in this problem is that Betelgeuse is 1000 times larger than the Sun. This information is not needed to solve the problem. Before we try and solve this problem, we need to change each unit of measure so that they have the same name. First, change 1.68 inches to feet.
1.68 inches ● 1/12 feet/inch = 0.14 feet
Next, we find the number of times 0.14 feet go into 1,472 feet.
1,472 feet ÷ 0.14 feet ≈ 10,514
This is how many times longer the height of one Empire State building is than the diameter of a single golf ball.
Finally, we multiply by 6 to find the number of times longer the height of 6 Empire State buildings are than the diameter of a single golf ball.
10,514 ● 6 = 63,084
This tells us that the diameter of Betelgeuse is approximately 63,084 times longer than the diameter of the Earth.
(Fun Fact: If Betelgeuse were to replace the Sun as the center of our solar system, it would engulf Mercury, Venus, Earth, Mars, and Jupiter.)

Algebra and Up:
Question: At 4.2 light years away, Proxima Centauri is the closest star to Earth. If the speed of light is about 9.84×108 feet per second, how many miles away is Proxima Centauri from the Earth?
Answer: 2.47 x 1013 miles away
Note: We start by converting 9.84×108 feet per second into miles per year to know how many miles are in a light year.
9.84×108 feet/sec ● 60 sec/min ● 60 min/hour ● 24 hours/day ● 365 days/year ● 1 mile/5280 feet
The statement above converts 9.84×108 feet/sec into 5.88×1012 miles/year.
Then we multiply the amount of miles in a light year by how far Proxima Centauri is, 4.2 light years.
5.88×1012 miles/year ● 4.2 years = 2.47×1013 miles away
(Fun fact: If it were possible to fly in a commercial jet plane to Proxima Centauri, it would take roughly 7.1 millions years to get there.)