Lower Elementary
Question: Mark, Scott, and Christian ordered an extra-large pepperoni pizza. Mark and Christian both had 3 slices each and Scott had 4 slices of pizza. If there were 6 slices of pizza left, how many slices of pizza does the extra-large pizza start with?
Answer: 16 slices
Solution: To find the answer to this problem we start by adding all the slices of pizza eaten by Mark, Christian, and Scott. Mark had 3 slices, Christian had 3 slices, and Scott had 4 slices of pizza. Together they had 10 slices of pizza (3 + 3 + 4 = 10). Because there were 6 slices of pizza remaining, the pizza started with 16 slices.
Upper Elementary
Question: Jane wants to make cupcakes for her class. The recipe she has calls for 2 eggs, 3 cups of flour, 1 cup of sugar, and ½ a cup of milk. If her recipe makes a dozen cupcakes, how much of each ingredient will Jane need to make 18 cupcakes?
Answer: 4½ cups of flour, 1½ cups of sugar, a ¾ cup of milk, and 3 eggs.
Solution: Jane’s recipe makes a dozen cupcakes. She needs to make 18 cupcakes which are 6 more than a dozen. Because 6 is half of 12, Jane needs the amount from the recipe plus half the amount from the recipe.
Eggs: Half of 2 is 1, so Jane needs 3 eggs (2 + 1 = 3).
Flour: Half of 3 is 1½, so Jane needs 4½ cups of flour (3 + 1½ = 4½).
Sugar: Half of 1 is ½, so Jane needs 1½ cups of sugar (1 + ½ = 1½).
Milk: Half of a ½ is ¼, so Jane needs ¾ of a cup of milk (½ + ¼ = ¾).
Middle School
Question: Find the area of the shaded region below.
Answer: 12.5 m2
Solution: Using the Pythagorean Theorem, we can find the hypotenuse of the white triangles.
a2 + b2 = c2 → 32 + 42 = c2 → 25 = c2 → c = 5
The white triangles both have a hypotenuse of 5 m, which are the base and height of the shaded triangle.
Now that we have the base and height of the triangle, we can solve for the area using the area of a triangle formula.
A= ½bh = ½(5)(5) = ½(25) = 12.5 m2
Another way to solve this problem is to find the area of the trapezoid and subtract out the area of the two white triangles.
Algebra and Up
Question: At 4.2 light years away, Proxima Centauri is the closest star to Earth. How many years would it take for 747 passenger jet cursing at 570 mph to reach Proxima Centauri from Earth? (Hint: The speed of light is measured to be about 9.84×108 feet per second.)
Answer: 4.95×106 years
Solution: Because a light year is measured to be how far light travels in a year, we will start by converting 9.84×108 feet per second into miles per year to know how many miles are in a light 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
Now that we know how far Proxima Centauri is from the Earth, we divide 2.47×1013 miles by the cruising speed of a 747 (570 mph).
(2.47×1013)/570 = 4.33×1010 hours
Finally we convert hours to years.
That is almost 5 million (4,950,000) years!
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