Lower Elementary:
Question: Bobby has a collection of marbles. He started the week with 30 marbles. He bought a bag of 24 marbles and gave 15 away to his younger brother. How many marbles does Bobby have left?
Answer: 39 marbles
Solution: Bobby’s collection begins with 30 marbles. He bought a bag of 24 marbles, so now he has 54 marbles (30 + 24 = 54). He then gave away 15 of the marbles so now he has 39 marbles left (54 – 15 = 39).
Upper Elementary:
Question: Lilly can read 75 words a minute. If there are 100 words on a page, how long will it take Lilly to ready 3 pages?
Answer: 4 minutes
Solution: If there are 100 words on a page, then there are 300 words on 3 pages (100 × 3 = 300). Lilly can read 75 words in 1 minute. This means that she can read 150 words in 2 minutes, 225 words in 3 minutes, and 300 words in 4 minutes. So, it takes Lilly 4 minutes to read 3 pages.
Middle School:
Question: Let’s define the symbol # as an operation symbol that finds the quotient of the two numbers and then squares the result. For example, 18 # 6 would equal 9, since 18 ÷ 6 = 3 and 3 squared is 9. In the order of operations, it comes after parenthesis. What is (12 × 5) # (13 – 9)?
Answer: 225
Solution: First, we need to do the parenthesis part of the operation. 12 × 5 = 60 and 13 – 9 = 4. Our problem now becomes 60 # 4. Following the steps for what the # does, 60 ÷ 4 = 15 and then 15 squared is 225. So, 60 # 4 is 225.
Algebra and Up:
Question: A small square is inscribed in a larger square such that the corners of the smaller square lie on the midpoints of the sides of the larger square. If the side length of the larger square is 4 inches, what is the area of the smaller square?
Answer: 8 square inches
Solution: One way to find the area of the smaller square is to find the side length for the smaller square and then square it. Because the corners of the small square lie of the midpoints of the sides of the larger square, the side length of the larger square is the same as the diagonal of the smaller square. Since all angles of a square are 90° and the diagonal of a square bisects the angles, we have a 45 – 45 – 90 triangle with a hypotenuse 4 inches. To go from the hypotenuse to the side of a 45 – 45 – 90, divide the side length by sqrt(2). 4/sqrt(2) = 4sqrt(2)/2 = 2sqrt(2). So the side length of the smaller triangle is 2sqrt(2). To find the area of the square, take the side length and square it. (2sqrt(2))2 = 4(2) = 8. The area of the smaller square is 8 square inches.
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