Lower Elementary
Question: Fred, Brian, Megan, Chris, and Sue are friends. Megan is taller than Chris. Fred is taller than Brian, but shorter than Sue. Brian is taller than Chris. Sue is shorter than Megan. List the friends in order from tallest to shortest.
Hint: Write each name on a piece of paper and move to test for possible answer.
Answer: Megan, Sue, Fred, Brian, Chris
Upper Elementary
Question: Veronica has 12 jellybeans in her pocket, 5 red, 4 blue, and 3 green. What is the minimum number of jellybeans she needs to take out of her pocket to guarantee she has a jellybean in each color?
Answer: 10 jelly beans
Note: Assume that in the worst case the first 5 jellybeans she pulls out are red and the next 4 she pulls out are blue. When she pulls out the 10th jellybean she will have one in each color.
Middle School
Question: Steven is standing in a line of people. 1/4 of the people in the line are in front of him and 2/3 of the people in the line are behind him. How many people are in the line?
Answer: 12 people
Note: In order to find the number of people in the line you add the fractional part of people in front and back of Steven, 1/4 + 2/3 = 11/12. That means Steven is 1/12. So there are 12 people in the line.
Algebra and Up
Question: A school has a rectangular playground. They want to make the playground larger by increasing the length by 40% and the width by 30%. What will be the resulting percentage increase in area of the playground?
Answer: 82%
Note: Given that percent increase = change/original, there are two ways to solve this problem, arithmetically and algebraically.
An arithmetic method would be to use real values. Suppose the length of the playground is 100 feet and the width is 100 feet. Then the area is 10,000 sq. ft. Increasing the length by 40% means it will be 140 feet. Increasing the width by 30% means it will be 130 feet. The resulting area will be 18,200 sq. ft. The increase in area is 8,200 sq. ft. The percent increase = 8,200/10,000 which gives 82%
An algebraic method would be to suppose the length of the park to be x and the width to by y. The area would then by xy. Increasing the length by 40% would mean the new area is x + .4x = 1.4x. Increasing the width by 30% would make the new width y + .3y = 1.3y. The resulting area would be 1.82xy. The change in the area is .82 which is 82%.
