Lower Elementary:
Question: Hannah has half as many tokens as Ivan. Ivan has half as many tokens as Jayleen. If Hannah has 13 tokens, how many tokens does Jayleen have?
Answer: 52 tokens
Solution: Hannah has half as many tokens as Ivan and she has 13. To find how many tokens Ivan has, we need to double the number of tokens that Hannah has. 13 doubled = 10 doubled + 3 doubled = 20 + 6 = 26. Ivan has 26 tokens. Ivan has half as many tokens as Jayleen. To find how many tokens Jayleen has, we have to double the number of tokens that Ivan has. 26 doubled = 20 doubled + 6 doubled = 40 + 12 = 52. Jayleen has 52 tokens.
Upper Elementary:
Question: A baker lays 4 rows of 3 cookies on multiple cookie sheets. It takes 10 minutes to bake each cookie sheet. How long would it take to bake 84 cookies?
Answer: 70 minutes
Solution: There are 4 rows of 3 cookies on each cookie sheet, so there are 4 × 3 = 12 cookies per cookie sheet. To bake 84 cookies, we need to bake 84 ÷ 12 = 7 cookie sheets. Since each sheet takes 10 minutes to bake, it will take 7 × 10 = 70 minutes to bake 84 cookies.
Middle School:
Question: Collin babysat for 2 hours. Mallory babysat for 3 hours. They both get paid $70. How should they split the money to be fair?
Answer: Collin: $28 and Mallory: $42
Solution: One way to solve this problem is to find the price earned for babysitting for one hour and use that to find how much each of them should earn. They worked for a total of 2 + 3 = 5 hours. That means that babysitting for 1 hour earns $70 ÷ $5 = $14. Collin earned $14 × 2 = $28 and Mallory earned $14 × 3 = $42.
Algebra and Up:
Question: What is the measure of the angle made between the hands of a clock at 3:30?
Answer: 75°
Solution: One way to solve this problem is to find how many degrees from 12 the hands are and find the difference between the two angle measurements. The minute hand is at the 6, which is at the half way past 12. A circle has 360°, and half of 360° is 180°, so the minute hand is 180° away from 12. Since the hour hand moves as time goes on, at 3:30 it is half way between the 3 and the 4. The 3 is 1/4 of the clock past 12, and 1/4 of 360° is 90°, so the 3 is 90° past the 12. The 4 is 1/3 of the clock past 12, and 1/3 of 360° is 120°, so the 4 is 120° past the 12. Since the hour hand is half way between 3 and 4, the hour hand will be 90° + 120° = 210° ÷ 2 = 105° away from 12. To find the angle between the hands of the clock, we can find the difference between the minute hand and the hour hand. 180° – 105° = 75°. The angle made between the hands of a clock at 3:30 is 75°.
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