Lower Elementary:
Question: Emily made 1 dozen chocolate chip cookies. If her recipe calls for ½ a cup of chocolate chips, how many chocolate chips does she need for 4 dozen cookies?
Answer: 2 cups
Solution: For one dozen cookies Emily uses ½ cup of chocolate chips. Since she wants to bake 4 dozen cookies, she will need to have four ½ cups of chocolate chips.
½ cup + ½ cup + ½ cup + ½ cup = 1 cup + 1 cup = 2 cups
Upper Elementary:
Question: A rope is cut into 3 pieces. The first piece is 3 inches longer than the second piece and second piece is 5 inches shorter than the third piece. If the third piece is 15 inches long, how long is the first piece?
Answer: 13 inches
Solution: The third piece is 15 inches long and the second piece is 5 inches shorter than the third, so the second piece is 10 inches long (15 – 5 = 10). The first piece is 3 inches longer than the second piece so the first piece is 13 inches long (10 + 3 = 13).
Middle School:
Question: 5 more than the integer n is positive and 3 less than the same integer is negative. What are the possible values for n?
Answer: –4, –3, –2, –1 , 0, 1, 2
Solution: If 5 more than the integer n is positive, the lowest number increased by 5 that will be a positive integer is –4 (–4 + 5 = 1). The largest integer decreased by 3 that will be a negative integer is 2 (2 – 3 = –1). Because –4 is the lowest number and 2 is the largest number that work for possible values of n, all the integers in between work as well. So, the possible values of n are –4, –3, –2, –1, 0, 1, and 2.
Algebra and Up:
Question: A party company sells red, blue, and yellow balloons. Steve purchased a box of balloons in which ¼ of the balloons were red. If there are half as many blue balloons as red balloons and 25 balloons are yellow, how many balloons are in the box Steve purchased?
Answer: 40 balloons
Solution: ¼ of the balloons are red and â…› of the balloons are blue (half of ¼ = â…›). Combining ¼ and â…› shows that â…œ of the balloons are either red or blue which means that â… of the total balloons are yellow. Because there are 25 balloons we can solve for the total number of balloons by finding â… of what number equals 25. Letting x be the total number of balloons:
â…(x) = 25
x = 40
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