Lower Elementary:
Question: One single-scoop ice cream cone costs $1.50. One double-scoop ice cream cone cost $2.50. How much do 2 single-scoop ice cream cones and 2 double-scoop ice cream cones cost in total.
Answer: $8
Solution: To find the cost of 2 single-scoop ice cream cones, double the cost of one single-scoop. $1.50 doubled is $3. To find the cost of 2 double-scoop ice cream cones, double the cost of one double-scoop ice cream cone. $2.50 doubled is $5. Add them together to get the total. $3 + $5 = $8.
Upper Elementary:
Question: Kyle needs some yarn for an art project. He has 2 feet of red yarn and 3 feet of green yarn. He needs 1 1/2 feet of red yarn and 1 3/4 feet of green yarn for the project. How much yarn will Kyle have left altogether?
Answer: 1 3/4 feet
Solution: Let’s find how much of each color yarn is left by subtracting the total amount with how much was used.
Red: 2 – 1 1/2 = 1/2 feet
Start by subtracting the whole numbers. 2 – 1 = 1 foot. Now subtract half. 1 take away a half is a half.
Green: 3 – 1 3/4 = 2 4/4 – 1 3/4 = 1 1/4 feet
Start by subtracting the whole numbers. 3 – 1 = 2 feet. Now take away the 3/4. If you make two wholes and take away 3/4, you are left with 1 1/4.
Now add the remaining amounts together. 1/2 + 1 1/4 = 2/4 + 1 1/4 = 1 3/4. Kyle will have 1 3/4 feet of yarn left over.
Middle School:
Question: The rhythm of music is measured in counts. Usually, a song is measured in 8-counts. This means that to the beat of the song, you count 1, 2, 3, 4, 5, 6, 7, 8 and that is one 8-count. The director of a dance team wants everyone to choreograph eight 8-counts of a song for an upcoming dance showcase. For Troy’s song choice, one 8-count is 3 seconds long. The song is 3 minutes and 20 seconds long. What percent of the song does Troy need to choreograph?
Answer: 12%
Solution: First, find how long eight 8-counts are. Each 8 count is 3 seconds, so eight 8-counts are 24 seconds (8 × 3 = 24). To find the percent, we need to find the total length of the song in seconds so that we are comparing things with the same name. 1 minute is 60 seconds, so 3 minutes is 180 seconds. Add the 20 additional seconds and we find that Troy’s song is 200 seconds. To find the percent, divide the length of the eight 8-counts by the total length of the song. Percent means for each hundred. So, we have 24/200 = 12/100. Troy needs to choreograph 12% of the song.
Algebra and Up:
Question: Find the sum of all the odd whole numbers from 1 to 99.
Answer: 2,500
Solution: Number sense:
Listing the numbers: 1 + 3 + 5 + 7 + 9 + 11 + … + 89 + 91 + 93 + 95 + 97 + 99
Notice: 1 + 99 = 100, 3 + 97 = 100, 5 + 95 = 100, 7 + 93 = 100, 9 + 91 = 100, 11 + 89 = 100, and so on.
Every number is paired with another number to equal 100. So we can multiply 100 times the number of pairs to get the total. There are 25 pairs that sum to 100, so 25 × 100 = 2,500.
Algebraic:
The formula for the sum of an arithmetic series is S = n/2 (a1 + an) where n is the number of terms in the series, a1 is the first term, and an is the last term. In this series, a1 = 1, an = 99, and n = 50. Plug these values into the formula to get the answer.
S = 50/2 (1 + 99)
S = 50/2 (100)
S = 25 (100)
S = 2,500
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