Lower Elementary:
Question: A bell tower rings every hour. It rings once at 1 o’clock, twice at 2 o’clock, three times at 3 o’clock, and so on. How many total times will the bell tower ring from 1 o’clock to 10 o’clock?
Answer: 55
Solution: The bell rings once at 1 o’clock, twice at 2 o’clock, three times at 3 o’clock, and continues. So, the number of bell rings between 1 o’clock and 2 o’clock will be 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10. One way to add these is to find pairs of numbers that add to 10. 1 + 9 = 10, 2 + 8 = 10, 3 + 7, 4 + 6 = 10. Now the addition becomes 10 + 10 + 10 + 10 + 5 + 10 = 55. The bell will ring 55 times between 1 o’clock and 10 o’clock.
Upper Elementary:
Question: 2 cups of rice can feed 3 people. 1 cup of rice costs 75¢. How much would it cost to feed 6 people?
Answer: $3
Solution: One way to solve this problem is to see how many total cups of rice are needed first, and then find the cost. 2 cups of rice can feed 3 people and we want to know how many cups of rice are needed to feed 6 people. 6 is twice as many as 3, so to find how many cups of rice are needed, we need to find out what is twice as many as 2. 4 is twice as many as 2, so we need a total of 4 cups of rice to feed 6 people. To find the cost of 4 cups of rice, we count by 75 four times. 75, 150, 225, 300. It will cost 300¢, or $3, to buy 4 cups of rice.
Middle School:
Question: A computer program takes the user’s numeric input and plugs it into the following formula: 3(n + 5)4/(n2 + 5) + 6n where n is the number the user input. If the user inputs 5, what value with the formula produce?
Answer: 1,030
Solution: The user plugs in the number 5, so we substitute 5 wherever we see an n.
3(5 + 5)4/(52 + 5) + 6(5)
We need to follow the order of operations, or PEMDAS. First, we do the parenthesis.
3(10)4/(52 + 5) + 6(5)
Next, we do the exponents.
3(10,000)/(25 + 5) + 6(5)
3(10,000)/(30) + 6(5)
Next, we do multiplication and division.
30,000/30 + 30
1,000 + 30
Finally, we do the addition.
1,030.
The program will give the numeric value 1,030.
Algebra and Up:
Question: A 100 ounce watermelon is 99% water and 1% melon. If the watermelon is dehydrated to 98% water, how much will the watermelon weigh?
Answer: 50 ounces
Solution: The watermelon started off as 99% water and 1% melon. That means that the watermelon was 99 ounces water and 1 ounce melon. The watermelon is dehydrated to 98% water. This means that the dehydrated watermelon is 2% melon. We know that originally the watermelon was 1 ounce, and that amount has not changed, therefore the dehydrated watermelon is 2% melon and that is 1 ounce. We need to find 2% of what number is 1 in order to find the weight of the dehydrated watermelon. 2% of 50 is 1, so the dehydrated watermelon is 50 ounces. Alternatively, 2% is melon and that is 1 ounce. To get from 2% to 100%, multiply by 50. So, multiply the weight by 50 to get the weight of the whole dehydrated watermelon. 1 × 50 = 50. The dehydrated watermelon weighs 50 ounces.
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