Lower Elementary:
Question: Sharks have more than one row of teeth in their mouths. One kind of shark has 5 rows of teeth, with 15 teeth in each row, on their bottom jaw line. How many teeth would 2 of these sharks have on their bottom jaw line in total?
Answer: 150 teeth
Solution: First, we will find the total number of teeth that one shark would have on its bottom jaw line. To do this, count 15, 5 times. 15, 30, 45, 60, 75. One shark has 75 teeth on the bottom jaw. To find how many teeth two shark have on their bottom jaw, double 75. 75 doubled is 150 (75 doubled = 70 doubled + 5 doubled = 140 + 10 = 150). 2 sharks have 150 teeth on their bottom jaw line in total.
Upper Elementary:
Question: Brenda is writing thank you cards to her friends. She plans on writing 10 cards. One pack of 5 thank you cards and envelopes cost $2.99. In order to mail the thank you cards, she needs to buy 10 stamps that cost 46¢ each. How much money does Brenda need to buy and send her thank you cards?
Answer: $10.58
Solution: One way to solve this is to find the total amount she spends on buying 10 cards and 10 stamps and then adding those totals together.
Cards and Envelopes:
A pack of 5 costs $2.99, so a pack of 10 costs $5.98. Since we are buying 2 packs, to find the total we can double the cost of one pack. 2.99 doubled = 3.00 doubled – 0.01 doubled = 6 – 0.02 = $5.98.
Stamps:
One stamp costs $0.46, so 10 stamps cost $4.60 ($0.46 × 10). Multiplying by 10 moves the decimal point one decimal place to the right.
Now add the two totals together: $5.98 + $4.60 = $10.58. Brenda needs $10.58 to buy and send thank you cards.
Middle School:
Question: Beth has $1,000 in her bank account. She has two options to accrue interest in the account. She can either choose an option that will compound annually at a rate of 3% or an option that will compound it semiannually at a rate of 2%. After one year, which option will give Beth more money and how much more money will she make?
Answer: Compound annually; $9.90 more
Solution: The formula for compounded interest is A = P(1 + (r/n))nt where:
A = ending amount
P = the beginning amount, also called the “principle”
r = the rate as a decimal
n = the number of times it is compounded per year
t = the time passed in years
Let’s find the value of A for each scenario.
Annually:
P = 1,000; r = 0.03; n = 1; t = 1
A = 1,000(1 + (0.03/1))1×1 = 1,000(1 + 0.03) = 1,000(1.03) = 1,030 = $1,030
Semiannually:
P = 1,000; r = 0.02; n = 2; t = 1
A = 1,000(1 + (0.02/2))2×1 = 1,000 (1 + 0.01)2 = 1,000(1.01)2 = 1,000(1.0201) = 1,020.1 = $1,020.10.
Compounding annually will give Beth more money. To see how much more, subtract the 2 amounts. $1,030 – $1,020.10 = $9.90.
Algebra and Up:
Question: Greg is flying a kite. He is 6 feet tall and is holding the kite string 4 feet above the ground. His brother Tom is 7 feet away from him and says that the kite is straight above his head. The kite string is 25 feet. How high off the ground is the kite?
Answer: 28 feet
Solution: Drawing a picture helps us see that the kite string and the two boys make a right triangle.
We have that the one of the legs is 7 feet and the hypotenuse is 25 feet. Let x be how high the kite is above Tom. Use the Pythagorean Theorem to find the length of the side.
72 + x2 = 252
49 + x2 = 625
x2 = 576
x = 24 feet
The kite is 24 feet above where Greg is holding it. Since Greg is holding the kite string 4 feet off the ground, the kite is 28 feet off the ground (24 + 4 = 28).
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