**Lower Elementary:**

*Question: *It was 72° on Monday. The temperature rose 5° on Tuesday, then the temperature dropped 2° on Wednesday. What is the temperature on Wednesday?

*Answer: *75°

*Solution: *First, we need to find the temperature on Tuesday. Since the temperature rose 5° on Tuesday, the temperature was 77° (72 + 5 = 77). The temperature dropped 2° on Wednesday, so the temperature on Wednesday is 75° (77 – 2 = 75).

**Upper Elementary:**

*Question: *A farmer plants 10 orange trees. Each orange tree produces 10 oranges. The farmer sells each orange for $1.75. How much money will the farmer make selling all of the oranges?

*Answer: *$175

*Solution: *The farmer plants 10 orange trees and each tree produces 10 oranges. 10 × 10 = 100. The farmer has 100 oranges to sell. Each orange sells for $1.75. 100 × 1.75 = 175. The farmer earns $175 from selling all of the oranges.

**Middle School:**

*Question: *Fiona baked 120 cookies and is putting them in bags. She decides to put either 2 cookies in each bag, 3 cookies in each bag, 4 cookies in each bag, 5 cookies in each bag, 6 cookies in each bag, 8 cookies in each bag, 9 cookies in each bag, or 10 cookies in each bag. Which option will not have an equal number of cookies in each bag?

*Answer: *9 cookies in each bag

*Solution: *Of the numbers 2, 3, 4, 5, 6, 8, 9, and 10, which number does not evenly divide into 120? 120 is even so it is divisible by 2. 1 + 2 + 0 = 3, which is divisible by 3, so 120 is divisible by 3. Dividing by 4 is the same as cutting in half twice. Half of 120 is 60 and half of 60 is 30, so 120 is divisible by 4. 120 ends in a 0, so it is divisible by 5. 120 is divisible by 2 and 3, so it is divisible by 6. Dividing by 8 is the same as cutting in half three times. Half of 120 is 60, half of 60 is 30, and half of 30 is 15, so 120 is divisible by 8. And 120 ends in a 0, so it is divisible by 10. 120 is not divisible by 9 because 1 + 2 + 0 = 3 and 3 is not divisible by 9. So if Fiona puts 9 cookies in each bag, there will not be an equal number of cookies in each bag because the last bag will not have 9 cookies.

**Algebra and Up:**

*Question: *What is the 6th number in the sequence 27, 36, 48, …?

*Answer: *1,024/9

*Solution: *First we need to see how to get the next number in the sequence. We can find this by dividing the second term by the first term to find the rate, or the number we multiply by to get to the next number. 36/27 = 4/3. We make sure this is the rate by multiplying the second term by 4/3 and make sure we get the third term. 36 × 4/3 = 48. So we know this is a geometric sequence with a rate of 4/3 and the first term being 27. The formula to find the nth term of a geometric sequence is: a_{n} = a_{1} × r^{n – 1}

We want to find the 6th term, so n = 6. a_{1} = 27. And r = 4/3. So, we have:

a_{6} = 27 × (4/3)^{6 – 1}

Simplify the exponent.

a_{6} = 27 × (4/3)^{5}

Distribute the exponent.

a_{6} = 27 × (4^{5}/3^{5})

Notice that we can rewrite 27 as 3^{3}, so we can simplify the fraction.

a_{6} = 3^{3} × (4^{5}/3^{5})

Simplify the fraction.

a_{6} = 4^{5}/3^{2}

Compute.

a_{6} = 1,024/9

The 6th term in the sequence is 1,024/9.