# Back to School Math Activity

### Answers and Explanations

NOTE: Questions 6, 9, and 10 are different for ZIP codes 85209 and 85212. Make sure to note the question and answer for the ZIP code you live in.

**AREA**

Bob and Sandy bought a home. The backyard already has a pool and a

small grass area, but the rest is dirt. The measurements for each are as

follows: Pool = 18’ x 35’ Small grass area = 12’ x 10’.

1. How many square feet is the pool? 18 x 35=**630 square feet**

2. How many square feet is the grass area? 12 x 10 = **120 square feet**

The pool and the grass area are in a 30’x80’ yard space.

3. How big is the total yard area? 30 x 80 = **2,400 square feet**

4. How much of the yard is covered by the pool and the grass? 630 + 120 = **750 square feet**

5. How much of the yard is uncovered and unlandscaped? 2400 – 750 = **1,650 square feet**

BONUS: If they want to put in landscaping rock 2” deep, how many

cubic feet of rock is needed for that space?

Cubic feet = width x length x height (or depth.) We have our area, which is width x height, so we need to multiple that times our depth/height of the rock. Before we do that, however, we need to convert inches to feet. We know there are 12 inches in a foot, so we’ll calculate 2 ÷ 12, which is .166667.

Thus, 1,650 x .16667 = **275 cubic feet of rock**

**PERCENTAGE INCREASE**

**85209:**Tony Stark just bought his house for $300,000. Houses in the 85209 zip

code are increasing in value at 11% annually.

6. If this stays true, how much will Tony’s house be worth in

a year?

First, divide the appreciation rate (the rate at which the value is growing annually) by 100 to convert it to a decimal, and then add 1. Thus, we begin with 1.11.

Next, multiply the home value by 1.11. $300,000 x 1.11 = **$333,000**.

**85212:**Tony Stark just bought his house for $300,000. Houses in the 85209 zip

code are increasing in value at 11% annually.

6. If this stays true, how much will Tony’s house be worth in

a year?

First, divide the appreciation rate (the rate at which the value is growing annually) by 100 to convert it to a decimal, and then add 1. Thus, we begin with 1.11.

Next, multiply the home value by 1.11. $300,000 x 1.11 = **$333,000**.

Vocabulary: Real Estate Professionals use the term **appreciation **when

describing an increase in home values. A good way to remember this is to

know that sellers **appreciate **the fact that their home value increased.

**INTEREST RATES**

Interest rates are at historic lows. Calculate how much interest would

need to be paid, assuming each borrower paid the $300,000 loan over a

period of 30 years.

A simple interest formula is: interest = principal x rate x years.

Vocabulary:**principal: **the sum of money that is lent or invested on which interest is paid.

rate: the proportion of a loan that is charged as interest to the borrower annually.

7. Elsa has an interest rate of 3% for 30 years for her $300,000

home. How much interest will Elsa have to pay over the 30 year

period, and how much will she pay back in total?

interest=principal x rate x years. Thus, $300,000 x .03 x 30 = Interest: **$270,000**

Total Paid Back is Principal + Interest: $300,000 + $270,000 = **$570,000**

8. Anna has an interest rate of 4% for 30 years for her $300,000

home. How much interest will Anna have to pay over the 30 year

period, and how much will she pay back in total?

interest=principal x rate x years. Thus, $300,000 x .04 x 30 = **$360,000**

Total Paid Back is Principal + Interest: $300,000 + $360,000 = **$660,000**

BONUS: How much did Elsa save with a lower interest rate than

Anna?

$360,000 – $270,000 = $90,000. **Elsa saves $90,000 with a lower interest rate.**

**AVERAGE (MEAN) AND MEDIAN – 85209**

Using the Augusta Ranch neighborhood on page 5, calculate the mean

(average) price and the median price for the neighborhood.

AUGUSTA RANCH

2024 S Baldwin St 102 | 1,132 Sqft | $212,000

9233 E Neville Ave 1066 | 1,064 Sqft | $230,000

9233 E Neville Ave 1158 | 1,550 Sqft | $250,000

9517 E Naranja Ave | 1,283 Sqft | $275,000

9506 E Kilarea Ave | 1,968 Sqft | $335,000

9708 E Navarro Ave | 2,478 Sqft | $449,900

9663 E Lobo Ave | 3,627 Sqft | $491,000

2140 S Drexel | 4,201 Sqft | $556,000

9. The average price in Augusta Ranch is **$349,862.50**.

The total of the above properties is $2,798,900. There are 8 properties in the list. $2,798,900 ÷ 8 = 349,862.50

10. The median price in Augusta Ranch is **$305,000**.

To calculate the median price, find the number halfway into the set. As there is an even number in the data set, the median is found by taking the average/mean of the two middle most numbers. $275,000+$335,000 = $610,000. $610,000 ÷ 2 = $305,000.

**AVERAGE (MEAN) AND MEDIAN (85212)**

Using the Eastmark neighborhood on page 5, calculate the mean

(average) price and the median price for the neighborhood.

EASTMARK RESALE

4827 S Tune | 1,629 Sqft | $313,000

9910 E Acceleration Dr | 1,564 Sqft | $335,000

4902 S Tune | 2,113 Sqft | $350,000

10716 E Palladium Dr | 2,237 Sqft | $395,000

10715 E Lincoln Ave | 2,740 Sqft | $420,000

10135 E Tripoli Ave | 2,334 Sqft | $462,500

10207 E Stealth Ave | 4,296 Sqft | $534,900

10315 E Starion Ave | 4,129 Sqft | $675,000

9. The average price in Eastmark is **$435,675.**

10. The total of the above properties is $3,485,400. There are 8 properties in the list. $3,485,400 ÷ 8 = 435,675

The median price in Eastmark is **$407,500**.

To calculate the median price, find the number halfway into the set. As there is an even number in the data set, the median is found by taking the average/mean of the two middle most numbers. $395,000+$420,000 = $815,000. $815,000 ÷ 2 = $407,500.

Vocabulary:**average:** the typical value in a set of data, calculated by dividing the sum of the

values in the set by the number of values.**median: **the middle value of a series arranged in order of magnitude. For example, the median number of the series 2, 4, 6, 8, 12, 25, 37 is 8.