MAth

W2Lesson.docx

Lesson 1.7

Problem Situation: Home Improvements

Bob and Carol Mazursky have purchased a home and they want to make some improvements to it. In the following problems, you will calculate the costs of those improvements. You will use scale drawing of the house and lot to assist you.

Review the drawing of the house and lot below.

#1 Points possible: 8. Total attempts: 5

Refer to the scale on the diagram.

The scale shows that each grid box is ft wide, and the area of each grid box is square feet.

#2 Points possible: 10. Total attempts: 5

Estimate and write the dimensions of the whole lot (all of their property)

Width: feet

Height: feet

#3 Points possible: 12. Total attempts: 5

Use the dimensions you determined to estimate the area and perimeter of their lot.

Area:

Perimeter:

#4 Points possible: 6. Total attempts: 5

Estimate the number of square feet in their house. (Assume it is a one-floor house.)

Area:

Reseeding the Lawn

The Mazurskys are expecting their first child in several months and want to get the backyard fertilized and reseeded before little Ted or Alice comes along. They found an ad for Gerry’s Green Team lawn service (see below).

Gerry's Green Team

Itemized Costs:	Grass seed	$3.50 per pound. 1 pound covers 250 sq. ft.
	Fertilizer	$1.25 per pound. 1 pound covers 350 sq. ft.
	Labor	4 hours @ $45 per hour

Gerry came to their house and said that the job would take about four hours and would cost about $600.

#5 Points possible: 28. Total attempts: 5

Using the area of the backyard, determine how much the job should cost, based on the advertised prices. Assume you have to buy full pounds of grass seed and fertilizer.

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.

Total cost: $

#6 Points possible: 5. Total attempts: 5

Is Gerry’s estimate of $600 consistent with the prices in his advertisement?

· Yes, the estimate is consistent

· No, the estimate is not consistent

Fencing the Yard

The Mazurskys want to build a chain link fence around the backyard (the fence is already shown in the diagram above). The fence would have two gates on either side of the house. They decide to do the work themselves. They need an inline post at least every 8 feet along the fence, a corner post at each corner, and a corner post on each side of the gates. The cost for the materials is shown below. The total cost will include 9.4% sales tax.

Chain-link fence	$7 per linear foot
48-inch wide gate	$75 each
Inline posts	$12.50 each
Corner/gate posts	$20 each

#7 Points possible: 36. Total attempts: 5

Calculate the cost of the materials required to fence in the backyard, after tax.

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.

Total cost: $

Building a Patio

There is a brick grill in the backyard. Bob and Carol are going to make a concrete patio in the shape of a semicircle next to the grill. (The patio is the shaded area marked in the figure below)

The patio’s concrete slab needs to be at least 2 inches thick. They will use 40-pound bags of premixed concrete. Each 40-pound bag makes 0.30 cubic feet of concrete and costs $6.50.

#8 Points possible: 20. Total attempts: 5

How much will the materials cost, including the 9.4% tax? Assume you can only buy whole bags of concrete.

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.

Total cost: $

Lesson 1.8

#1 Points possible: 5. Total attempts: 5

Which of the following are reasonable ways to estimate 2% of 150 people. There may be more than one reasonable method.

· 20% is 1/5. 1/5 of 150 is 30. 2% is one-tenth of 20%, so 3 people

· 1% of 150 is 1.5; two times that is 3 people

· 2% is 2 out of 10, so 2% of 150 would be 30 people

· 2% is 2 out of 100, so out of 150 that would be 3 people

· Multiply 2 by 150 to get 300 people

#2 Points possible: 5. Total attempts: 5

Which of the following are reasonable ways to estimate 15% of $29.95. There may be more than one reasonable method.

· 30% is 3 out of 10, so that would be 9 out of 30. 15% is half of that, so $4.5

· 15 times 30 is $450. Adjusting the decimal place gives $45

· 15 times 30 is $450

· 10% of 30 is 3. 5% is half of that, so 1.5. Together, 15% is $4.5

· 0.15 times 29.95 is $4.4925

#3 Points possible: 5. Total attempts: 5

Describe two quick ways to find approximately 33% of 59 books. Write out your methods, then compare to ours.

#4 Points possible: 5. Total attempts: 5

Estimate 25% of $98.50. Do not give the exact answer - use estimation.

#5 Points possible: 5. Total attempts: 5

Estimate 0.5% of $14.95. Do not give the exact answer - use estimation.

Convert the following fractions to percents, using estimation when appropriate.

#6 Points possible: 5. Total attempts: 5

5 out of 25 is about %

#7 Points possible: 5. Total attempts: 5

20 out of 80 is about %

#8 Points possible: 5. Total attempts: 5

3 out of 298 is about %

#9 Points possible: 5. Total attempts: 5

1 out of 1000 is about %

Estimations help you make calculations quickly in daily situations.

#10 Points possible: 6. Total attempts: 5

You are shopping for a coat and find one that is on sale. The coat’s regular price is $87.99. Which of the following are reasonable ways to estimate the sale price if coats are on sale for 25% off. There may be more than one reasonable method.

· The sale price after discount is 75% of the original price, or 3/4. Round 87.99 to 88. 1/4 of 88 is $22. 3 x $22 is $66.

· 25% is 1/4, so round $87.99 to $88. 1/4 of 88 is 22. Subtract 22 from 88 to get $66

· Round 87.99 to 90. 10% of $90 is $9. 25% is 2.5 times 10%, so 2.5 x $9 is about $22. Subtract 22 from 90 to get $68.

· 25% is half of 50%. Half of $88 is $44, and half again is $22. Subtract $22 from $88 to get $66

· 25% is 1/4, so round $87.99 to $88. 1/4 of 88 is 22

· 0.25 times 87.99 is $21.9975

#11 Points possible: 5. Total attempts: 5

You are shopping for a coat and find one that is on sale. The coat’s regular price is $87.99. Estimate the sale price if the coat is on sale for 70% off.

This next problem shows how estimates of percentages can be used to make comparisons among groups of different sizes.

#12 Points possible: 12. Total attempts: 5

A law enforcement officer reviews the following data from two precincts. She makes a quick estimate to answer the following question: “If a violent incident occurs, in which precinct is it more likely to involve a weapon?”

Precinct	Number of Violent Incidents	Number of Violent Incidents Involving a Weapon
1	25	5
2	122	18

Estimate the percent of violent incidents that involve a weapon in each precinct:

Precinct 1: %

Precinct 2: %

If a violent incident occurs, in which precinct is it more likely to involve a weapon?

· Precinct 1

· Precinct 2

· Not enough information

Exact Calculation

From Estimation to Exact Calculation

Being able to calculate with percentages is also very important. An estimate of the sale price will help you decide whether to buy the coat. However, the storeowner needs to make an exact calculation to know how much to charge. An estimate helps the officer get a sense of the situation, but if she is writing a report, she will want exact figures.

Calculate the exact answers for the situations in the remaining questions. You may use a calculator.

#13 Points possible: 10. Total attempts: 5

If the coat’s regular price is $87.99, what is the exact sale price based on each of the following discounts? (round to the nearest cent)

25% off. The sale price is $

70% off. The sale price is $

#14 Points possible: 10. Total attempts: 5

A law enforcement officer reviews the following data from two precincts. She makes a calculation to answer the following question: “If a violent incident occurs, in which precinct is it more likely to involve a weapon?”

Precinct	Number of Violent Incidents	Number of Violent Incidents Involving a Weapon
1	25	5
2	122	18

Calculate the percent of violent incidents that involve a weapon in each precinct. Round to 1 decimal place.

Precinct 1: %

Precinct 2: %