Paint by Numbers

House Painter Applications of Mathematics 9

Lesson Idea by: Cindy Botnen, Hollywood Middle School, Kelowna, B.C.

You may think that painting a house is just about picking the right colour -- but it involves way more than that. A house painter needs good people skills along with technical know-how. Plus, a painter has to use more math than you might expect!

Joe Wolfe owns his own house-painting business in Kelowna, British Columbia.

"I use math for pretty much everything," he says. "From wages, to determining how much paint I'll need, to figuring out paint/water ratios and pricing a job. Every aspect of painting requires some math."

Painters are contracted by clients to paint all kinds of buildings, both interiors and exteriors. They paint walls, ceilings, floors and cabinets using varnish, enamels, paint and other finishes.

Painters need more than a keen eye and a steady hand to be successful. They also have to be good at business. Often, getting a painting contract requires a painter to make a bid. A bid is an offer to do work or supply products at a certain price.

A client may ask three or four painters to bid on a job. Then, the client picks one, usually the cheapest. So, if a painter's bid is too high, a competitor will get the work. If the bid is too low, the painter won't make any money. Once a bid is accepted, the price cannot be changed. Due to these factors, a painter has to be careful in calculating the amount of work needed, and estimating a bid.

Get into groups of four and together prepare a bid to paint your classroom. You will need several paint store flyers, measuring tapes and calculators. Use the Student Worksheet below to guide your work.

Form a painting company, and give it a name. Measure the walls to calculate how many square feet you will have to paint. Discuss whether you will paint around the bulletin boards, or take them off. Do you need to subtract the space taken up by windows and doors? Is it necessary to get that fussy when preparing an estimate? Does the size of the job have anything to do with how precise your estimate should be?

How many gallons of paint will you need? (Note that one gallon of paint will cover 400-500 square feet of wall space.) What supplies will you need, and how much will they cost? Determine how many painters will be painting, for how many hours, and at what wage.

What is your estimate? Is it reasonable? That is, will the estimate be low enough so you'll get the job, but high enough to give you some profit?

Prepare the estimate and submit it to your teacher.

As a class, discuss the following:

• How important is it to prepare a precise estimate?
• Does the size of the job have anything to do with how precise an estimate should be?
• What happens if the estimate is too low? Too high?
• Why is area an important mathematical concept for house painters?
• Who else might need to understand area, and use it in their work?

Review what you know about area.

The formula for area is:
area = length x width

This calculation tells you the total area to be painted. Now you've got to calculate the amount of materials -- be it paint or wallpaper -- needed to cover that area. To calculate the amount of materials needed, divide the total area to be covered by the area the material will cover.

Usually, the packaging on the material will say how much area the product will cover. For example, a gallon of paint will cover 400 to 500 sq. ft.; while a single roll of wallpaper will cover about 25 sq. ft.

Paint and wallpaper are two of the more common wall coverings. Yet there are plenty of others. You may also need to calculate area for wallpaper borders, wainscoting, wooden panelling, and even fabric for cloth wall coverings. Clients may also want walls covered with big murals or collages made up of tiny little pictures.

Return to the Practice section for a moment. Your teacher is a little strange and wants one wall covered with one-hundred dollar bills.* Estimate how many one-hundred dollar bills you think you would need before you do any calculations.

Now, use math to make a more precise estimate. A one-hundred dollar bill measures 2.75 x 6 inches. How many would you need to cover the wall?

Does your guess match the estimate? Are you even close? Considering that the cost of supplies in this case is $100 dollars per bill, how important are good estimating skills?

Prepare a bid to renovate your own room or another room in your home. Consider painting the walls, changing the flooring, and picking new window coverings.

Get samples and prices from suppliers such as interior decorators or hardware shops. Often, suppliers are happy to give you discontinued sample books of fabrics, flooring, wallpaper. Pick your colours and fabrics to make a "colour board" displaying your choices. Be sure to show your measurements and estimate of the costs involved.

You've just been called to give an estimate for a paint job. It's a big house and the owner wants all of it painted. You must provide a written bid for the job. You know that the owner is getting bids from other painters in town. You want to get this job, so you have to prepare a really good bid.

The house has five rooms and a hallway. The kitchen is 25 feet by 20 feet. There are three bedrooms. Bedroom A is 30 ft. by 27 ft. Bedroom B is 15 ft. by 15 ft. and bedroom C is 12 ft. by 10 ft. The living area is a colossal 30 ft. by 35 ft. The hall is 20 ft. by 4 ft.

In this case, you estimate that one gallon of paint will cover only 100 square feet because of the kind of paint it is and because of the high ceilings. Paint costs $18 per gallon plus seven per cent tax.

Because it is such a big job, you may need help. An assistant will cost $7 per hour and you estimate that you'll need two assistants for about 80 hours each. You figure that you'll be working on the house for 100 hours -- and generally you make $10 per hour. Your usual price is $1.25 per square foot. You estimate that supplies will cost $200.

Write up your first estimate using $1.25 per square foot. How much money will you make? Will it cover everything? Can you afford to reduce your price per square foot? What is your break-even price per square foot?

*Thanks to Dave Sufrin, of Parksville, B.C. for his suggestion about using $100-bills in this exercise.

Course/Grade: Applications of Mathematics 9
Curriculum Organizer: Problem Solving, Number operations 1	Curriculum Sub-organizer(s): analyse problems and identify the significant factors, demonstrate group skills, solve real-life problems with formulae
Prerequisites: none	Resources: · calculator · measuring tape · flyers from paint stores

 

Student Worksheet: Estimates For Practice Section Name of Paint Company: _____________________________________________________________ Partners: _____________________________________________________________ Items to be considered: _____________________________________________________________ Area of walls to be painted: _____________________________________________________________ Number of gallons of paint required: _____________________________________________________________ Cost of paint: _____________________________________________________________ Estimated cost of painting supplies (rollers, brushes, pans, drop cloth, clean-up): _____________________________________________________________ Number of painters on the job: _____________________________________________________________ Number of hours to complete job: _____________________________________________________________ Hourly wage/painter: _____________________________________________________________ Total wages for painters: _____________________________________________________________ Profit that goes into the company (include possible overruns): _____________________________________________________________ Wages + paint + supplies + profit: _____________________________________________________________ FINAL BID FOR THE JOB: _____________________________________________________________

 

Solution to Learn First of all you need to calculate the total area. Remember, the formula is: area equals length times width. (Please note: This symbol, ^, called a caret, is used to indicate "to the power of.") Kitchen 25 ft. by 20 ft. Total area is 25 ft. x 20 ft. Area = 500 ft.^2 Bedroom A 30 ft. by 27 ft. Total area is 30 ft. x 27 ft. Area = 810 ft. ^2 Bedroom B 15 ft. by 15 ft. Total area is 15 ft. x 15 ft. Area = 225 ft. ^2 Bedroom C 10 ft. by 12 ft. Total area is 10 ft. x 12 ft. Area = 120 ft.^2 Living Room 30 ft. by 35 ft. Total area is 30 ft. x 35 ft. Area = 1050 ft.^2 Hallway 20 ft. by 4 ft. Total area is 20 ft. x 4 ft. Area = 80 ft. ^2 Total area of house = area of kitchen + bedroom A + bedroom B + bedroom C + living room + hallway Total Area = 500+810+225+120+1050+80 ft. ^2 Total Area = 2,785 ft. ^2 First estimate at $1.25 per square foot = 2785 ft.^2 x 1.25 ft.^2 = $ 3,481.25 Costs: Paint 1 gallon will cover 100 ft.^2 x gallons will cover 2785 ft.^2 1   =   x 100       2785 2785 = 100 x x = 27.85 It will take 27.85 gallons of paint to paint the house. Round up to the nearest full gallon to get 28. Paint costs $18 per gallon plus seven per cent tax Cost = (28 x $18) x 1.07 Cost = ($504) x 1.07 Cost = $ 539.28 Wages A) Assistants Two assistants @ $7.00 per hour for 80 hours Wages = 2 x $7.00 x80 Wages = $1,120.00 B) Your wages = $10.00 per hour x 100 hours Wages = $1,000.00 Total Wages = $560.00 + $1,000.00 Total Wages = $2,120.00 Supplies = $200.00 Total costs = paint + wages + supplies Totals Costs = $ 539.28 + $2120.00 +$200.00 Total Costs = $ 2,859.28 Your profit on the bid is based on $1.25 per square foot. Estimate based on per square foot price minus costs. $3,481.25 - $2,859.28 = $621.97 The minimum amount that you could charge per square foot would be: Minimum per square foot = Total Cost   Area of House Minimum per square foot = $2859.28   2785 ft. ^2 Minimum per square foot = $1.03   ft. ^2 "Unless there's an extreme circumstance, I would never bid at cost," says house painter Joe Wolfe. It's too risky. There's no cushion for overruns in paint, supplies or labor. The lowest he's ever priced a bid was for $1.05 per square foot.