Succeed with maths – Part 1

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# 7.1 Insulating the attic

Step 1: Describe the problem

My father has recently moved into an old terrace house that needs insulation in the attic. I have volunteered to take care of this task. Although I think it’s going to cost less to put in the insulation myself, my dad can get a grant from local government if the insulation is installed by an approved contractor. But which is the cheaper option?

Step 2: Collect information, make assumptions and simplify the problem

Now I need to write down what I know and what I still need to find out. After measuring the attic space and joists, visiting a DIY shop, contacting the local government department about the grant and local contractors for quotes, I wrote down the following lists:

## Table 2

I know:I want:
The attic is approximately 825 cm by 900 cm.To find the cheaper option
Each joist is 5 cm wide.
There are 17 joists.
The insulation fits perfectly between the joists.
A £200 grant is available.
The cheapest quote from a contractor is £650
The insulation comes in rolls that are 40 cm wide and 800 cm long.
Each roll costs £15 but there is a special 3 for 2 offer at the moment.
I need safety glasses, a face mask and gloves costing £40 to install the insulation.

Step 3: Do the maths!

This is a complicated problem, so a useful strategy would be to break it down into more manageable chunks. There are two separate problems

• How much would my father have to pay if he got the £200 grant and used the contractor?
• How much would the ‘do-it-yourself’ option cost? Broken down into:
• How much insulation will I need?
• How much will the materials cost?

Let’s focus on the first question.

## Activity 8 The contractor’s costs

Timing: Allow approximately 3 minutes

Work out how much will it cost if the contractor installs the insulation and the grant is used?

The contractor charges £650 and the grant is £200

So, overall cost = £650 − £200 = £450.

So the total cost using an approved contractor is £450.

Now for the ‘do-it-yourself’ option, starting with how much insulation is required.

How much insulation?

This means working out how many rolls are needed. In this case a diagram will probably help.

Here’s a rough plan of the attic:

Figure 9 Plan of joists in an attic

Note: the attic door is in the floor and will be covered by insulation. The insulation will later be cut to allow the door to open.

As the insulation fits perfectly between the joists, as well as the frame and outer joists, the amount of insulation needed will be easy to calculate.

One roll of insulation is 800 cm long.

The length of the attic minus the frame at each end is 900 cm − 10 cm − 10 cm = 880 cm.

So one roll between the joists is not quite enough to do the job because there is an extra 880 cm − 800 cm = 80 cm that need to be covered between any two joists.

## Activity 9 How many rolls do I need to buy?

Timing: Allow approximately 10 minutes

Use the information given above to work out how many rolls of insulation are needed.

First, you can see I will need 18 rolls to lie between the joists and between the frame and outer joists.

However, you know that each roll leaves an extra 80 cm not covered. This happens 18 times, so I am short 18 × 80 cm = 1440 cm. Since one roll is 800 cm, I will need to buy two more rolls of insulation (1440 cm ÷ 800 cm = 1.8). Therefore, I need a total of 20 rolls of insulation.