Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

6 Home improvement project

This section looks at a real-world problem that uses measurement. The following instructions were given on a DIY store’s website for calculating how many rolls of wallpaper are needed to decorate a room:

  • Step 1: A standard roll of wallpaper is approximately 33 ft long and 1 ft 9 in wide. If you measure the height of the walls from the skirting board to the ceiling, you can determine how many strips of paper you can cut from a standard roll – four strips are about average.
  • Step 2: Measure around the room (ignoring doors and windows) to work out how many roll widths you need to cover the walls. Divide this figure by the number of strips you can cut from one roll to calculate how many rolls you need to buy. Make a small allowance for waste.

Now try this next activity.

Activity _unit2.6.1 Activity 4 Following the instructions

Timing: Allow approximately 5 minutes

Read through the directions above. Write down the important information you need to know to work out the number of rolls of wallpaper required. Remember, you can click on ‘reveal comment’ for additional help.

Discussion

Try drawing a sketch, and think through the steps you would take to apply new wallpaper in your kitchen.

Answer

This is how Rebecca, a student, tackled the problem. Her notes are given below.

There are three calculations:

  • working out how many strips of paper you can cut from a standard roll
  • working out how many roll widths there are round the room
  • calculating how many rolls are needed.

A roll of wallpaper measures 33 feet in length and 1 ft 9 in, in width.

You may have a slightly different answer here, but as long as the main points convey the same ideas then that is fine!

Now use your notes from this activity to complete this next one.

Activity _unit2.6.2 Activity 5 How many rolls?

Timing: Allow approximately 10 minutes

The room that you want to wallpaper measures 3.2 m by 4 m and the height of the walls is 2.34 m. Work out how many rolls of wallpaper you will need.

Click on ‘reveal comment’ if you would like a quick hint.

Discussion

As well as using your notes, drawing a diagram of the room from above and one wall, may help you to visualise what you need to do.

Answer

The first thing you need to do is to make all the units the same. The room has been measured in metric and the wallpaper is imperial. It doesn’t matter if you changed from imperial to metric or metric to imperial!

Measurements for wallpaper in metric units:

multiline equation line 1 Length of roll equals 33 feet line 2 equation left hand side equals right hand side open 33 multiplication 12 close inches line 3 equals 396 inches

one inch equals 2.54 cm

multiline equation line 1 Length of roll in cm equation left hand side equals right hand side open 396 multiplication 2.54 close cm line 2 equals 1005.84 cm

one m equals 100 cm

multiline equation line 1 Length of roll in m equation left hand side equals right hand side open 1005.84 division 100 close m line 2 equals 10.06 m left parenthesis to two decimal places right parenthesis

For these purposes this can be called 10 m. As the assumption is that each roll is slightly shorter rather than longer, buying too few rolls would not therefore cause a problem.

multiline equation line 1 Width of wallpaper equals one ft nine in line 2 equals 12 inches prefix plus of nine inches line 3 equals 21 inches

multiline equation line 1 Width of wallpaper in cm equation left hand side equals right hand side open 21 multiplication 2.54 close cm line 2 equals 53.34 cm

one m equals 100 cm

multiline equation line 1 Width of wallpaper in m equation left hand side equals right hand side open 53.34 division 100 close m line 2 equals 0.53 m left parenthesis to two decimal places right parenthesis

Number of strips from one roll?

The first calculation is to work out how many lots of the height (2.34 m) you can get from a roll of wallpaper 10 m long.

multiline equation line 1 Number of strips of wallpaper equals 10 m prefix division of 2.34 m line 2 equals 4.27 strips

As 0.27 of a strip is not very useful, so it is best to say that you can get 4 strips from each roll.

How many strips are required to cover the room?

multiline equation line 1 The total length around the room equals 3.2 m plus 3.2 m plus four m plus four m line 2 equals 14.4 m

It is helpful to draw a quick sketch to show what the walls would look like if they were flattened out into one big wall:

Figure _unit2.6.1 Figure 4 A rough sketch representing how the walls would look as one big wall

Here again you could either calculate this using centimetres or metres.

multiline equation line 1 Number of strips required equals 14.4 m prefix division of 0.53 m line 2 equals 27.1 m

To make sure there is enough paper, this has to be rounded-up, giving 28 strips altogether.

How many rolls of wallpaper?

These calculations show:

  1. That 28 strips of wallpaper are needed
  2. Each roll will give 4 strips.

So, the

multiline equation line 1 number of rolls needed equation left hand side equals right hand side 28 division four line 2 equals seven

This should be plenty, as doors and windows have not been taken into account.

Well done for completing this activity. It had lots of steps to get to the answer and some unit conversions as well. It was therefore much more involved than any other activity this week and required you to make use of your problem-solving skills as well as your measurement knowledge.

That completes the study for this week, except for this week’s quiz.

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