Combining variables – Outside the maths classroomMastering Mathematics © Hodder and Stoughton 2014

Craft work

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Sarah works from home making bespoke high-quality gift boxes.

Customers tell Sarah the size of the box that they want and she then works out how much it will cost.

She needs to know the height, the width and the depth of the box.

She also needs to know how deep the lid is.

height

width depth

© Juri Samsonov – Fotolia.com

Combining variables – Outside the maths classroomMastering Mathematics © Hodder and Stoughton 2014

Sarah sketches a net for the box and uses this to work out the area of card that is needed.

She has used the labels h for the height, w for the width and d for the depth in cm.

Answer

1. Copy the net and mark each edge with h, w or d.

2. Write an expression for the area of each face of the box

Making gift boxes

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w

h

d

w

h

d

d

h

h

h

h

h

h

h

w hwhw

hd

hd

wd

w

h

d

Combining variables – Outside the maths classroomMastering Mathematics © Hodder and Stoughton 2014

Making gift boxes

A customer wants a box that is 15 cm high, 8 cm deep and 6 cm wide.

The total area is:

hd + wd + hd + hw + hw

= 2 hd + 2 hw + wd

= 2 ×15 × 8 + 2 ×15 × 6 + 6 × 8

= 240 +180 + 48

= 468 cm2

1. Write an expression for the total area.

2. Simplify your expression and use it to calculate the area of card needed for this box.

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w

h

d

d

h

h

h

h

h

h

h

w hwhw

hd

hd

wd

Make a formula to work out the total area of card in the lid.• What extra variable is needed?• How will your formula change if the

height of the lid is always 2 cm?• How will it change if the height of the lid

is always a quarter of the height of the box?

• Will the lid fit your box? How should the formula be changed to guarantee that the lid will always fit?

Combining variables – Outside the maths classroomMastering Mathematics © Hodder and Stoughton 2014

height

width depth

© Juri Samsonov – Fotolia.com

Making gift boxes

Sarah also needs to work out how much ribbon is required.

She uses the expression

4h + 2d + 2w + 30

Look at the picture of the box.

The ribbon runs along four heights, two depths and two widths.

The ribbon also has to be tied into a bow. This always takes 30 cm of ribbon whatever the size of the box.

1. Explain how Sarah has worked this out. Why is 30 added to the expression?

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Sarah needs a formula to calculate the total cost of the box.Use c to stand for the cost of 1 cm2 of card. Use r to stand for the cost of 1 cm of ribbon.

Use your formula to work out the cost of a box.

Set up a spreadsheet to work out the cost of any box.

Combining variables – Outside the maths classroomMastering Mathematics © Hodder and Stoughton 2014

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