© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Goldfish bowl:

rearrange formulae

Goldfish need oxygen in their water.

The amount of dissolved oxygen depends on the surface area of the water.

Each fish needs 24 square inches of water surface.

What is the minimum radius of a bowl for 5 fish?

The surface is a circle with area A = r 2

But in this case it is r that is needed.

Goldfish bowl: rearrange formulae

A = r 2Area of a circle r cm

Think about…How to make the subject r

A = r 2

A = r

Ar =

This allows the radius to be found for any area.

Back to the goldfish!

Each fish needs 24 square inches. 5 fish need 5 24 = 120 square inches

Ar =

120r =

r = 6.2 inches

Goldfish bowl: rearrange formulae

Think about…How to work this out on a calculator

y = mx + cEquation of a line

y – mx = c

y – c = mx

c = y – mx

y = mx + c

y – c x = m

y – c x m =

Think about …How to make the subject c

Think about …How to make the subject m

c gradient m

0

y

x

Goldfish bowl: rearrange formulae

A =h (a + b)

2

Area of a trapezium

h

b

a

2A = h (a + b)

= h2A

a + b

h = 2Aa + b

2A = h (a + b)

= a + b2Ah

= a 2Ah

– b

2Ah

a = – b

Think about …How to make the subject h

Think about…How to make the subject a

Resistance in an electrical circuit

R =PQ

P + Q = PQR (P + Q)

= PQRP + RQ

= PQ – RP RQ

= P(Q – R) RQ

= PRQQ – R

P = RQQ – R

Q

P

Total resistance R

Think about …How to make the subject P

At the end of the activity

When rearranging a formula, how do you decide which term to move first?

What do you do if the subject is in the denominator of a fraction?What do you do if the subject appears twice?

Goldfish bowl: Rearrange formulae

The area of the water surface in the goldfish bowl is given by A = πr2. Re-write this formula to make the subject r.