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Nuffield Free-Standing Mathematics Activity Goldfish bowl: rearrange formulae

Nuffield Free-Standing Mathematics Activity Goldfish bowl: rearrange formulae. 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.

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Nuffield Free-Standing Mathematics Activity Goldfish bowl: rearrange formulae

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  1. Nuffield Free-Standing Mathematics Activity Goldfish bowl: rearrange formulae

  2. 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 = pr 2 But in this case it is r that is needed.

  3. r cm A = r2 p A = r p A p A = p r2 Area of a circle Think about…How to make the subject r r= This allows the radius to be found for any area.

  4. 120 A r= r= p p Goldfish bowl: rearrange formulae Back to the goldfish! Each fish needs 24 square inches. 5 fish need 5  24 = 120 square inches Think about…How to work this out on a calculator r = 6.2 inches

  5. y = mx + c Equation of a line y – c = m x y – c m = x Goldfish bowl: rearrange formulae y c gradient m y – mx = c Think about …How to make the subject c x 0 c = y – mx y = mx + c y – c = mx Think about …How to make the subject m

  6. a h b h (a + b) 2A = 2A = h (a + b) h (a + b) A = 2 2A 2A a + b a + b 2A 2A 2A = h = a + b h h h – b = a h = – b a = Area of a trapezium Think about…How to make the subject a Think about …How to make the subject h

  7. PQ P R = P + Q Q = PQ RP + RQ = PQ R (P + Q) RQ = PQ – RP RQ = P(Q – R) RQ = P Q – R RQ P = Q – R Resistance in an electrical circuit Think about …How to make the subject P Total resistanceR

  8. Goldfish bowl: Rearrange formulae • At the end of the activity The area of the water surface in the goldfish bowl is given by A = πr2. Re-write this formula to make the subject r. 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?

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