1. There were originally 6 cakes and 4 biscuits, giving the ratio 6:4. This was shown to be the same as a ratio of 3:2. Pupils could suggest other equivalents, and revise the method of simplifying ratios. What if Katie had 30 cakes? 12 biscuits? And so on.

2. Ben took one cake, making the ratio 5:4. What if he had taken a biscuit instead? What if Katie had taken one of Ben’s goodies?

3. The recipe given serves 4:

4 ounces chick peas
5 fluid ounces tahini paste
4 tablespoons olive oil
2 cloves garlic

We saw how to increase this to serve 8, 12 and 30 people. Students could compare the intuitive method for 8 and 12 with the unitary method used to calculate amounts for 30 people.

4. The dip takes 37.5 fluid ounces of tahini. Students could discuss the variety of different units used in the above recipe, and other commonly used measures in cookery. What kind of measuring equipment are they familiar with, and what units are used for different types of ingredient? Scales, measuring jugs, standard spoons and cup sizes could be investigated, for example. Conversion between imperial and metric measures can also be discussed.

5. Neil’s recipe (unusually) uses grams for all the ingredients, including liquids. This is because in the factory the ingredients are all measured out by weight, in the tubs shown. Students could consider why it is convenient to do it in this way and why the similar containers were used for all the ingredients.

6. The recipe makes 3 jars:

150g single cream
150g coconut milk
135g creamed coconut
120g curry paste

7. 180kg of creamed coconut are required to produce 4,000 jars. Students could look in detail at the calculation performed here. Further examples could be generated for different numbers of jars. Recipes in books could be scaled up to ‘factory proportions’. Students might like to reflect on how smaller quantities like ‘a pinch of salt’ could be translated for use in large-scale production.

8. £35,250,370 was raised in 1999. The programme shows how this could be shared between the UK and Africa in the ratio 1:2. Ben rounded the results to the nearest pound — students could consider how to deal with decimals in this kind of calculation.

9. The ratio is 5:2:4. Ben correctly recognised that women should receive 5 out of a total of 11 parts. Katie’s answer was clearly wrong, as she calculated that women would receive more than the original amount given. Methods of checking solutions against the original conditions could be discussed here.

10. The slogan was: ‘Are You Reddy’.

Worksheet 2: Tick or Trash

Question 1

Student A is correct. Student B has failed to understand that the total number of parts is 9 and incorrectly interprets the meaning of the ratio 5:4. Checking, by addition of the amounts worked out, could have highlighted the error.

Question 2

Student B is correct. Student A has incorrectly converted 1kg to 100g. The method, however, is correct, and can be contrasted with that of Student B. Both students have correctly avoided rounding too early in the calculation: a common mistake.

Worksheet 3: Exam Practise Questions (Edexcel)

This is a selection of past exam questions from Edexcel, targeted at the middle ability range. You can use the sequence as it stands or select individual questions to suit your needs.

Given below is the mark scheme for each question, which will help you to see how marks are allocated and what the examiner is especially looking out for. The mark schemes use the following abbreviations:
oe
or equivalent
cao
correct answer only
ft
follow-through marks
dep
dependent
indep
independent
M
method marks
A
accuracy marks
B
benefit-of-doubt mark
SC
special case

Question 1

(a) 6 + 3 + 1 = 10

128 ÷ ’10’ = 12.8

6 x 12.8 = 76.8 = £76.80

(b) (‘76.8’ ÷ 3) x 2 = £51.20

Question 2

(a) £9.40

(b) 120 x 5 ÷ 8 = 75

120 ÷ 8, x 5 = 75

(45 ÷ 120) x 100 = 37¹/₂%

Notes:

(a) M1 8 x 1.175 (oe)

(b) M1 for ÷8. M1 for x5 (dep). A1 cao.

Question 3

1 man takes 6 x 8 = 48 days

4 men take 48 ÷ 4 = 12 days

Question 4

1 costs 3.48 ÷ 12

20 costs 3.48 ÷ 12 x 20 = £5.80

Question 5

35 ÷ (3 + 4) (= 5)

3 x 5 = 15 OR ³/₇ x 35 = 15

Question 6

(a) Method is implied. Answers 9, 3, 1¹/₂, 225, 15

(b) 150g ÷ 450 x 16. Answer = 5

Notes:

(a) B3 for 5 correct. B2 for 3 correct. B1 for 1 correct.

(b) Alternatives:

150 ÷ 450 (M1) and x 16 (M1)
16 x 450 (M1) and÷/ 50 (M1)
16 ÷ 450 (M1) and x 150 (M1)
450 ÷ 16 (M1 only) then 150 ÷ ‘ans’ (M1)

M2 for 450 ÷ 150 (=3), 16 ÷ 3. A1 5(.33...) (to the nearest ounce is advisory).