Worked example · Food and Nutrition · Year 10
LNF: Numeracy → Understanding the number system helps us to represent and compare relationships between numbers and quantities → Calculation
A secure Year 10 response, annotated so you can see which success criterion each part meets. It is also the answer key. It is practice only, not NEA work. Key figures: scale factor 7.5; healthier amounts lamb 3,000 g, leeks and carrots 2,700 g, swede 3,600 g, salt 22.5 g; added salt per portion 1.25 g before and 0.75 g after; total cost £41.40, £1.38 a portion, £3.60 under the £45 budget and £4.42 cheaper than the original.
(a) Scale factor = 30 ÷ 4 = 7.5.
| Ingredient | For 4 | For 30 |
|---|---|---|
| Neck of lamb | 500 g | 500 × 7.5 = 3,750 g |
| Leeks | 300 g | 300 × 7.5 = 2,250 g |
| Carrots | 300 g | 300 × 7.5 = 2,250 g |
| Swede | 400 g | 400 × 7.5 = 3,000 g |
| Potatoes | 500 g | 500 × 7.5 = 3,750 g |
| Onion | 150 g | 150 × 7.5 = 1,125 g |
| Water | 1,200 ml | 1,200 × 7.5 = 9,000 ml |
| Stock cubes | 2 | 2 × 7.5 = 15 |
| Salt | 5 g | 5 × 7.5 = 37.5 g |
| Parsley | 10 g | 10 × 7.5 = 75 g |
One scale factor is used for every ingredient, which keeps the recipe in proportion. A quick check: 4 × 7.5 = 30. Evidences criterion 1.
| Question | Working | Answer |
|---|---|---|
| Lamb in kg | 3,750 ÷ 1,000 | 3.75 kg |
| Water in litres | 9,000 ÷ 1,000 | 9 litres |
| Onions | 1,125 ÷ 150 = 7.5 | 8 onions |
| Carrots | 2,250 ÷ 100 = 22.5 | 23 carrots |
| Bags of potatoes | 3.75 kg ÷ 2.5 kg = 1.5 | 2 bags (1.25 kg spare) |
| Bunches of parsley | 75 ÷ 30 = 2.5 | 3 bunches |
| Packs of stock cubes | 15 ÷ 8 = 1.875 | 2 packs (1 cube spare) |
Every answer is rounded up, because rounding down would leave the class short of an ingredient. The pupil also notes what is left over. Evidences criteria 2 and 3.
| Ingredient | Change | Multiplier | For 30 | Healthier amount |
|---|---|---|---|---|
| Lamb | reduce by 20% | 0.8 | 3,750 g | 3,750 × 0.8 = 3,000 g |
| Leeks | increase by 20% | 1.2 | 2,250 g | 2,250 × 1.2 = 2,700 g |
| Carrots | increase by 20% | 1.2 | 2,250 g | 2,250 × 1.2 = 2,700 g |
| Swede | increase by 20% | 1.2 | 3,000 g | 3,000 × 1.2 = 3,600 g |
| Salt | reduce by 40% | 0.6 | 37.5 g | 37.5 × 0.6 = 22.5 g |
(b) Before: 37.5 ÷ 30 = 1.25 g per portion. After: 22.5 ÷ 30 = 0.75 g per portion.
Multipliers do the percentage change in one step. Check for the lamb: 20% of 3,750 is 750, and 3,750 − 750 = 3,000. Evidences criterion 4.
| Ingredient | Amount to buy | Working | Cost (£) |
|---|---|---|---|
| Lamb | 3 kg | 3 × 8.00 | 24.00 |
| Leeks | 2.7 kg | 2.7 × 1.50 | 4.05 |
| Carrots | 2.7 kg | 2.7 × 0.70 | 1.89 |
| Swede | 3.6 kg | 3.6 × 1.00 | 3.60 |
| Potatoes | 2 bags | 2 × 1.20 | 2.40 |
| Onions | 1.125 kg | 1.125 × 0.90 = 1.0125 | 1.01 |
| Stock cubes | 2 packs | 2 × 1.00 | 2.00 |
| Salt | 22.5 g | given | 0.05 |
| Parsley | 3 bunches | 3 × 0.80 | 2.40 |
| Total cost for 30 portions | 41.40 | ||
| Cost per portion | 41.40 ÷ 30 = 1.38 | ||
(b) Budget: 30 × £1.50 = £45.00. The healthier cawl costs £41.40, so it is inside the budget by 45.00 − 41.40 = £3.60 (12p a portion).
(c) 45.82 − 41.40 = £4.42 cheaper. Cutting the lamb saved the most: 750 g less at £8.00 per kg is 0.75 × 8.00 = £6.00. Meat is by far the most expensive ingredient per kilogram, so a small cut saves more than the extra vegetables cost (£0.67 + £0.31 + £0.60 = £1.58).
Grams are changed to kilograms before multiplying by a price per kg, and pack items are costed by the number of packs, not the amount used. The total is checked against both the budget and the original cost. The original lamb cost was 3.75 × 8.00 = £30.00, so the saving is 30.00 − 24.00 = £6.00. Evidences criterion 5.
(a) 225 ÷ 8 = 28.125 g per scone, and 28.125 × 20 = 562.5 g. (Or scale factor 20 ÷ 8 = 2.5, and 225 × 2.5 = 562.5 g.)
(b) 150 × 0.7 = 105 g.
(c) 900 ÷ 6 = 150 ml per person, and 150 × 4 = 600 ml.
(d) Cooking time depends on how long it takes the meat to become tender and the vegetables to soften, not on how many portions there are. Each chunk of lamb still needs about an hour of simmering, so the cawl will not need 12 hours and 30 minutes. What does change is that a much bigger pan of 9 litres takes longer to come to the boil, and it may need to be split between 2 or 3 pans.
Each quick question shows a method, and (d) explains why time does not scale in proportion (1 hour 40 minutes × 7.5 would be 12 hours 30 minutes). Evidences criteria 1 and 4.
45 people: scale factor 45 ÷ 30 = 1.5. Lamb 3,000 × 1.5 = 4,500 g; leeks 2,700 × 1.5 = 4,050 g; salt 22.5 × 1.5 = 33.75 g.
Leeks at 25p each: 2,700 ÷ 150 = 18 leeks, and 18 × £0.25 = £4.50, which is 45p more than buying by weight.
Salt: 0.75 ÷ 6 × 100 = 12.5% of the adult daily limit, from the added salt alone. The stock cubes add more.