Maths
Multi-step problem solver: revision-pack budget
For Years 9 to 13 Mathematics pupils, solve a revision-pack budget in stages, show a bar model and check the surplus with a second method.
Read the material
For Years 9 to 13 Mathematics pupils, solve a revision-pack budget in stages, show a bar model and check the surplus with a second method.
Pupil worksheet. Use the preview for diagrams and layout.
Page 1
Multi-step problem solver: revision-pack budget Pupil activity Audience: Years 9 to 13 Mathematics pupils Break a budget problem into unit costs, total cost, revenue and surplus, then check the result with a second method. Problem A club assembles 40 revision packs. Each pack uses 3 notebooks at £1.20 each and 2 pens at 65p each. The club sells 38 packs at £6.50 each. What is the surplus or shortfall before any other costs? 1. Plan and calculate Step My calculation My answer Cost of 3 notebooks £ Cost of 2 pens £ Cost of one pack £ Cost of 40 packs £ Income from 38 packs £ Income minus total cost £ Pupil activity Page 1 of 2
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Multi-step problem solver: revision-pack budget 2. Model the amounts Draw or label one bar for total income and one for the cost of all 40 packs. Mark the difference as a surplus or shortfall. Total income: ________ Total production cost: ________ Surplus / shortfall and amount: ________ 3. Check with a second method Margin on each sold pack: £6.50 − cost of one pack = £________ Margin from 38 sold packs: ______ × 38 = £________ Cost of the 2 unsold packs: ______ × £________ = £________ Second-method result: margin from sold packs − cost of unsold packs = £________ Pupil activity Page 2 of 2
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Multi-step problem solver: revision-pack budget Teacher key and guidance supporting this exact edition Teacher check Each pack costs 3 × £1.20 + 2 × £0.65 = £4.90. Total cost is 40 × £4.90 = £196. Income is 38 × £6.50 = £247. The direct method gives £247 − £196 = £51 surplus. Second method: (£6.50 − £4.90) × 38 − (£4.90 × 2) = £60.80 − £9.80 = £51. This counts the cost of the two unsold packs. Teacher companion Page 1 of 1
A teaching sequence
Break a budget problem into unit costs, total cost, revenue and surplus, then check the result with a second method.
Find the unit pack cost
Find the cost of one pack and show the multiplication for each item.
Have you converted 65p consistently into pounds?
Calculate production and sales
Calculate the cost of making 40 packs and the income from 38 sales.
Why are forty packs costed but only thirty-eight counted as sales?
Model surplus or shortfall
Use a bar model to compare income with total production cost.
Which bar is longer, and what does their difference represent?
Check the unsold-pack cost
Check by finding the margin on sold packs and subtracting the cost of the two unsold packs.
Does the second method subtract the cost of both unsold packs?
Before you teach
Look for the thinking behind an answer, choose the support your class needs and leave room for an independent response.
What to look for
One pack costs £4.90; 40 cost £196; sales bring in £247; surplus is £51 before other costs. The second method is £1.60 × 38 − £4.90 × 2 = £51. Ask, “Why must the unsold packs still count as a cost?”
Give a little support
Work in pence first: calculate the notebook cost and pen cost separately, then convert the total to pounds. Keep the two unsold packs visible in the model.
Take the idea further
Find the selling price per pack needed to break even if all 40 are sold.
Things to keep in mind
This fictional calculation excludes tax, staffing and other costs; it does not represent a real budget.
Keep the idea. Make it yours.
Bring your topic, learning goal and class context to PLAI™, then review what you create.
Another starting point
Explore a different teaching task from this selection.
Multi-step problem solver: event budget
Mark each figure as a ticket price, ticket quantity, fixed cost or per-attendee cost.
Explore resourceIdeas to try with your class
Sample teaching perspectives on what to try, what to adapt and what to watch for.
Meet The Creators
Meet a creator whose teaching interests connect with this template.
Book and Biscuit
This budget task asks for the cost of three £1.20 notebooks and two 65p pens per pack, the cost of 40 packs and income from 38 sold at £6.50. The second page checks the result by separating margin from unsold packs.
Kindly Red Pen
For Years 9 to 13, the two methods make the unsold two packs visible as a cost even though they produced no income. The task asks for surplus or shortfall before other costs, narrowing the conclusion.
Little Lightbulbs
Complete the unit cost for one pack before multiplying by 40, then compare total cost with income. The bar model provides a visual check on the difference between those amounts.
Margin Note
The scenario excludes costs beyond the listed materials and is not a full business budget. State the £ result as surplus or shortfall before other costs, as the prompt requires, and retain the unsold-pack calculation in the check.