Mathematics K–6 · Years 5–6

Planning a class event to a set budget from advertised prices, then checking the spend

Number and algebra

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

A plan is built by turning a number of people into a number of packs, packs into a cost and a cost into a decision against a fixed budget, and the model is only finished when the real docket is set beside the plan and the difference is accounted for.

Safety card

Low riskAn adult supervises

Hazards

an allergy or a dietary requirement among the group
a docket or a catalogue can carry a family name, card digits or a loyalty number
handling money and food on the day of the event
travel to a shop where the class visits one

Controls

check the brief's dietary requirement against the label of every item before it is bought, and keep the labels for the class to read
cover any name, card digits or loyalty number before a docket is used in class
an adult holds the money and makes the purchase; the class works from the docket afterwards
record prices from a catalogue or a website rather than visiting a shop where a trip is not possible
hands washed and food served on clean plates on the day

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; food handling, allergy management and any excursion follow the school's usual risk management procedures.

What you need

a written brief from the teacher giving the number of people, the fixed budget in dollars and cents, and any dietary requirement the class must meet
two current printed supermarket catalogues, or two price lists printed from supermarket websites, each page showing the shop name and the dates the prices apply
a planning table with columns: item, pack size, pack price, price source and date, number needed, packs needed, cost, left over
a calculator per group, and a spreadsheet where one is available
measuring jugs and a set of cups, to measure one serve of a drink in millilitres before the quantity rule is written
the real docket from the purchase, or a photograph of it, with any name and card digits covered

How to do it

Read the brief aloud and write, for each item, the quantity rule as a full sentence: how much of that item one person gets. Check any drink serve by pouring it into a cup and reading the jug, so the rule is in millilitres rather than in cups.
Record for every item its pack size, its pack price, the shop and the dates printed on the catalogue. A price without its source and date does not go into the table.
Work out the number needed as the number of people times the quantity rule; then the packs needed by dividing by the pack size and rounding up to the next whole pack; then the cost as packs times pack price; then how much is left over.
Write a rounded estimate of the plan total, every cost to the nearest dollar, and a second estimate with every cost rounded up. Say from the two estimates alone which side of the budget the plan falls on, and only then add the costs exactly.
Compare the exact total with the budget. If the plan is over, change one quantity rule or one item, record what changed and why, and recompute. If it is under, work out the cost a person to the nearest cent and the share of the budget the plan spends, as a percentage.
Compare the two catalogues for one item where pack sizes differ, using the price for a single item or for 100 mL, and record which pack is the cheaper way to cover the number needed rather than the cheaper pack.
After the purchase, enter the price paid at the till for each item in a second column beside the planned price, taken from the docket.
Work out the difference between the docket total and the plan total, in dollars and as a percentage of the plan, and write one sentence for every line that differs by more than 50 cents, naming the reason, for example a catalogue price that had ended or a pack size that was out of stock.
Write the decision the class would make next time in two sentences, quoting the numbers that support it.

What you should see

Worked on the example brief of 28 people and a $60.00 budget, with the quantity rules of one cup, two biscuits, one popcorn bag, 200 mL of juice and one napkin a person plus one watermelon for the group, and the example price set of paper cups in packs of 20 at $2.50, plain biscuits in packs of 32 at $2.20, single-serve popcorn in packs of 6 at $3.00, orange juice in 2 L bottles at $3.40, one watermelon at $6.00 and paper napkins in packs of 100 at $1.80, entered by the teacher as an example and not offered as any shop's prices: 28 cups needs 2 packs at $5.00 with 12 left over; 56 biscuits needs 2 packs at $4.40 with 8 left over; 28 popcorn bags needs 5 packs at $15.00 with 2 left over; 5,600 mL of juice needs 3 bottles at $10.20 with 400 mL left over; the watermelon is $6.00; the napkins are 1 pack at $1.80 with 72 left over. The plan totals $42.40, which is $17.60 under the budget, 70.67 per cent of it, and $1.51 a person to the nearest cent. The nearest-dollar estimate of the plan is $42 and the estimate with every cost rounded up is $44, so both say the plan clears a $60 budget before any exact addition is done, which is the point of writing them first. Where the docket then reads $44.85, the difference is $2.45, which is 5.78 per cent of the plan, and the lines that moved are found by reading the docket against the planned column rather than by recomputing the plan. The learner knows the model is sound when every packs-needed figure is the smallest whole number of packs that covers the number needed, when no cost is worked out from a fraction of a pack, and when each left-over amount can be named as either waste or a deliberate spare.

What changes

What you change: the quantity rule for one item, for example two biscuits a person rather than three, or the pack size chosen for that item
What you measure: the packs needed and the cost of that item, the plan total, and whether the plan clears the budget
What you keep the same: the number of people in the brief
the budget in the brief
pack sizes and pack prices taken from the same catalogue on the same date
packs needed always rounded up to the next whole pack
the dietary requirement in the brief met by every version of the plan

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

2.8 bottles can be bought, so the cost of the juice is 2.8 times the bottle price.
The pack with the lowest price is always the cheapest way to cover the number needed.
A plan that comes in under budget needs no comparison with the docket.
A catalogue price holds until the shopping is done, so the date it was read does not matter.
The left-over part of the last pack is a mistake in the plan rather than a quantity to decide about.
The cost a person is found by dividing the budget by the number of people rather than the plan total.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards Authority, Stage 3 focus area Additive relations AMA3-AR-01
Mathematics K-10 Syllabus (2022), NSW Education Standards Authority, Stage 3 focus area Multiplicative relations AMA3-MR-01
Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMAO-WM-01
Australian Curriculum v9AC9M6N09AC9M5N09AC9M6N08

Sources

The pages the author read to write this activity.

All Concept Studio activities