LESSON PLAN

Budgeting and Consumer Math

Apothem Team

Grade 6 · Financial Literacy

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Formalize

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Post a phone-plan ad: "\$35/month plus \$0.10 per text over 200." Ask: "What does a month REALLY cost — and what do you need to know before answering?" The room discovers the answer is "it depends," and the dependency (your text count) must be estimated from your own behaviour.

That's the unit in one ad: budgeting is arithmetic applied to ESTIMATES of your own life, and consumer math is reading price structures with your eyes open.

Explore

Budget-build simulation: each pair receives a monthly scenario card (income from allowance + part-time dog-walking, say \$120; fixed wants and needs lists with prices). They build a budget table — income, fixed expenses, variable expenses, savings — that must balance, then survive two "life events" drawn from a deck (bike repair \$25; found \$10).

Debrief on the design choices: who padded a buffer? Who zeroed savings to afford wants? The vocabulary lands with the pain: needs vs wants, fixed vs variable, and the golden inequality — income must cover outgo, with savings as a planned expense, not leftovers.

Formalize

Formalize the budget identity and the unit-price comparison tool:

$\text{income} = \text{expenses} + \text{savings} \qquad \text{unit price} = \frac{\text{total price}}{\text{quantity}}$

Percent re-enters as the language of money: sales tax adds a percent, discounts subtract one, and "20% off then 12% tax" compounds rather than cancels. The order-of-operations of shopping: discount first, then tax on the discounted price (in most jurisdictions — reading the rule is part of the skill).

Practice

Practice: complete a budget table with one unknown; two unit-price showdowns; one discount-plus-tax computation with the steps ordered and labelled; one "phone plan" comparison where the best plan depends on usage (compute the crossover point).

Exit ticket: "A $40 game is 25% off. Tax is 10%. Final price, shown in two labelled steps." ( $40 \times 0.75 = 30$ ; $30 \times 1.10 = \$33$ .)

Exit ticket

Exit ticket: "A $40 game is 25% off. Tax is 10%. Final price, shown in two labelled steps." ( $40 \times 0.75 = 30$ ; $30 \times 1.10 = \$33$ .)

TIP Percent-off errors melt when re-framed as "you pay the COMPLEMENT": 25% off means pay 75%. One multiplication, no subtraction slip, and it chains cleanly with tax.

WORKED EXAMPLES

Example 1 — Balance the babysitting budget

The month: income \$95 (babysitting + allowance). Committed: bus pass \$25, phone data top-up \$15, club fee \$10. Goal: save \$20. What remains for wants?

Step 1: Apply the identity: $\text{income} = \text{expenses} + \text{savings}$ → $95 = (25 + 15 + 10 + W) + 20$ where $W$ is wants money.

Step 2: Solve: fixed expenses total 50; so $95 = 50 + W + 20$ → $W = 25$ .

Step 3: Stress-test: movie night (\$16) AND the new-release game rental (\$12) total \$28 — over by \$3. Choose, defer, or shave savings? Present the three options and their costs honestly.

Step 4: The budgeting habit made visible: the \$20 savings was written BEFORE wants were computed — pay-yourself-first as an equation ordering, not a slogan.

Example 2 — The shrinking cereal: unit price as a lie detector

The shelf: the "family size" box, 650 g for \$6.49, sits beside the regular 500 g for \$4.79. A sticker on the family size shouts "BETTER VALUE."

Step 1: Unit prices in cents per 100 g: family — $649 \div 6.5 = 99.8$ ¢ per 100 g. Regular — $479 \div 5 = 95.8$ ¢ per 100 g.

Step 2: Verdict: the REGULAR box is cheaper per gram. The "better value" sticker is marketing, not arithmetic.

Step 3: When would the family box still be right? If the regular sells out weekly and shopping trips cost time/bus fare — real budgets price convenience too. But that's a chosen premium, not a bargain.

Step 4: The consumer's reflex to build: any "value/jumbo/family" label triggers a ten-second unit-price check. Stores count on shoppers not doing the division; the division is the whole defence.

Example 3 — Discount, tax, and the receipt that reveals the order

The purchase: headphones listed \$60, on sale 30% off, tax 13%.

Step 1: Pay-the-complement for the discount: $60 \times 0.70 = \$42$ .

Step 2: Tax on the DISCOUNTED price: $42 \times 1.13 = \$47.46$ .

Step 3: The tempting wrong orders, computed to bury them: tax first then discount: $60 \times 1.13 = 67.80$ , then $\times 0.70 = 47.46$ — identical! (Multiplication commutes.) But "30% off minus 13% tax = 17% off": $60 \times 0.83 = 49.80$ — wrong, because the percents apply to different bases.

Step 4: Harvest both surprises: the ORDER of the two multiplications doesn't matter (each is just a scaling), but COMBINING the percents by addition does violence. Percents multiply as factors ( $0.70 \times 1.13 = 0.791$ — the true combined effect: pay 79.1%).

Step 5: Receipt-reading exit: find the line where tax was applied and confirm the base it used.

MATERIALS

•Scenario and life-event cards

•Budget table templates

•Store flyers

•Calculators

•Practice set (PDF)

WATCH FOR

!Discount and tax percents added or cancelled ("25% off + 10% tax = 15% off"). They apply to DIFFERENT bases; compute sequentially.

!Savings treated as "whatever's left" — the identity places it as a planned line item, and simulations show leftover-savers ending at zero.

!Unit prices compared across different units (per-100g vs per-kg). Convert to one unit before judging.