Ōrau me ngā Whakaaro Āhua · Percentages and Proportional Reasoning
Mark-ups, discounts, GST, percentage change, and ratios · Years 9–10
Ngā Whāinga Akoranga · Learning Intentions
- Find a percentage of a number and find the original whole amount given a percentage of it.
- Apply percentage mark-ups, discounts, and calculate GST on dollar amounts.
- Calculate percentage increase and decrease between two numbers.
- Use whole-number ratios to represent and solve proportional relationship problems.
Paearu Angitu · Success Criteria
- I can calculate a percentage of a given amount and reverse-calculate the original from a percentage.
- I can calculate a GST-inclusive price and find the pre-GST price from a final price.
- I can calculate percentage change and say whether it is an increase or decrease.
- I can write and simplify a ratio, and use it to solve a proportion problem.
Hononga Marautanga · Curriculum Connections
This activity addresses the following Mathematics curriculum statements (Draft 2025, Phase 4 — Years 9, 10):
- Number: Percentages are a way of expressing a fraction of 100. Percentages can be used to proportionally increase or decrease a quantity by multiplication.
- Number: Finding a fraction or percentage of a number; finding the whole amount given a fraction or percentage (e.g. 20% of an amount is 30 — what is the original?).
- Number: Applying percentage mark-ups and discounts; calculating simple interest and GST on dollar amounts (e.g. finding 15% GST on $432).
- Number: Applying a proportional increase or decrease to a number; calculating the percentage increase or decrease between two numbers.
- Number: Increasing or decreasing a number by a given proportion; representing proportional relationships using whole-number ratios, including reducing to simplest form.
Wāhanga 1 · Percentages of Amounts
A percentage is a fraction out of 100. To find a percentage of an amount, convert the percentage to a decimal (divide by 100) and multiply.
- Find 35% of $240 → 0.35 × 240 = $84
- If 20% of an amount = $30, then the whole = 30 ÷ 0.20 = $150
Calculate (show working):
a) 45% of $380
b) 30% of an amount is $96. Find the original amount.
Wāhanga 2 · Mark-ups, Discounts, and GST
In Aotearoa, GST (Goods and Services Tax) is 15% and is added to most prices. Businesses add mark-ups to make a profit; discounts reduce prices for sales.
Price incl. GST = original × 1.15
Original = GST price ÷ 1.15
Selling price = cost × 1.20
Profit = cost × 0.20
Sale price = original × 0.75
Saving = original × 0.25
Solve these problems (show working):
a) A jacket costs $180 before GST. What is the GST-inclusive price?
b) A shop sells shoes for $230 including GST. What was the pre-GST price?
c) A store buys a basketball for $45 and marks it up by 40%. What is the selling price?
Wāhanga 3 · Percentage Change
Percentage change tells you how much something has increased or decreased relative to the original.
Positive = increase. Negative = decrease.
a) A phone's price dropped from $850 to $680. What is the percentage decrease?
b) A student's test score rose from 48 to 60. What is the percentage increase?
c) A town's population was 12,400 and is now 13,950. Find the % change.
Wāhanga 4 · Ratios and Proportional Reasoning
A ratio compares two or more quantities. Proportional reasoning means scaling up or down while keeping the ratio constant.
E.g. 12:8 → divide by 4 → 3:2
a) Simplify these ratios: 15:25 = 24:36 = 100:60 =
b) A recipe uses flour and sugar in the ratio 3:1. To make a large batch needing 360 g of flour, how much sugar is needed?
c) Two people share a prize of $500 in the ratio 3:2. How much does each person receive?
Aronga Mātauranga Māori · Te Ao Māori Lens
Proportional reasoning runs deep in te ao Māori. Rongoā Māori (traditional medicine) required precise proportional knowledge — knowing the right ratio of plant materials for each remedy, and how to scale recipes up or down for different amounts. Getting the ratio wrong could be harmful; getting it right was life-sustaining.
Harakeke (flax) weaving also requires exact proportional planning — the ratio of strips to finished product, the balance of colour patterns, the structural ratios that make the weave both beautiful and strong. Mathematics was embedded in craft as a form of encoded knowledge.
Think of another context — Māori or otherwise — where proportional reasoning is essential. What happens if the proportions are wrong?
Tuhia ōu whakaaro · Write Your Thoughts
Percentages are everywhere in daily life — sales, interest rates, wages, tax, statistics. When are percentages used to mislead people? How can you use your mathematical skills to read figures critically?