Ontario Grade 12 MEL4E Mathematics for Work and Everyday Life (Grade 12, Workplace Preparation)
Chapters: 3
1. A. Reasoning with Data
1 Interpreting and Displaying Data · 2 Investigating Probability
- Data Analysis – Data analysis means turning raw data into answers. It follows a cycle: ask a question, collect data, clean it (remove errors, repeats and blanks), organise and transform it, analyse it with summaries such as mean, median, range and patterns, show it with a good chart, and draw a careful conclusion. Watch for outliers, small samples and bias, and remember that a correlation between two things does not prove that one causes the other. Data must also be stored safely and used with permission.
- Introduction to Probability: Scale, Experiments, Sample Spaces and Trees – Probability is a number from 0 to 1 that tells how likely something is. 0 means it can never happen, 1 means it will surely happen. We can find it by doing an experiment many times (empirical probability), or by listing every possible result (the sample space) and counting the ones we want. Tree diagrams and tables help us list results when two things happen together.
2. B. Personal Finance
1 Renting or Owning Accommodation · 2 Designing Budgets · 3 Filing Income Tax
- Consumer Mathematics: Earning, Buying and Travelling – Consumer mathematics is everyday money maths. Gross pay is all you earn: hourly wage (hours × rate), salary, commission (a % of sales), piecework, tips, bonus and overtime (often 1.5 × rate). Deductions such as income tax, pension and insurance are taken off, leaving net pay (take-home pay). When buying, take the discount first, then add sales tax (GST or VAT): price × (1 − d) × (1 + t). Unit price = price ÷ quantity, so you can compare packs. Count up to give correct change. A car costs fuel (distance × litres per 100 km ÷ 100 × price), insurance (higher for new drivers), licence, loan, repairs and parking; compare it with bus, train or plane for each trip.
- Smart Ways to Manage Your Finances – Inflation makes prices rise, so the same money buys less. Money kept in a bank earns interest: simple interest is paid only on the original amount, while compound interest also earns interest on earlier interest, so it grows faster over time. A budget plans income into needs, wants and savings. Savings are kept safe; investments can grow but carry risk, and higher possible returns mean higher risk. Insurance shares risk among many people. Income tax is paid on income above a limit, at rates that rise with income.
- Filing an Income Tax Return – An income tax return is a form you send to the tax office once a year. On it you show all the money you earned, the deductions and credits you can claim, the tax you owe, and the tax already taken from your pay. If too much tax was taken, you get a refund. If too little, you pay the balance. You need documents: pay slips, interest slips, receipts for donations or pension savings. Self-employed people also report business income and costs. Today most returns are filed online, and free help is available.
3. C. Applications of Measurement
1 Measuring and Estimating · 2 Applying Measurement and Design · 3 Solving Measurement Problems Using Proportional Reasoning
- Measurement Conversions: Within and Between Systems – To change a measurement to another unit, multiply or divide by a conversion factor. Inside the metric system each step on the ladder (km, hm, dam, m, dm, cm, mm) is a factor of 10. Between the metric and imperial systems we use fixed factors such as 1 in = 2.54 cm, 1 mi ≈ 1.609 km and 1 lb ≈ 0.454 kg. Estimate first with benchmarks, then convert and check that the answer makes sense.
- Surface Area and Volume of Cuboid, Cylinder, Cone, Pyramid and Sphere – Surface area is the total area of the outside skin of a solid, like the paper needed to wrap it. Volume is the space inside, like the water it can hold. A cuboid's volume is the number of 1 cm cubes that fit in it. A cone holds one third of a cylinder with the same base and height, and a pyramid holds one third of the matching prism.
- Ratio and Proportion – A ratio a : b compares two amounts of the same kind. Divide both parts by the same number to simplify it. To share an amount in a ratio, add the parts, find one part, then multiply. Two quantities are in direct proportion when y = k·x (double one, double the other) and in inverse proportion when x·y = k (double one, halve the other).