Ontario · Grade 12
Mathematics for Work and Everyday Life, Grade 12 (Workplace)
- MEL4E
Ontario’s Grade 12 math course, from Reasoning With Data to Applications of Measurement.
- Units
- 3
- Lessons
- 8
- Skills
- 52
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 14 skills
Reasoning With Data
Reasoning with Data
Interpreting and Displaying Data
Reading and interpreting graphs from real sources
I can read and interpret graphs from real sources like newspapers and Statistics Canada.
Skill 1.1
Population versus sample and why sampling is necessary
I can explain the difference between a population and a sample, and why sampling is needed.
Skill 1.2
Collecting categorical data from primary and secondary sources
I can collect categorical data from primary and secondary sources.
Skill 1.3
Representing categorical data by constructing graphs
I can represent categorical data by constructing graphs.
Skill 1.4
Making and justifying inferences from graphed data
I can make and justify inferences based on graphed data.
Skill 1.5
Investigating a topic of personal interest using collected data
I can investigate a topic of personal interest by collecting, organizing, and analyzing data.
Skill 1.6
How the media and advertisers use and misuse statistics
I can explain how the media and advertisers use and misuse statistics.
Skill 1.7
Gathering information about data management in the workplace and daily life
I can find and describe how data management is used in the workplace and daily life.
Skill 1.8
Investigating Probability
Determining and representing theoretical probability
I can determine and represent the theoretical probability of an event.
Skill 1.9
Identifying probability in the media and its representations
I can identify examples of probability used in the media and its representations.
Skill 1.10
Performing probability experiments and finding experimental probability
I can perform probability experiments and determine experimental probability.
Skill 1.11
Comparing theoretical and experimental probability
I can compare theoretical and experimental probability and explain why they might differ.
Skill 1.12
How experimental probability approaches theoretical probability with more trials
I can show how experimental probability approaches theoretical probability as trials increase.
Skill 1.13
Using probability and statistics in the media to make informed decisions
I can use probability and statistics from the media to make informed decisions.
Skill 1.14
The official wording · 14 outcomes
- 1.1
- read and interpret graphs (e.g., bar graph, broken-line graph, histogram) obtained from various sources (e.g., newspapers, magazines, Statistics Canada website)
- 1.2
- explain the distinction between the terms population and sample, describe the character- istics of a good sample, and explain why sampling is necessary
- 1.3
- collect categorical data from primary sources, through experimentation involving observation (e.g., by tracking food orders in restaurants offering healthy food options) or measurement, or from secondary sources
- 1.4
- represent categorical data by constructing graphs (e.g., bar graph, broken-line graph, circle graph) using a variety of tools
- 1.5
- make inferences based on the graphical repre- sentation of data (e.g., an inference about a sample from the graphical representation of a population), and justify conclusions orally or in writing using convincing arguments
- 1.6
- make and justify conclusions about a topic of personal interest by collecting, organizing (e.g., using spreadsheets), representing (e.g., using graphs), and making inferences from categorical data
- 1.7
- explain how the media, the advertising indus- try, and others (e.g., marketers, pollsters) use and misuse statistics
- 1.8
- gather, interpret, and describe information about applications of data management in the workplace and in everyday life
- 1.9
- determine the theoretical probability of an event (i.e., the ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely), and represent the probability in a variety of ways
- 1.10
- identify examples of the use of probability in the media (e.g., the probability of rain, of winning a lottery, of wait times for a service exceeding specified amounts) and various ways in which probability is represented
- 1.11
- perform simple probability experiments (e.g., rolling number cubes, spinning spinners, flip- ping coins, playing Aboriginal stick-and-stone games), record the results, and determine the experimental probability of an event
- 1.12
- compare, through investigation, the theoretical probability of an event with the experimental probability, and describe how uncertainty explains why they might differ
- 1.13
- determine, through investigation using class- generated data and technology-based simula- tion models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator), the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases
- 1.14
- interpret information involving the use of probability and statistics in the media, and describe how probability and statistics can help in making informed decisions in a variety of situations
Key ideas
Bar graphs, broken-line graphs, and histograms each show data in a slightly different way.
Theoretical probability is the ratio of favourable outcomes to all possible outcomes, when every outcome is equally likely.
Reading a graph well means checking its title, axis labels, and units before drawing conclusions.
Probability can be shown as a fraction, a percent, or a decimal between 0 and 1.
A population is everyone or everything you're interested in; a sample is a smaller group taken from it.
Watch out for
- Skipping the axis labels and misreading what the graph actually measures.
- Miscounting the total number of possible outcomes when calculating a probability.
- Assuming every graph type works the same way without checking which type it is.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 19 skills
Personal Finance
Renting or Owning Accommodation
Financial and non-financial implications of living independently
I can identify the financial and non-financial effects of living independently.
Skill 2.1
Comparing the costs and advantages of different rental accommodation types
I can compare the costs and advantages of different types of rental accommodation.
Skill 2.2
Comparing purchase prices of different owned accommodation types
I can compare purchase prices of different types of owned accommodation.
Skill 2.3
Comparing ongoing living expenses of renting and owning
I can compare the ongoing living expenses of renting and owning.
Skill 2.4
Rights and responsibilities of tenants and landlords
I can describe the rights and responsibilities of tenants and landlords.
Skill 2.5
Generating a moving checklist and estimating moving costs
I can create a moving checklist and estimate the total cost of moving.
Skill 2.6
Designing Budgets
Categorizing expenses as discretionary or non-discretionary
I can categorize expenses as discretionary or non-discretionary.
Skill 2.7
Categorizing non-discretionary expenses as fixed or variable
I can categorize non-discretionary expenses as fixed or variable.
Skill 2.8
Reading and interpreting prepared budgets and how they reflect values
I can read a prepared budget and describe how budgets reflect personal values.
Skill 2.9
Designing, explaining, and justifying a monthly budget from a case study
I can design, explain, and justify a monthly budget from a case study.
Skill 2.10
Identifying factors in the affordability of accommodation
I can identify the factors that affect whether accommodation is affordable.
Skill 2.11
Adjusting a budget for changed circumstances
I can adjust a budget when circumstances change.
Skill 2.12
Filing Income Tax
Why Canadians file a tax return and its major parts
I can explain why Canadians file a tax return and describe its major parts.
Skill 2.13
Gathering the documents required to file a tax return
I can gather the documents required to file a tax return and explain why each is needed.
Skill 2.14
Comparing common tax credits and tax deductions
I can compare common tax credits and tax deductions.
Skill 2.15
Completing a simple personal income tax return
I can complete a simple personal income tax return.
Skill 2.16
Additional tax-filing information for a self-employed individual
I can describe additional tax-filing information needed for a self-employed individual.
Skill 2.17
Comparing tax-filing services and resources
I can compare services and resources available for filing a tax return.
Skill 2.18
Gathering information about personal finance applications in the workplace
I can find and describe how workplaces use personal finance math.
Skill 2.19
The official wording · 19 outcomes
- 2.1
- identify the financial implications (e.g., res- ponsibility for paying the cost of accommoda- tion and furnishings; greater responsibility for financial decision making) and the non- financial implications
- 2.2
- gather and compare, through investigation, information about the costs and the advan- tages and disadvantages of different types of rental accommodation in the local community
- 2.3
- gather and compare, through investigation, information about purchase prices of different types of owned accommodation in the local community
- 2.4
- gather, interpret, and compare information about the different types of ongoing living expenses associated with renting and owning accommodation
- 2.5
- gather, interpret, and describe information about the rights and responsibilities of tenants and landlords
- 2.6
- generate a checklist of necessary tasks asso- ciated with moving (e.g., change of address, set-up of utilities and services, truck rental), and estimate the total cost involved under various conditions
- 2.7
- categorize personal expenses as non- discretionary (e.g., rent, groceries, utilities, loan payments) or discretionary (e.g., enter- tainment, vacations)
- 2.8
- categorize personal non-discretionary ex- penses as fixed (e.g., rent, cable, car insur- ance) or variable (e.g., groceries, clothing, vehicle maintenance)
- 2.9
- read and interpret prepared individual or family budgets, identify and describe the key components of a budget, and describe how budgets can reflect personal values
- 2.10
- design, with technology (e.g., using spread- sheet templates, budgeting software, online tools) and without technology (e.g., using budget templates), explain, and justify a monthly budget suitable for an individual or family described in a given case study
- 2.11
- identify and describe factors to be considered in determining the affordability of accommo- dation in the local community
- 2.12
- make adjustments to a budget to accommo- date changes in circumstances (e.g., loss of hours at work, change of job, change in per- sonal responsibilities, move to new accommo- dation, achievement of a long-term goal, major purchase), with technology
- 2.13
- explain why most Canadians are expected to file a personal income tax return each year, and identify and describe the major parts of a personal income tax return
- 2.14
- gather, interpret, and describe the information and documents required for filing a personal income tax return (e.g., CRA guides, forms, and schedules; T4 slips; receipts for charitable donations), and explain why they are required
- 2.15
- gather, interpret, and compare information about common tax credits (e.g., tuition fees, medical expenses, charitable donations) and tax deductions (e.g., moving expenses, child care expenses, union dues)
- 2.16
- complete a simple personal income tax return (i.e., forms and schedules), with or without tax preparation software
- 2.17
- gather, interpret, and describe some addition- al information that a self-employed individual should provide when filing a personal income tax return
- 2.18
- gather, interpret, and describe information about services that will complete a personal income tax return (e.g., tax preparation serv- ice, chartered accountant, voluntary service in the community) and resources that will help with completing a personal income tax return
- 2.19
- gather, interpret, and describe information about applications of the mathematics of personal finance in the workplace
Key ideas
Financial implications include new costs like rent and furnishings, and new financial decision-making.
Non-discretionary expenses (rent, groceries, utilities) must be paid; discretionary expenses (entertainment, vacations) are optional.
Most Canadians are expected to file a personal income tax return every year.
Non-financial implications include more freedom, but also new demands like time management or possible loneliness.
Knowing this distinction helps decide where to cut back if money is tight.
Watch out for
- Focusing only on the financial side and ignoring non-financial changes like time management.
- Treating a discretionary expense (like a streaming subscription) as non-discretionary out of habit.
- Thinking only high earners need to file a tax return.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 19 skills
Applications of Measurement
Measuring and Estimating
Measuring lengths and capacities with metric and imperial tools
I can measure lengths and capacities using metric and imperial tools.
Skill 3.1
Estimating lengths and capacities using personal referents
I can estimate lengths and capacities using personal referents.
Skill 3.2
Estimating quantities and describing the strategies used
I can estimate quantities and describe the strategies used.
Skill 3.3
Converting measures within the same system
I can convert measures within the same system (metric or imperial).
Skill 3.4
Converting measures between the metric and imperial systems
I can convert measures between the metric and imperial systems.
Skill 3.5
Applying Measurement and Design
Constructing accurate right angles and connecting to the Pythagorean theorem
I can construct accurate right angles in practical contexts using the Pythagorean theorem.
Skill 3.6
Applying perimeter in familiar contexts
I can apply the concept of perimeter in familiar contexts.
Skill 3.7
Estimating the areas and volumes of irregular shapes
I can estimate the areas and volumes of irregular shapes and figures.
Skill 3.8
Solving real-world problems with areas of rectangles, triangles, circles, and composite shapes
I can solve real-world problems with areas of rectangles, triangles, circles, and composite shapes.
Skill 3.9
Solving real-world problems with volumes and surface areas of prisms and cylinders
I can solve real-world problems with volumes and surface areas of prisms and cylinders.
Skill 3.10
Constructing a 2D scale drawing of a familiar setting
I can construct a 2D scale drawing of a familiar setting.
Skill 3.11
Constructing a 3D scale model of a personal-interest object or environment
I can construct a 3D scale model of an object or environment of personal interest.
Skill 3.12
Planning, designing, and budgeting for a household improvement
I can plan, design, and prepare a budget for a household improvement.
Skill 3.13
Solving Measurement Problems Using Proportional Reasoning
Identifying applications of ratio and rate, and equivalent ratios and rates
I can identify applications of ratio and rate, and recognize equivalent ratios and rates.
Skill 3.14
Using unit rates to make comparisons
I can use unit rates to compare and solve problems.
Skill 3.15
Distinguishing proportional from non-proportional real-world situations
I can distinguish between proportional and non-proportional situations.
Skill 3.16
Identifying consequences of errors in proportional reasoning
I can identify the consequences of errors in proportional reasoning.
Skill 3.17
Solving everyday-life problems using proportional reasoning
I can solve everyday-life problems using proportional reasoning.
Skill 3.18
Solving work-related problems using proportional reasoning
I can solve work-related problems using proportional reasoning.
Skill 3.19
The official wording · 19 outcomes
- 3.1
- measure, using a variety of tools (e.g., meas- uring tape, metre or yard stick, measuring cups, graduated cylinders), the lengths of common objects and the capacities of com- mon containers, using the metric system and the imperial system
- 3.2
- estimate lengths, distances, and capacities in metric units and in imperial units by applying personal referents
- 3.3
- estimate quantities (e.g., bricks in a pile, time to complete a job, people in a crowd), and describe the strategies used
- 3.4
- convert measures within systems (e.g., cen- timetres and metres, kilograms and grams, litres and millilitres, feet and inches, ounces and pounds), as required within applications that arise from familiar contexts
- 3.5
- convert measures between systems (e.g., cen- timetres and inches, pounds and kilograms, square feet and square metres, litres and U.S. gallons, kilometres and miles, cups and milli- litres, millilitres and teaspoons, degrees Celsius and degrees Fahrenheit), as required within applications that arise from familiar contexts
- 3.6
- construct accurate right angles in practical contexts (e.g., by using the 3-4-5 triplet to construct a region with right-angled corners on a floor), and explain connections to the Pythagorean theorem
- 3.7
- apply the concept of perimeter in familiar contexts (e.g., baseboard, fencing, door and window trim)
- 3.8
- estimate the areas and volumes of irregular shapes and figures, using a variety of strat- egies (e.g., counting grid squares; displacing water)
- 3.9
- solve problems involving the areas of rectan- gles, triangles, and circles, and of related composite shapes, in situations arising from real-world applications
- 3.10
- solve problems involving the volumes and surface areas of rectangular prisms, triangular prisms, and cylinders, and of related compo- site figures, in situations arising from real- world applications
- 3.11
- construct a two-dimensional scale drawing of a familiar setting (e.g., classroom, flower bed, playground) on grid paper or using design or drawing software
- 3.12
- construct, with reasonable accuracy, a three- dimensional scale model of an object or envi- ronment of personal interest (e.g., appliance, room, building, garden, bridge)
- 3.13
- investigate, plan, design, and prepare a budg- et for a household improvement (e.g., land- scaping a property; renovating a room), using appropriate technologies
- 3.14
- identify and describe applications of ratio and rate, and recognize and represent equivalent ratios
- 3.15
- identify situations in which it is useful to make comparisons using unit rates, and solve problems that involve comparisons of unit rates
- 3.16
- identify and describe real-world applications of proportional reasoning (e.g., mixing con- crete; calculating dosages; converting units; painting walls; calculating fuel consumption; calculating pay; enlarging patterns), distinguish between a situation involving a proportional relationship
- 3.17
- identify and describe the possible consequences (e.g., overdoses of medication; seized engines; ruined clothing; cracked or crumbling concrete) of errors in proportional reasoning
- 3.18
- solve problems involving proportional reason- ing in everyday life (e.g., applying fertilizers; mixing gasoline and oil for use in small engines; mixing cement; buying plants for flower beds; using pool or laundry chemicals; doubling recipes; estimating cooking time from the time needed per pound; determining the fibre content of different sizes of food servings)
- 3.19
- solve problems involving proportional reason- ing in work-related situations (e.g., calculating overtime pay; calculating pay for piecework; mixing concrete for small or large jobs)
Key ideas
Tools like a measuring tape, metre stick, and measuring cups each suit different measurement tasks.
The 3-4-5 triplet is a practical trick for constructing a true right angle without special tools.
A ratio compares two quantities of the same kind; a rate compares two quantities of different kinds.
Canada uses metric officially, but imperial units (feet, inches, cups) are still common in daily life.
This trick works because 3² + 4² = 5², connecting directly to the Pythagorean theorem.
Watch out for
- Misreading a measuring tool's scale, especially between metric and imperial markings.
- Using the wrong ratio (not 3-4-5) and ending up with an inaccurate angle.
- Thinking two ratios with different numbers can't be equivalent.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
Which course?
Ontario has 6 math courses for Grade 12. Here they are side by side.
- Advanced Functions, Grade 12 (University)MHF4U4 units · 72 skillsNo provincial examWhat it coversExponential and Logarithmic Functions · Trigonometric Functions · Polynomial and Rational Functions · Characteristics of Functions
- Calculus and Vectors, Grade 12 (University)MCV4U3 units · 54 skillsNo provincial examWhat it coversRate of Change · Derivatives and Their Applications · Geometry and Algebra of Vectors
- Foundations for College Mathematics, Grade 12 (College)MAP4C4 units · 59 skillsNo provincial examWhat it coversMathematical Models · Personal Finance · Geometry and Trigonometry · Data Management
- Mathematics for College Technology, Grade 12 (College)MCT4C4 units · 57 skillsNo provincial examWhat it coversExponential Functions · Polynomial Functions · Trigonometric Functions · Applications of Geometry
- Mathematics for Work and Everyday Life, Grade 12 (Workplace)This courseMEL4E3 units · 52 skillsNo provincial examWhat it coversReasoning With Data · Personal Finance · Applications of Measurement
- Mathematics of Data Management, Grade 12 (University)MDM4U5 units · 57 skillsNo provincial examWhat it coversCounting and Probability · Probability Distributions · Organization of Data for Analysis · Statistical Analysis · Culminating Data Management Investigation
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Ontario’s own curriculum for Mathematics for Work and Everyday Life, Grade 12 (Workplace).
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| AReasoning with Data | Outcomes 14 | Taught in Unit 1 |
| BPersonal Finance | Outcomes 19 | Taught in Unit 2 |
| CApplications of Measurement | Outcomes 19 | Taught in Unit 3 |
Study it in MapleMind
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Course Companion
Your year in one workbook
A fun way to keep Mathematics for Work and Everyday Life, Grade 12 (Workplace) organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
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Questions about Mathematics for Work and Everyday Life, Grade 12 (Workplace)
What is Mathematics for Work and Everyday Life, Grade 12 (Workplace)?
Ontario’s Grade 12 math course: 3 units and 52 skills, from Reasoning With Data to Applications of Measurement.
What units are in Mathematics for Work and Everyday Life, Grade 12 (Workplace)?
1. Reasoning With Data, 2. Personal Finance and 3. Applications of Measurement.
Is there a provincial exam for Mathematics for Work and Everyday Life, Grade 12 (Workplace)?
No. Ontario gives no provincial exam for Mathematics for Work and Everyday Life, Grade 12 (Workplace).
Can MapleMind help with Mathematics for Work and Everyday Life, Grade 12 (Workplace)?
Yes. MapleMind teaches every skill of Mathematics for Work and Everyday Life, Grade 12 (Workplace), step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
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