Manitoba · Grade 10
Essential Mathematics, Grade 10 (20S)
Manitoba’s Grade 10 math course, from Analysis of Games and Numbers to Angle Construction.
- Units
- 7
- Lessons
- 9
- Skills
- 27
- Provincial exam
- None
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 2 skills
Analysis of Games and Numbers
Puzzles and Games with Spatial Reasoning
Winning strategies for spatial puzzles
I can find and explain a strategy that wins a spatial puzzle or game.
Official code: 10E1.A.1
Inventing and adapting a spatial puzzle
I can invent a variation of a spatial puzzle and describe how to win it.
Official code: 10E2.A.1
The official wording · 2 outcomes
- 10E1.A.1
- Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
- 10E2.A.1
- Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
Key ideas
A strategy is a plan you can repeat and explain, like guess-and-check, look-for-a-pattern, or work-backward.
Testing a strategy against the game shows whether it really wins.
Changing a rule or a board turns one puzzle into a new one with its own strategy.
A good variation still has a describable winning plan.
Watch out for
- Thinking a lucky win is the same as a strategy.
- Stopping at one answer instead of checking the strategy always works.
- Making a variation that is impossible or has no strategy.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 4 skills
Personal Finance
Earning Income and Pay
Ways of earning income
I can describe and compare the ways people earn income.
Official code: 10E1.P.1
Calculating gross pay
I can calculate gross pay with regular, overtime, tips, and commission.
Official code: 10E1.P.1
Deductions and net pay
I can find net pay after all the deductions.
Official code: 10E1.P.1
Rearranging income formulas
I can apply and rearrange a formula to solve an income problem.
Official code: 10E1.P.2
The official wording · 4 outcomes
- 10E1.P.1
- Demonstrate an understanding of calculations for gross pay and net pay earned through income sources, including wages salary contracts commissions piecework
- 10E1.P.1
- Demonstrate an understanding of calculations for gross pay and net pay earned through income sources, including wages salary commissions piecework
- 10E1.P.1
- Demonstrate an understanding of calculations for gross pay and net pay earned through income sources, including wages salary
- 10E1.P.2
- Solve problems that require the manipulation and application of formulas related to income.
Key ideas
Income can come as an hourly wage, a salary, a contract, a commission, or piecework.
Each method has advantages and disadvantages for the worker.
Overtime is often paid at time-and-a-half (1.5x) or double time (2x) the base wage.
Gross pay = regular pay + overtime pay + tips or commission, before deductions.
Net pay = gross pay minus CPP, EI, income tax, and other deductions.
Watch out for
- Thinking a higher hourly wage always means more take-home pay.
- Confusing commission with a fixed salary.
- Paying overtime hours at the regular rate.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 10 skills
Measurement
The SI and Imperial Systems
The SI system and its units
I can describe the SI system and its base-ten units.
Official code: 10E1.M.1
Converting within SI
I can convert between SI units.
Official code: 10E1.M.1
The imperial system
I can describe imperial units and how they relate.
Official code: 10E1.M.2
Converting between imperial and SI
I can convert measurements between imperial and SI units.
Official code: 10E1.M.2
Linear Measurement and Formulas
Measuring with SI and imperial tools
I can estimate and measure lengths accurately in either system.
Official code: 10E1.M.3
Solving linear measurement problems
I can solve real linear-measurement problems and check they are reasonable.
Official code: 10E1.M.3
Applying and rearranging conversion formulas
I can apply and rearrange a conversion formula to solve a problem.
Official code: 10E1.M.4
2-D Area and Perimeter
Area of regular and composite shapes
I can find the area of regular, composite, and irregular shapes.
Official code: 10E1.G.1
Changing dimensions and unit conversion
I can convert areas between squared units and predict how changing dimensions affects area.
Official code: 10E1.G.1
Rearranging perimeter and area formulas
I can apply and rearrange perimeter and area formulas.
Official code: 10E1.G.2
The official wording · 10 outcomes
- 10E1.M.1
- Demonstrate an understanding of the Système International (SI) by describing relationships of the units for length, area, volume, capacity, and mass.
- 10E1.M.1
- Demonstrate an understanding of the Système International (SI) by describing relationships of the units for length, area, volume, capacity, and mass.
- 10E1.M.2
- Demonstrate an understanding of the imperial system by describing the relationships of the units for length, area, volume, capacity, and mass comparing the American and British imperial units for capacity
- 10E1.M.2
- Demonstrate an understanding of the imperial system by applying strategies to convert between imperial and SI units
- 10E1.M.3
- Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.
- 10E1.M.3
- Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.
- 10E1.M.4
- Solve problems that require the manipulation and application of formulas related to converting measurement.
- 10E1.G.1
- Solve problems that involve SI and imperial area measurements of regular, composite, and irregular 2-D shapes, including decimal and fractional measurements.
- 10E1.G.1
- Solve problems that involve SI and imperial area measurements of regular, composite, and irregular 2-D shapes, including decimal and fractional measurements.
- 10E1.G.2
- Solve problems that require the manipulation and application of formulas related to perimeter area
Key ideas
SI is built on base ten: each prefix is a power of ten (kilo = 1000, centi = 1/100).
A referent is a familiar length used to estimate, like a thumb-width for a centimetre.
A composite shape is broken into rectangles, triangles, and circles to find its area.
Base units include the metre, litre, and gram for length, capacity, and mass.
Different tools suit different jobs: tape measure, ruler, or calipers.
Watch out for
- Thinking centi means 1/10 instead of 1/100.
- Reading a tape measure past the wrong fraction mark.
- Using the perimeter formula for area.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 4 skills
Trigonometry
Right Triangles and Trigonometry
The Pythagorean theorem
I can use the Pythagorean theorem to find a side of a right triangle.
Official code: 10E2.TG.1
Sine, cosine, and tangent ratios
I can define sine, cosine, and tangent for a right triangle.
Official code: 10E2.TG.2
Solving with trig ratios
I can use a trig ratio to find an unknown side or angle.
Official code: 10E2.TG.2
Rearranging Pythagorean and trig formulas
I can rearrange Pythagorean and trig formulas to solve a problem.
Official code: 10E2.TG.3
The official wording · 4 outcomes
- 10E2.TG.1
- Solve problems involving right triangles using the Pythagorean theorem.
- 10E2.TG.2
- Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by applying similarity to right triangles generalizing patterns from similar right triangles
- 10E2.TG.2
- Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by solving problems
- 10E2.TG.3
- Solve problems that require the manipulation and application of formulas related to the Pythagorean theorem primary trigonometric ratios
Key ideas
In a right triangle, a squared + b squared = c squared, where c is the hypotenuse.
The theorem only applies to right triangles.
For an acute angle: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent.
Similar right triangles have equal ratios for the same angle.
Choose the ratio that links the known and unknown sides for the angle.
Watch out for
- Applying the theorem to a non-right triangle.
- Adding the sides instead of squaring them.
- Mixing up opposite and adjacent sides.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 2 skills
Consumer Decisions
Smart Shopping and Currency
Unit pricing and best buys
I can use unit price to find the best buy and figure out sale prices.
Official code: 10E2.C.1
Currency exchange
I can convert money between currencies using an exchange rate.
Official code: 10E2.C.1
The official wording · 2 outcomes
- 10E2.C.1
- Solve problems that involve unit pricing and currency exchange, using proportional reasoning.
- 10E2.C.1
- Solve problems that involve unit pricing and currency exchange, using proportional reasoning.
Key ideas
Unit price = total price divided by the quantity, letting you compare sizes fairly.
A sale price = original price minus the discount (percent of the price).
An exchange rate is a proportion linking two currencies.
The selling rate and purchasing rate differ; the bank profits on the spread.
Watch out for
- Judging value by total price instead of unit price.
- Subtracting the percent instead of the discount amount.
- Multiplying when you should divide by the rate.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 6 · 2 skills
Transformations
Transforming 2-D Shapes
Translations, rotations, and reflections
I can slide, turn, and flip a shape and use these in designs.
Official code: 10E2.TF.1
Dilations and similarity
I can draw a dilation and explain how it stays proportional.
Official code: 10E2.TF.1
The official wording · 2 outcomes
- 10E2.TF.1
- Demonstrate an understanding of transformations on a 2-D shape, including translations rotations reflections
- 10E2.TF.1
- Demonstrate an understanding of transformations on a 2-D shape, including dilations
Key ideas
A translation slides, a rotation turns, and a reflection flips a shape.
Combining transformations creates patterns and designs.
A dilation resizes a shape by a scale factor, keeping it similar.
Corresponding sides of the original and image stay proportional.
Watch out for
- Confusing a rotation with a reflection.
- Changing the shape's size during a rigid motion.
- Adding a length instead of multiplying by the scale factor.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 7 · 3 skills
Angle Construction
Angles and Lines
Drawing and measuring angles
I can draw, estimate, and measure angles of every type.
Official code: 10E2.AC.1
Replicating and bisecting angles
I can copy an angle and bisect it with construction tools.
Official code: 10E2.AC.1
Parallel lines and transversals
I can find unknown angles formed by parallel lines and a transversal.
Official code: 10E2.AC.2
The official wording · 3 outcomes
- 10E2.AC.1
- Demonstrate an understanding of angles, including acute, right, obtuse, straight, and reflex, by drawing
- 10E2.AC.1
- Demonstrate an understanding of angles, including acute, right, obtuse, straight, and reflex, by replicating and constructing bisecting solving problems
- 10E2.AC.2
- Solve problems that involve parallel, perpendicular, and transversal lines, and pairs of angles formed between them.
Key ideas
Angles are named by size: acute, right, obtuse, straight, and reflex.
Referent angles like 45, 90, and 180 degrees help estimate before measuring.
An angle can be replicated exactly with a compass and straightedge.
Bisecting an angle splits it into two equal halves.
A transversal crossing parallel lines makes equal corresponding and alternate angles.
Watch out for
- Reading the wrong scale on a protractor.
- Confusing a reflex angle with its smaller partner.
- Changing the compass width partway through a construction.
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?
Manitoba has 2 math courses for Grade 10. Here they are side by side.
- Essential Mathematics, Grade 10 (20S)This course7 units · 27 skillsNo provincial examWhat it coversAnalysis of Games and Numbers · Personal Finance · Measurement · Trigonometry · Consumer Decisions · Transformations · Angle Construction
- Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)3 units · 29 skillsNo provincial examWhat it coversMeasurement · Algebra and Number · Relations and Functions
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 Manitoba’s own curriculum for Essential Mathematics, Grade 10 (20S).
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Questions about Essential Mathematics, Grade 10 (20S)
What is Essential Mathematics, Grade 10 (20S)?
Manitoba’s Grade 10 math course: 7 units and 27 skills, from Analysis of Games and Numbers to Angle Construction.
What units are in Essential Mathematics, Grade 10 (20S)?
1. Analysis of Games and Numbers, 2. Personal Finance, 3. Measurement, 4. Trigonometry, 5. Consumer Decisions, 6. Transformations and 7. Angle Construction.
Is there a provincial exam for Essential Mathematics, Grade 10 (20S)?
No. Manitoba gives no provincial exam for Essential Mathematics, Grade 10 (20S).
What comes after Essential Mathematics, Grade 10 (20S)?
Applied Mathematics, Grade 11 (30S), Essential Mathematics, Grade 11 (30S) and Pre-Calculus Mathematics, Grade 11 (30S).
Can MapleMind help with Essential Mathematics, Grade 10 (20S)?
Yes. MapleMind teaches every skill of Essential Mathematics, Grade 10 (20S), 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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