Manitoba · Grade 11
Applied Mathematics, Grade 11 (30S)
Manitoba’s Grade 11 math course, from Measurement to Mathematics Research Project.
- Units
- 6
- Lessons
- 6
- Skills
- 19
- Provincial exam
- None
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 4 skills
Measurement
Rates and Scale
Applying rates
I can model and solve problems using rates.
Skill 1.1
Scale diagrams
I can use a scale diagram to find real dimensions.
Skill 1.2
Scale factor and similar shapes
I can predict how a scale factor changes a shape's area.
Skill 1.3
Scale factor, surface area, and volume
I can predict how a scale factor changes surface area and volume.
Skill 1.4
The official wording · 4 outcomes
- 1.1
- Solve problems that involve the application of rates.
- 1.2
- Solve problems that involve scale diagrams, using proportional reasoning.
- 1.3
- Demonstrate an understanding of the relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D objects.
- 1.4
- Demonstrate an understanding of the relationships among scale factors, areas, surface areas, and volumes of similar 2-D shapes and 3-D objects.
Key ideas
A rate compares two quantities with different units, like km/h.
The slope of a rate graph is the rate itself.
A scale factor relates a diagram's size to the real object.
Proportional reasoning scales any dimension up or down.
Area scales by the square of the scale factor.
Watch out for
- Comparing rates with different units without converting.
- Reading the rate off a graph with the axes swapped.
- Inverting the scale factor.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 4 skills
Geometry
Angles, Triangles, and the Sine and Cosine Laws
Proving angle and triangle properties
I can prove properties of angles and triangles.
Skill 2.1
Solving angle and triangle problems
I can find unknown angles using angle and triangle properties.
Skill 2.2
The sine and cosine laws
I can solve a non-right triangle with the sine or cosine law.
Skill 2.3
The ambiguous case
I can handle the ambiguous case of the sine law.
Skill 2.4
The official wording · 4 outcomes
- 2.1
- Derive proofs that involve the properties of angles and triangles.
- 2.2
- Solve problems that involve the properties of angles and triangles.
- 2.3
- Solve problems that involve the cosine law and the sine law, including the ambiguous case.
- 2.4
- Solve problems that involve the cosine law and the sine law, including the ambiguous case.
Key ideas
Inductive reasoning spots a pattern; deductive reasoning proves it always holds.
The interior angles of a triangle sum to 180 degrees.
Angle relationships at a transversal find unknown angles.
Triangle properties constrain the remaining angles.
The cosine law relates all three sides and one angle.
Watch out for
- Treating a single example as a proof.
- Assuming parallel-line rules when lines are not parallel.
- Applying transversal rules to non-parallel lines.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 2 skills
Logical Reasoning
Reasoning, Proof, and Puzzles
Conjectures and proof
I can make, prove, or disprove a conjecture.
Skill 3.1
Analyzing puzzles and games
I can analyze a puzzle or game and justify a winning strategy formally.
Skill 3.2
The official wording · 2 outcomes
- 3.1
- Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems.
- 3.2
- Analyze puzzles and games that involve spatial reasoning, using problem-solving strategies.
Key ideas
Inductive reasoning proposes a conjecture from patterns.
A single counter-example disproves a conjecture.
A strategy can be justified with a reasoning chain, not just tried.
Analyzing errors sharpens the strategy.
Watch out for
- Believing many examples prove a conjecture.
- Overlooking a counter-example.
- Describing a strategy without justifying why it works.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 3 skills
Statistics
Normal Distribution and Statistical Inference
Standard deviation and the normal curve
I can find and interpret the standard deviation of a normal distribution.
Skill 4.1
Z-scores
I can find and interpret a z-score.
Skill 4.2
Confidence intervals and margin of error
I can interpret confidence intervals and margin of error in real data.
Skill 4.3
The official wording · 3 outcomes
- 4.1
- Demonstrate an understanding of normal distribution, including standard deviation
- 4.2
- Demonstrate an understanding of normal distribution, including z-scores
- 4.3
- Interpret statistical data, using confidence intervals confidence levels margin of error
Key ideas
Standard deviation measures the spread of data around the mean.
A normal curve is symmetric, with mean, median, and mode at the centre.
A z-score tells how many standard deviations a value is from the mean.
z = (value - mean) divided by the standard deviation.
A margin of error gives a range around a sample estimate.
Watch out for
- Confusing standard deviation with the mean.
- Assuming any spread-out data is normal.
- Forgetting to divide by the standard deviation.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 5 · 3 skills
Relations and Functions
Inequalities and Quadratic Models
Systems of linear inequalities and linear programming
I can model and solve a system of linear inequalities and optimize.
Skill 5.1
Vertex and intercepts of a quadratic model
I can find the vertex and intercepts of a quadratic model with technology.
Skill 5.2
Domain, range, and symmetry of a quadratic model
I can describe a quadratic model's domain, range, and symmetry and use it.
Skill 5.3
The official wording · 3 outcomes
- 5.1
- Model and solve problems that involve systems of linear inequalities in two variables.
- 5.2
- Demonstrate an understanding of the characteristics of quadratic functions, including vertex intercepts
- 5.3
- Demonstrate an understanding of the characteristics of quadratic functions, including domain and range axis of symmetry
Key ideas
Each inequality shades a half-plane; the overlap is the feasible region.
Linear programming optimizes an objective at a vertex of the feasible region.
The vertex is the maximum or minimum point of a parabola.
The x-intercepts are the zeros of the function and roots of the equation.
The axis of symmetry passes vertically through the vertex.
Watch out for
- Shading the wrong side of a boundary line.
- Using a solid line where a broken line is needed.
- Confusing the vertex with an intercept.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 6 · 3 skills
Mathematics Research Project
Mathematics Research Project
Designing the research inquiry
I can choose a historical mathematics topic and plan my inquiry.
Skill 6.1
Researching and analyzing the data
I can gather data and judge whether it is reliable and relevant.
Skill 6.2
Presenting the research project
I can organize and present my mathematics research clearly.
Skill 6.3
The official wording · 3 outcomes
- 6.1
- Research and give a presentation on a historical event or an area of interest that involves mathematics.
- 6.2
- Research and give a presentation on a historical event or an area of interest that involves mathematics.
- 6.3
- Research and give a presentation on a historical event or an area of interest that involves mathematics.
Key ideas
A good inquiry question is focused and connects to real mathematics.
Primary data is collected first-hand; secondary data comes from existing sources.
Sources should be checked for bias, reliability, and relevance.
Statistical methods help interpret the collected data.
A clear presentation walks the audience from question to evidence to conclusion.
Watch out for
- Picking a topic too broad to research.
- Confusing primary and secondary data.
- Accepting a source without checking for bias.
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 3 math courses for Grade 11. Here they are side by side.
- Applied Mathematics, Grade 11 (30S)This course6 units · 19 skillsNo provincial examWhat it coversMeasurement · Geometry · Logical Reasoning · Statistics · Relations and Functions · Mathematics Research Project
- Essential Mathematics, Grade 11 (30S)8 units · 25 skillsNo provincial examWhat it coversAnalysis of Games and Numbers · Interest and Credit · 3-D Geometry · Statistics · Managing Money · Relations and Patterns · Trigonometry · Design Modelling
- Pre-Calculus Mathematics, Grade 11 (30S)3 units · 32 skillsNo provincial examWhat it coversAlgebra and Number · Trigonometry · 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 Applied Mathematics, Grade 11 (30S).
Study it in MapleMind
MapleMind teaches Applied Mathematics, Grade 11 (30S) one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Applied Mathematics, Grade 11 (30S) organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
- 33
- Fillable fields
- 1,334
- Price
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Questions about Applied Mathematics, Grade 11 (30S)
What is Applied Mathematics, Grade 11 (30S)?
Manitoba’s Grade 11 math course: 6 units and 19 skills, from Measurement to Mathematics Research Project.
What units are in Applied Mathematics, Grade 11 (30S)?
1. Measurement, 2. Geometry, 3. Logical Reasoning, 4. Statistics, 5. Relations and Functions and 6. Mathematics Research Project.
Is there a provincial exam for Applied Mathematics, Grade 11 (30S)?
No. Manitoba gives no provincial exam for Applied Mathematics, Grade 11 (30S).
What comes after Applied Mathematics, Grade 11 (30S)?
Applied Mathematics, Grade 12 (40S), Essential Mathematics, Grade 12 (40S), Pre-Calculus Mathematics, Grade 12 (40S) and Introduction to Calculus, Grade 12 (40S).
Can MapleMind help with Applied Mathematics, Grade 11 (30S)?
Yes. MapleMind teaches every skill of Applied Mathematics, Grade 11 (30S), 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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