Manitoba · Grade 10
Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)
Manitoba’s Grade 10 math course, from Measurement to Relations and Functions.
- Units
- 3
- Lessons
- 7
- Skills
- 29
- Provincial exam
- None
- Official curriculum
- Manitoba Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 6 skills
Measurement
Linear Measurement and Conversion
Referents and estimating linear measure
I can pick referents and estimate lengths in SI and imperial.
Skill 1.1
Measuring with instruments
I can measure real objects accurately with the right tool.
Skill 1.2
Converting within and between SI and imperial
I can convert measurements within and between SI and imperial.
Skill 1.3
Surface Area, Volume, and Trigonometry
Surface area and volume of solids
I can find the surface area and volume of cones, cylinders, prisms, pyramids, and spheres.
Skill 1.4
Composite solids and unknown dimensions
I can work backwards from surface area or volume and handle composite solids.
Skill 1.5
Primary trig ratios in right triangles
I can solve right triangles using sine, cosine, and tangent.
Skill 1.6
The official wording · 6 outcomes
- 1.1
- Solve problems that involve linear measurement, using SI and imperial units of measure estimation strategies
- 1.2
- Solve problems that involve linear measurement, using measurement strategies
- 1.3
- Apply proportional reasoning to problems that involve conversions within and between SI and imperial units of measure.
- 1.4
- Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including right cones right cylinders right prisms right pyramids spheres
- 1.5
- Solve problems, using SI and imperial units, that involve the surface area and volume of 3-D objects, including right cones right cylinders right prisms right pyramids spheres
- 1.6
- Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
Key ideas
A referent is a familiar length used to estimate, like a doorway height for a metre.
Surface area sums the areas of all faces or curved surfaces of a solid.
SI units include mm, cm, m, km; imperial units include inch, foot, yard, mile.
Each solid has its own volume formula, like V = pi r squared h for a cylinder.
Different tools suit different jobs: tape measure, ruler, calipers, micrometer.
Watch out for
- Choosing a referent much larger or smaller than the unit.
- Using a volume formula for surface area.
- Mixing SI and imperial referents.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 8 skills
Algebra and Number
Factors and Roots
Prime factors, GCF, and LCM
I can find prime factors, the GCF, and the LCM.
Skill 2.1
Square roots and cube roots
I can find square and cube roots of perfect squares and cubes.
Skill 2.2
Understanding irrational numbers
I can identify and simplify irrational numbers and radicals.
Skill 2.3
Ordering irrational numbers
I can order irrational numbers and place them among the real numbers.
Skill 2.4
Exponents and Polynomials
Powers with rational exponents
I can apply the exponent laws to powers with rational exponents.
Skill 2.5
Multiplying polynomials
I can multiply polynomials and combine like terms.
Skill 2.6
Common factors and trinomial factoring
I can factor out common factors and factor trinomials.
Skill 2.7
Difference of squares
I can recognize and factor a difference of squares.
Skill 2.8
The official wording · 8 outcomes
- 2.1
- Demonstrate an understanding of factors of whole numbers by determining prime factors greatest common factor least common multiple
- 2.2
- Demonstrate an understanding of factors of whole numbers by determining square root cube root
- 2.3
- Demonstrate an understanding of irrational numbers by representing, identifying, and simplifying irrational numbers
- 2.4
- Demonstrate an understanding of irrational numbers by ordering irrational numbers
- 2.5
- Demonstrate an understanding of powers with integral and rational exponents.
- 2.6
- Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials, and trinomials), concretely, pictorially, and symbolically.
- 2.7
- Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially, and symbolically.
- 2.8
- Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially, and symbolically.
Key ideas
Every whole number greater than 1 factors uniquely into primes.
Exponent laws: product adds exponents, quotient subtracts, power multiplies.
The GCF is the largest shared factor; the LCM is the smallest shared multiple.
A rational exponent is a radical: x to the 1/2 equals root x.
A perfect square is a whole number squared; its square root is a whole number.
Watch out for
- Stopping factorization before reaching primes.
- Multiplying exponents when the law says add.
- Confusing the GCF with the LCM.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 15 skills
Relations and Functions
Graphs, Relations, and Functions
Data, graphs, and contexts
I can connect data, graphs, and the contexts they describe.
Skill 3.1
Relations and functions
I can decide whether a relation is a function.
Skill 3.2
Slope as rise, run, and rate of change
I can find slope as rise over run and interpret it as a rate.
Skill 3.3
Parallel and perpendicular slopes
I can use slope to tell if lines are parallel or perpendicular.
Skill 3.4
Representing Linear Relations
Linear relations in words and ordered pairs
I can describe a linear relation in words and as ordered pairs.
Skill 3.5
Linear relations in tables and graphs
I can build a table and a graph for a linear relation.
Skill 3.6
Linear relations as equations
I can represent a linear relation as an equation and match it to other forms.
Skill 3.7
Characteristics of linear graphs
I can find the intercepts, slope, domain, and range of a linear graph.
Skill 3.8
Forms of a Line, Systems, and Distance
Forms of a linear equation
I can move between the three forms of a line and graph each.
Skill 3.9
Equation of a line from a graph or point-slope
I can write a line's equation from its graph or from a point and slope.
Skill 3.10
Equation of a line from two points or a scatterplot
I can write a line's equation from two points or a scatterplot.
Skill 3.11
Function notation
I can write and use function notation for a linear function.
Skill 3.12
Solving systems graphically
I can solve a system of linear equations by graphing.
Skill 3.13
Solving systems algebraically
I can solve a system of linear equations algebraically.
Skill 3.14
Distance and midpoint
I can find the distance between two points and the midpoint of a segment.
Skill 3.15
The official wording · 15 outcomes
- 3.1
- Interpret and explain the relationships among data, graphs, and contexts.
- 3.2
- Demonstrate an understanding of relations and functions.
- 3.3
- Demonstrate an understanding of slope with respect to rise and run line segments and lines rate of change
- 3.4
- Demonstrate an understanding of slope with respect to parallel lines perpendicular lines
- 3.5
- Describe and represent linear relations, using words ordered pairs
- 3.6
- Describe and represent linear relations, using tables of values graphs
- 3.7
- Describe and represent linear relations, using equations
- 3.8
- Determine the characteristics of the graphs of linear relations, including the intercepts slope domain range
- 3.9
- Relate linear relations expressed in slope–intercept form (y = mx + b) general form (Ax + By + C = 0) slope–point form (y – y1 = m(x – x1 )) to their graphs.
- 3.10
- Determine the equation of a linear relation, given a graph a point and the slope
- 3.11
- Determine the equation of a linear relation, given two points a point and the equation of a parallel or perpendicular line a scatterplot
- 3.12
- Represent a linear function, using function notation.
- 3.13
- Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
- 3.14
- Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
- 3.15
- Solve problems that involve the distance between two points and the midpoint of a line segment.
Key ideas
A graph's shape matches the story of its context.
The independent variable is the input; the dependent variable responds to it.
Slope-intercept form y = mx + b shows slope and y-intercept directly.
Whether points are connected depends on whether the data is continuous.
Ordered pairs (x, y) record matched values of the two variables.
Watch out for
- Connecting discrete data points that should stay separate.
- Swapping the independent and dependent variables.
- Misreading the slope in general form.
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)7 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)This course3 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 Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S).
Study it in MapleMind
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Course Companion
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Questions about Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)
What is Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)?
Manitoba’s Grade 10 math course: 3 units and 29 skills, from Measurement to Relations and Functions.
What units are in Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)?
1. Measurement, 2. Algebra and Number and 3. Relations and Functions.
Is there a provincial exam for Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)?
No. Manitoba gives no provincial exam for Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S).
What comes after Introduction to Applied and Pre-Calculus 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 Introduction to Applied and Pre-Calculus Mathematics, Grade 10 (20S)?
Yes. MapleMind teaches every skill of Introduction to Applied and Pre-Calculus 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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