Math Secondary One
563-100
The secondary one math program has three main competencies listed below. Each competency has key areas and main criteria
to be learned. As well, a global objective specific to secondary one is to help students acquire skills prerequisite to the study of
algebra.
Key areas
To solve problems involving
several operations on
natural numbers
(16% of year)
Competency/Skill 1
To help students develop number and operation sense (52% of year)
To associate the power of a given natural number with its exponential notation and vice versa.
To write a natural number as a product of prime factors.
(9% of year)
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To calculate the value of a chain of operations on natural numbers, following the order of
operations. The chain may include one or two sets of parentheses.
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To express a given natural number, using one or more operations and following the rules of writing
associated with the order of operations.
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To generate equivalent numerical expressions, each containing one or more arithmetic operations,
using, for example, the properties of the operations and of the equivalent relation.
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To translate a chain of operations on natural numbers into a verbal problem.
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To explain in their own words the rule relating a number and its rank in a sequence.
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To express in symbolic language the rule relating a number and its rank in a sequence
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To use the rule relating a number and its rank in a sequence to find either the number occupying a
certain rank in the sequence or the rank of a number belonging to the sequence.
Key areas
To apply algorithms to
integers in various
situations
Check when
completed
To compare integers.
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To perform the following operations on integers: addition, subtraction, multiplication, division and
exponentiation (exponents should be limited to the positive integers).
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To calculate the value of a chain of operation performed on integers, following the order of
operations. The chain may include one or two sets of parentheses.
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To express a given integer, performing one or more operations and following the rules of writing
associated with the order of operations.
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Key areas
To apply algorithms to
integers in various
situations
Continued…Competency/Skill 1
To help students develop number and operation sense
To read a rational number expressed in decimal notation.
(15% of year)
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To write a rational number in decimal notation.
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To order rational numbers expressed in decimal notation.
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To write a decimal number in expanded form, and vice versa
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To round off a rational number expressed in decimal notation (the order of magnitude will either be
given, or determined by the context).
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To convert a rational number from decimal notation to scientific notation, and vice versa.
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To convert a decimal number from decimal notation to fractional notation (a/b).
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To convert a rational number from fractional notation (a/b) to decimal notation.
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To convert a decimal number into a percentage, and vice versa.
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To convert a rational number from fractional notation (a/b) into a percentage.
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To perform the following operations on decimal numbers: addition, subtraction, multiplication,
division and exponentiation (exponents should be limited to the positive integers).
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To calculate the value of a chain of operations on decimal numbers. The chain may include one or
two sets of parentheses.
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To convert a fraction into an equivalent fraction.
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To compare fractions.
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To perform the following operations on fractions: addition, subtraction, multiplication, division and
exponentiation (exponents should be limited to the positive integers).
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To calculate the value of a chain of operations on fractions. The chain may include one or two sets
of parentheses.
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(12% of year)
Key areas
To solve problems involving
rational numbers
Check when
completed
Competency/Skill 2
To enable students to apply their knowledge of geometric figures (36% of year)
Key areas
To construct the image of a figure under a translation.
To create figures by means
To construct the image of a figure under a rotation.
of isometric
transformations
To construct the image of a figure under a reflection.
(7.25% of year)
To construct the axis or axes of symmetry of an angle (bisector), of a segment (median) or of a
polygon.
Key areas
To solve problems involving
straight lines or angles
To identify segments whose straight lines are parallel or perpendicular.
(7.25% of year)
To measure an angle in various figures.
To construct a straight line parallel or perpendicular to another straight line, in accordance with
certain requirements.
To construct angles with the same vertex, using a protractor.
To determine the measure of an angle on the basis of a statement (flat, straight or full angle;
perpendicular lines; complement, supplement or bisector of an angle; angles with the same
vertex).
To justify an assertion in solving a problem involving angles with the same vertex.
Key areas
To solve problems involving
triangles
To construct a triangle given the measures of the three sides, the measures of two angles and the
adjacent side, or the measures of one angle and two adjacent sides.
(7.25% of year)
To express the relationships between the various types of triangles.
To construct the altitudes, medians, and perpendicular bisectors of a triangle.
To determine the measure of an angle or a segment on the basis of a statement pertaining to the
various types of triangles, or to the altitudes, medians or perpendicular bisectors of triangles.
To justify an assertion in solving a problem involving triangles.
Check when
completed
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Key areas
To solve problems involving
convex quadrilaterals
(7% of year)
Key areas
To solve problems involving
the perimeter or the area of
certain polygons
(7.25% of year)
Continued…Competency/Skill 2
To enable students to apply their knowledge of geometric figures
To construct a quadrilateral, given sufficient data.
Check when
completed
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To express the relationships between the various types of convex quadrilaterals.
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To determine the measure of an angle or a segment on the basis of a statement pertaining to the
various types of convex quadrilaterals.
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To justify an assertion used in solving a problem involving convex quadrilaterals.
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To distinguish between situations in which it is appropriate to calculate the area and those in which
it is appropriate to calculate the perimeter
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To calculate the perimeter of a triangle or a quadrilateral, given sufficient data.
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To express the relationship between the perimeter and the sides of a triangle or a quadrilateral,
using variables and taking into account the characteristics of the different types of figures.
To calculate the length of one side of a triangle or a quadrilateral, given the perimeter and
sufficient data.
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To convert a measure of length from one unit to another.
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To calculate the area of a triangle or a trapezoid, given sufficient data.
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To express the relationship between the area and certain dimensions of a triangle or a trapezoid,
using variables.
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To convert a measure of surface area from one unit to another.
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To calculate the perimeter or area of a polygon by
transforming it or breaking it down into triangles trapezoids
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Key areas
To interpret tables and
graphs
Competency/Skill 3
To enable students to work with representation of statistical data (12% of year)
To interpret the information in a table.
Check when
completed
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To interpret the information in various graphs.
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To tabulate data.
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To present data in a horizontal or vertical bar graph.
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To present data in a broken-line graph.
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To present data in a circle graph.
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To highlight a detail in a table or graph.
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(4% of year)
Key areas
To present information
about a situation by means
of a table or graph
(8% of year)
For more information please refer to
http://www.meq.gouv.qc.ca/DGFJ/dp/programmes_etudes/secondaire/pdf/mata116.pdf
http://www.qesnrecit.qc.ca/mst/math116.php
Math Secondary Two 568-216
The secondary two math program has four main competencies listed below. Each competency has key areas and main criteria to
be learned.
Competency/Skill 1
To help student develop the ability to use algebra to solve problems (25% of year)
To express the relationship among the data in a problem, using his or her own words or a drawing.
Key areas
To translate one
representation of a situation
into another
(7% of year)
To give a comprehensive description of a situation represented by a table of values.
To give a comprehensive description of a situation represented by a graph.
To represent a situation, using a table of values.
To represent a situation comprehensively, using a graph.
Key areas
To solve problems that can
be expressed as a firstdegree equation
(18% of year)
To express the relationships among the data in a problem, using his/ her own words or a drawing.
To translate a verbal problem into an equation.
To translate an equation into a verbal problem.
To add and subtract expressions containing one variable and constants.
To multiply and divide by a constant expression containing one variable and constants.
To solve a first-degree equation containing one unknown
Check when
completed
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Competency/Skill 2
To help student develop their proportional-reasoning ability (25% of year)
Key areas
To translate a situation into a ratio or a rate.
To solve problems involving
To interpret a ratio or a rate.
ratios and rates
To compare a ratio or rate.
(8% of year)
To interpret, for a given situation, the effect of a change in one of the quantities that form a ratio or
Check when
completed
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a rate.
Key areas
To solve problems involving
proportions and
percentages
(17% of year)
To indicate the change(s) made to the quantities that form a ratio or a rate, given the qualitative
direction of change in the value of that ratio or rate.
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To distinguish situations that involve proportions from situations that do not.
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To establish a proportion.
To establish a series of proportions.
To apply the properties of equal ratios.
To express the ratio between two numbers as a percentage.
To calculate a given percentage of a number.
To determine the number corresponding to one hundred percent, given a number and the
percentage value it represents.
Competency/Skill 3
To enable students to apply their knowledge of geometric figures (35% of year)
Key areas
To construct the image of a figure under a similarity transformation. The ratio of similitude may be
To solve problems that
positive or negative.
involve enlarging or
To determine the ratio of similitude, given a figure and its image.
reducing a figure
To distinguish figures that are similar from those that are not, given a set of figures.
(8% of year)
Key areas
To determine the position of a point in a Cartesian plane.
To solve problems involving
To express the relationship between a point and its image by means of variables. The relationship
isometric or similar figures
may represent a translation, a similarity transformation (the centre must be at the origin), a rotation
in a Cartesian plane
(the rotation angle must be a multiple of 90° and the centre must be at the origin) or a reflection
(with respect to the axes or the bisectors of the quadrants).
(8% of year)
To identify a transformation by indicating the rule that describes it, given a figure and its image.
To construct the image of a given figure by performing a given operation on its coordinates and
applying a transformation rule.
Key areas
To solve problems involving
polygons
(11% of year)
To construct a 5-, 6-, 8- or 10-sided regular polygon, given sufficient data
To construct the axes of symmetry of a regular polygon.
To express the relationship between the perimeter of a regular polygon and the measure of its
side, using variables.
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To calculate the perimeter and area of a regular polygon, given sufficient data.
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To calculate the measure of one of the dimensions of a triangle, a trapezium or a regular polygon,
given its area and sufficient data.
To construct a circle, given sufficient data.
To express the relationship between the circumference of a circle and its radius, using variables.
To calculate the circumference of a circle, given sufficient data.
(8% of year)
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To express the relationship between the area of a regular polygon and some of its dimensions,
using variables.
To determine the square root of a number.
Key areas
To solve problems involving
circles
Check when
completed
To express the relationship between the area of a circle and its radius.
To calculate the area of a circle, given sufficient data.
To calculate the radius of a circle, given sufficient data.
To justify an assertion used in solving a problem involving circles.
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Competency/Skill 4
To introduce students to the mathematical interpretation of phenomena involving chance (15% of year)
Key areas
To distinguish experiments that are random from those that are not.
To solve problems that
To enumerate some of the outcomes of a random experiment.
involve calculating the
probabilities of the outcome To list all the possible outcomes of a random experiment.
of a random experiment
To assign a probability value to one of the outcomes of a random experiment.
(8% of year)
Key areas
To solve problems that
involve calculating the
probability of certain events
during a random experiment
To identify complementary events.
To identify mutually exclusive events.
To calculate the probability of an event.
(7% of year)
For more information please refer to
http://www.meq.gouv.qc.ca/DGFJ/dp/programmes_etudes/secondaire/pdf/math216a.pdf
http://www.qesnrecit.qc.ca/mst/math216.php
Check when
completed
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Math Secondary Three
568-314
The secondary three math program has three main competencies listed below. Each competency has key areas and main criteria
to be learned.
Competency/Skill 1
To help students learn to use algebra to generalize situations (45% of year)
To determine the dependent variable and the independent variable in a given situation.
Key areas
To illustrate the type of
dependence characterizing
the relationship between the
variables in a situation
(9% of year)
Key areas
To solve problems related
to situations in which a
linear relationship exists
between the variables
(12% of year)
Key areas
To convert an arithmetic or
algebraic expression into an
equivalent expression
(14% of year)
To represent the rule that applies in a given situation, using a table of values.
To represent a situation and its corresponding rule by means of a graph, given a table of values.
Check when
completed
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To express in their own words the relationship between the variables in a specific situation, given
the description of that situation, a table of values or a graph.
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To translate a situation involving direct variation or partial variation into an equation.
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To translate an equation involving direct variation or partial variation into a word problem.
To determine the rate of change in a situation involving direct variation or partial variation, given
the corresponding equation or graph.
To provide a qualitative description of how a parameter change will affect a graph, given the
equation for a situation involving direct variation or partial variation.
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To apply the properties of exponents in transforming arithmetic expressions.
To apply the following properties in transforming algebraic expressions:
a
a
a+b
n ·n =n where a,b  N
a
a-b
n =n where a,b  N
b
n
To add and subtract polynomials.
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To multiply a monomial by a polynomial and a binomial by a binomial.
To divide a polynomial by a monomial.
Key areas
To solve problems using
the Pythagorean theorem
To express the Pythagorean relationship between the measures of the sides of a right triangle,
using variables.
(10% of year)
To locate some irrational numbers on a number line.
To justify an assertion used in solving a problem that involves applying the Pythagorean theorem.
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Competency/Skill 2
To enable students to apply their knowledge of geometric figures (40% of year)
Key areas
To construct the image of a figure under a composite of transformations.
To solve problems involving
To describe the inverse of different transformations of the plane.
isometries or dilatations
To identify the transformation that is equivalent to a given composite of transformations.
(13% of year)
To state the main properties of the different transformations.
Key areas
To solve problems involving
three-dimensional objects
To describe three-dimensional objects, using words or drawings.
To represent three-dimensional objects in two dimensions.
To build a three-dimensional object on the basis of a description or a drawing.
(7% of year)
Key areas
To solve problems involving
solids
To generate a cone, sphere or cylinder by rotating a figure 360° about an axis.
To generate a prism by translating a polygon.
To represent solids in two or three dimensions.
(7% of year)
To classify solids.
To split a cube into sections to obtain a solid with one triangular or quadrilateral face.
To deduce the measure of a segment from an appropriate definition or property.
To justify an assertion used in solving a problem involving solids.
Key areas
To solve problems related to
the area or volume of certain
solids
(13% of year)
To distinguish between situations in which the area should be calculated and those in which the
volume should be calculated.
To calculate the area of solids that can be broken up into right solids or hemispheres
To express the relationship between the volume of a solid and some of its measures.
To calculate the volume of objects that can be broken up into right solids or hemispheres.
To convert a measure of volume from one unit to another.
To establish the connection between units of volume and units of capacity.
To calculate a measure of a solid, given its area and sufficient data.
To calculate a measure of a solid, given its volume and sufficient data.
To justify an assertion used in solving a problem involving solids.
Check when
completed
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Competency/Skill 3
To help students develop the ability to analyze statistical data (15% of year)
Key areas
To tabulate data.
To solve problems involving
situations represented by
To present data in the form of a histogram.
one-variable statistical
distribution
To calculate the mean, median, mode and range of a distribution consisting of data that has not
been grouped into classes.
(15% of year)
To derive qualitative information about a distribution from its mean, median, mode or range.
To describe a distribution, given its mean, median, mode or range.
For more information please refer to
http://www.meq.gouv.qc.ca/DGFJ/dp/programmes_etudes/secondaire/pdf/mata314.pdf
http://www.qesnrecit.qc.ca/mst/math314.php
Check when
completed
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Math Secondary Four
568-416
The secondary four (416) math program has three main competencies listed below. Each competency has key areas and main
criteria to be learned.
Key areas
To analyze variations using
different modes of
representation
(17% of year)
Key areas
To solve problems dealing
with systems of linear
relations
(21% of year)
Key areas
To solve problems using
the concept of similarity
(20% of year)
Key areas
To solve problems using
trigonometric ratios
(18% of year)
Competency/Skill 1
To help students apply their knowledge of algebra (38% of year)
To determine the dependent variable and the independent variable in a given situation.
Check when
completed
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To determine the most appropriate scale for the graph of a given situation.
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To draw a graph representing a particular situation, given a table of values.
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To compare different situations expressed by means of the same mode of representation.
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To represent a situation by a system of linear relations.
To describe a real-life situation expressed as a system of linear relations.
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To make a table of values for a given situation.
To make a table of values for a system of linear relations.
To determine the most appropriate scale for the graph of a system of linear relations.
To draw a graph representing a system of linear relations.
To justify the interpretation of a system of linear relations by using one or more modes of
representation.
To determine specific values of a system of linear relations with the degree of precision required
for that situation.
Competency/Skill 2
To enable students to analyze geometric situations (38% of year)
To distinguish similar or isometric figures from those that are not.
To describe a similarity transformation or an isometry involving two polygons.
To support an assertion used in presenting a proof involving the concepts of similarity or isometry.
To deduce certain measures in similar figures from an appropriate geometric principle.
To justify an assertion used to solve a problem involving the concept of similarity.
To deduce the measures of a right triangle using trigonometric ratios.
To deduce the measures of triangles from various geometric principles.
To justify an assertion used to solve a problem.
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Check when
completed
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Key areas
To solve problems that
involve gathering data
Competency/Skill 3
To help students develop the ability to analyze statistical data (24% of year)
To distinguish between a sample and a population.
To justify the decision to prepare a census, a poll or a study to obtain information.
To describe the characteristics of a representative sample of a given population.
(10% of year)
To choose an appropriate sampling method when gathering data.
To determine the possible sources of bias when gathering data.
To compare two samples from the same population.
Key areas
To solve problems using
measures of position
To distinguish between measures of central tendency, measures of position and measures of
dispersion
(14% of year)
To determine the data value(s) that are assigned a given rank.
To assign a quintile, a quartile or a percentile rank to a data value in a distribution.
To use measures of position to compare data.
To construct a box-and-whisker plot.
To interpret a box-and-whisker plot.
To find qualitative information about the dispersion of the data in a one-variable distribution, using
measures of position and measures of central tendency.
For more information please refer to
http://www.meq.gouv.qc.ca/DGFJ/dp/programmes_etudes/secondaire/mata416.htm
or
http://www.qesnrecit.qc.ca/mst/math416.php
Check when
completed
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Math Secondary Five
568-514
The secondary five (514) math program has three main competencies listed below. Each competency has key areas and main
criteria to be learned.
Key areas
To solve problems using a
graph
Competency/Skill 1
To help the students learn to apply optimization techniques (50% of year)
To represent a situation by a graph, a directed graph (digraph) or a weighted graph.
(22% of year)
To distinguish between a path and a circuit.
To use Euler's path or circuit, Hamilton's path or circuit, or a weighted tree diagram to determine
an optimum solution.
To interpret a graph.
To justify a statement made in solving a problem that involves using a graph.
Key areas
To solve problems using a
system of linear inequalities
To represent a situation using a system of linear inequalities.
To graph a system of linear inequalities.
To formulate an algebraic expression that will represent the function to be optimized.
(28% of year)
To determine the best solution(s) for a particular situation, given a number of different possibilities.
To justify the choice of values that optimize the function.
Competency/Skill 2
To help the students develop their ability to analyze statistical data or data related to probabilities (30% of year)
Key areas
To construct a two-variable distribution table.
To solve problems using
To construct a scatter plot.
the concept of correlation
To describe the correlation between two variables in one's own words.
(12% of year)
To estimate the correlation coefficient.
To interpret the correlation between two variables.
Key areas
To solve problems using
probabilities
To distinguish between odds (for or against) and probability.
(18% of year)
To calculate the mathematical expectation of a random variable.
To evaluate the probability that an event will occur during a random experiment, knowing that
another event has occurred during that experiment.
To interpret the mathematical expectation of a random variable.
Competency/Skill 3
Check when
completed
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Check when
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Check when
Key areas
To solve problems using
the concept of distance
(12% of year)
To have the students analyze geometric situations (20% of year)
To calculate the distance between two points.
To determine the coordinates of the point on a line segment which divides that segment in a given
ratio.
To compare distances.
To justify a statement in the solution of a problem.
Key areas
To solve problems using
the concept of probability in
a geometric context
To estimate the probability of an event in a geometric context.
To calculate the probability of an event in a geometric context.
To justify a statement in the solution of a problem.
(8% of year)
For more information please refer to
http://www.meq.gouv.qc.ca/DGFJ/dp/programmes_etudes/secondaire/pdf/mata514.pdf
http://www.qesnrecit.qc.ca/mst/math514.php
completed
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