Intermediate Objectives
The global objectives of the courses are described at length in
the Quebec government document found in this pdf
file The intermediate objectives extracted below and annotated give a skill
and concept checklist.
My comments and reflections are
preceded by (W:) in order to distinguish between them from the MEQ objectives
as is or paraphrased.
Some words to explain "Modes of Representation"
will follow later.
| Intermediate Objectives:
Objectives that specify the scope of a terminal objective,
intermediate objectives might also be described as "reference.
objectives." They are not intended as a series of steps to be
completed one after the other. Such a process would give a very fragmented
picture of teaching and learning. Rather, intermediate objectives are:
-
Aspects of a theme that have been chosen for the
program.
-
Clarifications to ensure that the terminal objective
is clearly understood
-
Guidelines that indicate the relationship between the
terminal objective and student learning
-
Prerequisites for attaining a terminal objective
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Connections With Previous Studies
Students will review the following skills and concepts acquired in previous
programs:
- number sense and facility with operations;
- the habit of estimating;
- proportionality;
- the concept of a variable;
- translation from one mode of representation to another;
- the types of dependence characterizing the relationship between variables;
- definitions, properties, theorems or corollaries related to different
geometric concepts;
- spatial relationships;
- the ability to organize and process statistical data;
- simulation of random events and the concept of probability
OBJECTIVE 1 - apply algebra
Intermediate Objective 1.1
analyze variations (W: functional dependence)
- determine the dependent variable and the independent variable in a given
situation.
- make a table of values for a given situation.
- determine the most appropriate scale for the graph of a given
situation.
- draw a graph representing a particular situation, given a table of
values.
- compare different situations expressed by means of the same mode of
representation.
Intermediate Objective 1.2
Solve problems dealing with systems of linear relations
- To represent a situation by a system of linear relations.
- To describe a real-life situation expressed as a system of linear
relations.
- 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
OBJECTIVE 2
To enable students to analyze geometric situations
Intermediate Objective 2.1
master the concept of similarity
- 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
See Appendix for geometric facts known to students.
Intermediate Objective 2.2
solve problems using trigonometric ratios
- 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
OBJECTIVE 3 - analyze data
Intermediate Objective 3.1
gathering data
- distinguish between a sample and a population.
- justify the decision to prepare a census, a poll or a study to obtain
information.
- describe the characteristics of a representative sample of a given
population.
- choose an appropriate sampling method when gathering data.
- determine the possible sources of bias when gathering data.
- compare two samples from the same population
Intermediate Objective 3.2
using measures of position
- distinguish between measures of central tendency, measures of position and
measures of dispersion.
- assign a quintile, a quartile or a percentile rank to a data value in a
distribution.
- determine the data value(s) that are assigned a given rank.
- use measures of position to compare data.
- construct a box-and-whisker plot.
- interpret a box-and-whisker plot.
- find qualitative information about the dispersion of the data in a
one-variable distribution, using measures of position and measures of
central tendency.
Appendices - Geometric Principles
Principles Related to Themes Introduced in Mathematics 416
Through their activities in geometry, the students increase their
understanding of concepts and perfect several skills. Using definitions,
properties, theorems and corollaries related to similarity or certain
relations dealing with measurements in a triangle, they can deduce
measures and justify an assertion used to present a proof or solve a
problem.
1. The term figure designates a plane figure or a solid below.
- If two corresponding (or alternate interior or alternate exterior)
angles are congruent, then they are formed by two parallel lines and a
transversal.
- If a transversal intersects two parallel lines then:
- the alternate interior angles are congruent;
- the alternate exterior angles are congruent;
- the corresponding angles are congruent.
- The angles and sides of isometric figures 1 are equal in measure.
- Figures are isometric if and only if there is an isometry or a
composite of isometries that makes one figure coincide with the other.
- Two triangles whose corresponding sides are congruent must be
congruent.
- If two sides and the contained angle of one triangle are congruent
to two sides and the contained angle of another triangle, then the
triangles must be congruent.
- If two angles and the contained side of one triangle are congruent
to two angles and the contained side of another triangle, then the
triangles must be congruent.
- Transversals intersected by parallel lines are divided into segments
of proportional lengths.
- Any straight line that intersects two sides of a triangle and is
parallel to a third side forms a smaller triangle similar to the
larger triangle.
- The line segment joining the midpoints of two sides of a triangle is
parallel to the third side and its length is one- half the length of
the third side.
- Similar figures have congruent corresponding angles and proportional
corresponding sides.
- Two figures are similar if and only if there is a dilatation or a
composite of transformations that preserves the order of points, the
measures of the corresponding angles and the ratio of the
corresponding sides.
- If two angles of one triangle are congruent to two angles of another
triangle, then the triangles must be similar.
- If the lengths of the corresponding sides of two triangles are in
proportion, then the triangles must be similar.
- If the lengths of two sides of one triangle are proportional to the
lengths of two sides of another triangle and the contained angles are
isometric, then the triangles are similar.
- In similar plane figures or solids:
- the ratio between the measures of the corresponding angles is 1;
- the ratio between the lengths of the corresponding segments is equal
to the ratio between the lengths of the corresponding sides;
- the ratio of the areas is equal to the square of the ratio between
the lengths of the corresponding sides;
- the ratio of the volumes is equal to the cube of the ratio between
the lengths of the corresponding sides.
- Plane figures or solids with a scale factor of 1 are
isometric.
- In a right triangle, the length of the side opposite a 30o
angle is equal to half the length of the hypotenuse.
- Hero's or Heron's Formula
The area of a triang whose sides measure a, b and c is
S = sqrt( p(p-a)(p-b)(p-c) )
where p = (½)(a+b+c) is the semi- or half-perimeter of the
triangle.
- The law of sines: The lengths of the sides of any triangle
are proportional to the sines of the angles opposite these
sides.
a
sin A |
= |
b
sin B |
= |
c
sin C |
(w): the common value of the these three ratios gives the
proportionality constant.
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Appendices
Geometrically Statements and Assertions in previous courses
In the Secondary I, II, III and IV mathematics programs, the students
gradually built up a system of axioms.
MEQ: Connection to 514
Using the principles listed below, the students can deduce certain
measurements and justify certain steps involved in solving problems.
They will thus be able to structure an argument and present simple
proofs.
W: That being said by the MEQ, where proofs occur in this
course?
Secondary I Program
1. Adjacent angles whose external sides are in a straight line are
supplementary.
2. Vertically opposite angles are congruent.
3. The sum of the measures of the interior angles of a triangle is
180º.
4. In any triangle, the length of any side is less than the sum of
the lengths of the other two sides.
5. In any triangle, the length of any side is greater than the
difference of the lengths of the other two sides.
6. In any triangle, the longest side is opposite the largest angle.
7. In any isosceles triangle, the angles opposite the congruent sides
are congruent.
8. In any equilateral triangle, each angle measures 60º.
9. In any right triangle, the acute angles are complementary.
10. In any isosceles right triangle, each acute angle measures 45º.
11. The axis of symmetry of an isosceles triangle contains a median,
a perpendicular bisector, an angle bisector and an altitude of the
triangle.
12. The axes of symmetry of an equilateral triangle contain the
medians, perpendicular bisectors, angle bisectors and altitudes of the
triangle.
13. The opposite angles of a parallelogram are congruent.
14. The opposite sides of a parallelogram are congruent. 15. The
diagonals of a parallelogram bisect each other. 16. The diagonals of a
rectangle are congruent. 17. The diagonals of a rhombus are
perpendicular to each other.
15. The diagonals of a parallelogram bisect each other.
16. The diagonals of a rectangle are congruent.
17. The diagonals of a rhombus are perpendicular to each
other.
Secondary II Program
1. The diagonals from one vertex of a convex polygon form n - 2
triangles, where n is the number of sides in that polygon.
2. In a convex polygon, the sum of the measures of the exterior angles,
one at each vertex, is 360º.
3. The sum of the measures of the interior angles of a polygon is
180º (n - 2), where n is the number of sides in the polygon.
4. Three non-collinear points determine one and only one circle.
5. All the perpendicular bisectors of the chords of a circle meet at
the centre of that circle.
6. All the diameters of a circle are congruent. 7. In a circle, the
measure of the radius is half the measure of the diameter.
8. The axes of symmetry of a circle contain its centre.
9. The ratio of the circumference of a circle to its diameter is a
constant known as .
10. In a circle, the measure of the central angle is equal to the
measure of its intercepted arc.
11. In a circle, the ratio of the measures of two central angles is
equal to the ratio of the measures of their intercepted arcs.
Secondary III Program
1. In a right triangle, the square of the length of the hypotenuse is
equal to the sum of the squares of the lengths of the other two sides.
2. A triangle is right-angled if the square of the length of one of its
sides is equal to the sum of the squares of the lengths of the other two
sides.
3. In any convex polyhedron, the sum of the number of vertices and
the number of faces is equal to the number of edges plus two.
4. Any translation and any dilatation will transform a straight line
into another line parallel to it.
5. Isometries or dilatations have one or more of the following
properties :
- they preserve collinearity;
- they preserve parallelism;
- they preserve the order of points;
- they preserve the orientation of the plane;
- they preserve distances and measures of angles.
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Quebec English Mathematics Education
A farce is a farce is a farce.
Area Intro
Copy Right Matters
Curriculum Cuts
Intermediate Objectives
MEQ Objectives
116 Textbooks
116 Objectives
116 Check List
116 Suggestions
216 Objectives
216 Check List
216 Book Review
216 Nonsense or BullShit
216 Suggestions
314 Objectives
314 Check List
314 Suggestions
416 Objectives
416 Check List
416 Suggestions
436 Objectives
436 Checklist
436 Suggestions
436 Book Reviews
436 Nonsense in
514 Objectives
514 Suggestions
514 Book Reviews
536 Objectives
536 Suggestions
536 Book Reviews
Area pages represent an effort to follow and understand the objectives of the
1997-2005, the prior reform, and the
text books required and used 1997-2005. In retrospect, the objectives and texts
in question
are too incoherent, too full of nonsense, for rational comprehension and for
service as a base for the current reform. A farce is a farce,
is a farce
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