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314 Check List   [ Back ] [ Up ] [ Next ]

Mathematics 314
A Secondary III Course

This is a third year high school mathematics course taught in Quebec. A list of the intermediate objectives in the Quebec government course below provide a skills and concept checklist for the pre-reform 314 course. For the sake of clarity, compare and contrast with the content objectives in the current reform program.

The immediate objectives here come from the Quebec government course objectives online in a  pfd file

My comments and reflections on mathematics 216 are preceded by (W:) in order to distinguish between them from the MEQ objectives as is or paraphrased. 

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

1.1 Intermediate Objectives 

use algebra

  1. Determine the dependent variable and the independent variable in a given situation. 
  2. Represent a rule that applies in a given situation, using a table of values. 
  3. Represent a situation and its corresponding rule by means of a graph, given a table of values. (w) The word rule here may mean a formula.
  4. 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.

1.2 Intermediate Objectives

Solve problems related to situations in which a linear relationship exists between the variables 

  1. Translate a situation involving direct variation or partial variation into an equation. 
  2.  Translate an equation involving direct variation or partial variation into a word problem. 
  3. Determine the rate of change in a situation involving direct variation or partial variation, given the corresponding equation or graph.
  4. 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.

Intermediate Objectives 1.3 

Convert an arithmetic or algebraic expression
 into an equivalent expression 

  1. Apply the properties of exponents in transforming arithmetic expressions. 
  2. Apply the following properties in transforming algebraic expressions:

  3. Add and subtract polynomials. 
  4. Multiply a monomial by a polynomial and a binomial by a binomial.  
  5. Divide a polynomial by a monomial.

Intermediate Objectives 1.4

Solve problems using the Pythagorean theorem

  1. To express the Pythagorean relationship between the measures of the sides of a right triangle, using variables. 
  2. To justify an assertion used in solving a problem that involves applying the Pythagorean theorem. See appendix. 
  3. To locate some irrational numbers on a number line.

The appendix provides two examples:

  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 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 sides.

Intermediate Objectives 2.1

Solve problems involving isometries or dilatations

  1. Construct the image of a figure under a composite of transformations.
  2. Describe the inverse of different transformations of the plane.
  3. Identify the transformation that is equivalent to a given composite of transformations.
  4. To state the main properties of the different transformations.*

Intermediate Objectives 2.2

Solve problems involving three-dimensional objects 

  1. describe three-dimensional objects, using words or drawings. 
  2. represent three-dimensional objects in two dimensions. • 
  3. build a three-dimensional object on the basis of a description or a drawing.

Intermediate Objectives 2.3

To solve problems involving solids

  1. generate a cone, sphere or cylinder by rotating a figure 360 degrees about an axis. 
  2. generate a prism by translating a polygon. 
  3. Represent solids in two or three dimensions. 
    (w) What does this mean?
  4. classify solids. 
  5. split a cube into sections to obtain a solid with one triangular or quadrilateral face. 
  6. Deduce the measure of a segment from an appropriate definition or property. See appendices.
  7. justify an assertion used in solving a problem involving solids. See Appendices

Intermediate Objectives 2.4

solve problems related to the area or volume of certain solids

  1. distinguish between situations in which the area should be calculated and those in which the volume should be calculated. 
  2. calculate the area of solids that can be broken up into right solids or hemispheres.
  3. express the relationship between the volume of a solid and some of its measures.
  4. calculate the volume of objects that can be broken up into right solids or hemispheres. 
  5. convert a measure of volume from one unit to another.
  6. establish the connection between units of volume and units of capacity.
  7. calculate a measure of a solid, given its area and sufficient data. 
  8. calculate a measure of a solid, given its volume and sufficient data. 
  9. justify an assertion used in solving a problem involving solids. See Appendix

Intermediate Objectives 3.1

analyze statistical data -  situations represented by a one-variable statistical distribution

  1. tabulate data. 
  2. present data in the form of a histogram. 
  3. calculate the mean, median, mode and range of a distribution consisting of data that has not been grouped into classes
  4. derive qualitative information about a distribution from its mean, median, mode or range.
  5. describe a distribution, given its mean, median, mode or range.

Appendix

Geometric Statements
Covered in Mathematics 314 

  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 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 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. 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 the measures of angles.

  5. Any translation and any dilatation will transform a straight line into another line parallel to it.

Geometric Statements
Studied in Mathematics 116

  1.  Adjacent angles whose external sides are in a straight line are supplementary.
  2. Vertical angles are congruent. 
  3. The sum of the measures of the interior angles of a triangle is 180degrees.
  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 of the angles measures 60degrees.
  9. In any right triangle, the acute angles are complementary. 
  10. In any isosceles right triangle, each of the acute angles measures 45 degrees.
  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.

Geometric Statements
Studied in Mathematics 216

 The diagonals from one vertex of a convex polygon form n - 2 triangles, where n is the number of sides in that polygon. 

  1.  In a convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 3600. 
  2. The sum of the measures of the interior angles of a polygon is 1800(n - 2), where n is the number of sides in the polygon. 
  3. Three non-collinear points determine one and only one circle. 
  4. All the perpendicular bisectors of the chords of a circle meet at the centre of that circle. 
  5. All the diameters of a circle are congruent. 
  6. In a circle, the measure of the radius is half the measure of the diameter. 
  7. The axes of symmetry of a circle contain its centre. 
  8. The ratio of the circumference of a circle to its diameter is a constant known as p. 
  9.  In a circle, the measure of the central angle is equal to the measure of its intercepted arc. 
  10.  In a circle, the ratio of the measures of two central angles is equal to the ratio of the measures of their intercepted arcs.

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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