Mathematics 314
Site Lesson Plans plans for secondary III departs from the MEQ objectives and course design. Site lesson plans represent a proposal for secondary III instruction in Quebec or elsewhere.
Here in Quebec for student engagement, I would like to see secondary III recast as the year of applications of mathematics in consumer, business, construction trades, navigation and even science. And then continue with the old MEQ curriculum for Mathematics 436 minus the discussion of transformation geometry.
|
Mathematics 314 consists of the following topics
|
| The above description comes from a page describing mathematics 116, 216 and 314. I am not sure of its origin. |
The following may help with the current objectives in mathematics 314 if they are still being followed - have not been put aside by the current reform process in Quebec high schools.
A guiding focus for high school and college mathematics could be preparation for calculus. Preparation for calculus prepares for all arts, trades and disciplines involving mathematics.
The following site areas include ideas useful for mathematics 116, 216 and 314.
Logic & Algebra Solving Linear Equations with Stick Diagrams, Fractions, Ratios, Rates, Proportions & Units Euclidean Geometry, Number Theory.
Students in the first year of high school may come with a weak to non-existence command of the times table (addition table too) and with a weak to non-existence fraction sense and abilities. The most important service of first year mathematics in high school is to consolidate fraction sense and skills. See Solving Linear Equations with Stick Diagrams if your students have a weak command of fractions or if you want to develop algebraic thinking skills.
The ability to follow a multi-step process in a repeatable and reproducible manner, modulo some accidents, is a sign that the students master further multi-step operations in and outside of arithmetic. That is the skill or intelligence we seek. Start emphasizing in it in arithmetic. Calculators betray students by allowing them to skip a first example of a multi-step process in which accuracy is demanded at each and every step. The last topic, statistics, should be exploited as much as possible to develop and reinforce fraction skills and sense.
Ideas for Spatial Geometry
- Geometry: What is Area?, What is Volume? Develop idea of covering regions and solids with small squares and cubes to approximate what should be their area or volume, and say if taking smaller and smaller squares or cubes converges a single real number then that number is taken to be the area or volume of the region or solid in question. Give formulas for volumes of boxes (parallelepipeds), prism and cylinders (V = base areas time height). Review formulas for area of plane regions that may serve as a base,
- Geometry - Physical checking or confirmation of consequences of volume formulas: Show physically how the volume or capacity of a cone is one third that of a circular cylinder with same height and based. Show via a physically example how the volume or capacity of a semi-sphere plus the volume of a cone equals the volume of a circular cylinder when all have the same height and same base area.
- More Geometry: properties of transformations (movements) and the generation of further transformation from rotation, translation and reflection by their use one at a time and one after another (composition). I see this listed in a curriculum. Not quite sure what it means. Nice (?) but not necessary for a first course in calculus nor further learning for most students. Here is material that is not necessary for further instruction in mathematics at the secondary V level and beyond. This material may overwhelm and overburden students and teachers. Since it has to be taught put it last in a course.
- Still More Geometry: Polygonal nets for surface of polyhedron, Counting and relating edges, faces and vertices of polyhedron and Euler formula. Not necessary for a first course in calculus nor further learning for most students. Formulas can be verified or tested via examples. The discussion of prism could be left to a geology course which discusses crystals or a physic course which discusses lens. Nice but Not necessary for a first course in calculus nor further learning for most students - could however provide a cross-curricular activity.
- Spatial Sense and its representation: Technical Drawing, Perspective Drawing in art, and Computer Graphics may provide a context or motivation for developing and describing different view of solids. One applied project may be to draw or design, a computer support table or just a counter, or a set of shelves from a large piece of plywood or press-wood. The question here is how does draw a 3D object in a way that others can construct it. Examples of solid objects may be used to illustrate concepts.
Spatial Sense Construction Exercises
These appear to be compatible with MEQ objectives.The hand-ons or manipulative nature of these exercise may engage the boys.
| Purchase a rectangular piece of plywood or press-word and have it cut into rectangles A to E as shown. Piece E can be thrown away. Pieces B and C are identical. |  |
Attach the pieces together as shown using 15
braces and 60 short screws. |
 |
| Tools required: screwdriver
and electric drill. There is some flexibility in deciding the dimensions
of the pieces A, B, C and D. Students could make a scale model
from a piece of paper.
Note: The middle piece D of the supporting H (formed from A, B and D) is shorter than end-pieces A and B. Making all three the same height leads to imbalance problems on uneven floors. |
|
|
Other Plywood Construction Projects Book Shelves
|
 Computer Table |
| The question of how much paint is required to cover this furniture or other three dimensional objects points to a practical reason for calculating surface area. | |
More Spatial Sense Exercises:
 |
|
Physical Verification of Formulas: The calculation of volume or capacity from the product of base area times height can checked or tested in the mathematics or physical science. The foregoing shows how formula for the volume of a sphere can be related to formulas of volumes of cylinders and cones. Prior to testing formulas for volumes, we may test formulas for area calculations for circles or disks: For example, take a piece of paper or carboard with with a constant thickness and area per square unit (centimeter or inch) and verify that the weight or mass of a disk of radius R of the material is pR2 times the weight of a square unit. |
Quebec English Mathematics Education
A farce is a farce is a farce.
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