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# Foundations of Mathematics and Pre-Calculus 10

An introduction, overview, analysis, and general discussion of the new academic math 10 course.
by

## James Caudle

on 29 November 2010

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#### Transcript of Foundations of Mathematics and Pre-Calculus 10

Measurement Algebra & Number Relations & Functions 5. Polynomials 4. Exponents
& Radicals 3. Trigonometry 2. Surface Area
& Volume 1. Measurement
Systems B1. Demonstrate an understanding of factors of whole numbers by determining the:
prime factors
greatest common factor
least common multiple
square root
cube root.
[CN, ME, R] B2. Demonstrate an understanding of irrational numbers by:
representing, identifying and simplifying irrational numbers
ordering irrational numbers.
[CN, ME, R, V] B3. Demonstrate an understanding of powers with integral and rational exponents. [C, CN, PS, R] B4. Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically. [CN, R, V] B5. Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.
[C, CN, R, V]
C1. Interpret and explain the relationships among data, graphs and situations.
[C, CN, R, T, V] C2. Demonstrate an understanding of relations and functions.
[C, R, V] C3. Demonstrate an understanding of slope with respect to:
rise and run
line segments and lines
rate of change
parallel lines
perpendicular lines.
[PS, R, V] C4. Describe and represent linear relations, using:
words
ordered pairs
tables of values
graphs
equations.
[C, CN, R, V] C5. Determine the characteristics of the graphs of linear relations, including the:
intercepts
slope
domain
range.
[CN, PS, R, V] C6. 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.
[CN, R, T, V] C7. Determine the equation of a linear relation, given:
a graph
a point and the slope
two points
a point and the equation of a parallel or perpendicular line
to solve problems.
[CN, PS, R, V] C8. Represent a linear function, using function notation.
[CN, ME, V] C9. Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
[CN, PS, R, T, V] 6. Linear Relations 7. Linear Equations 8. Systems of Linear Equations:
Solving Graphically
&
9. Systems of Linear Equations:
Solving Algebraically B1. Demonstrate an understanding of factors of whole numbers by determining the:
prime factors
greatest common factor
least common multiple
square root
cube root.
[CN, ME, R] C3. Demonstrate an understanding of slope with respect to:
rise and run
line segments and lines
rate of change
parallel lines
perpendicular lines.
[PS, R, V] C4. Describe and represent linear relations, using:
words
ordered pairs
tables of values
graphs
equations.
[C, CN, R, V] C5. Determine the characteristics of the graphs of linear relations, including the:
intercepts
slope
domain
range.
[CN, PS, R, V] 25% of class time* 30% of class time* 45% of class time* * Foundations of Mathematics
& Pre-Calculus 10 Foundations of
Mathematics 11 Foundations of
Mathematics 12 Pre-Calculus 11 Pre-Calculus 12 Mathematics 9 Apprenticeship & Workplace Mathematics 10 Apprenticeship & Workplace Mathematics 11 Apprenticeship & Workplace Mathematics 12 You got your minimal university entrance requirement! Note: Only a very small percentage of students actually make it into university programs with only Principles 11; this trend will likely continue. But now you hate math because it wasn't the math that interested you, that you were good at, or that you actually need. see http://www.bced.gov.bc.ca/irp/program_delivery/choosing_high_school_pathways.pdf While some universities (SFU) might treat the two streams as "equal," others such as UVic & UBC accept Foundations 12 and Pre-Calc 11 as equivalent for the purposes of admission requirements. WNCP Mathematics Curriculum Structure Perfect for future studies in... fine arts social sciences humanities most of the time - eg. psychology? science & mathematics engineering business & finance Perfect for future studies in... The BC Ed. overview:
http://www.bced.gov.bc.ca/irp/program_delivery/high_school_pathways_01122010.pdf ...where calculus is not involved. ...where calculus is studied A1. Solve problems that involve linear measurement, using:
SI and imperial units of measure
estimation strategies
measurement strategies.
[ME, PS, V] A2. Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
[C, ME, PS] A3. 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.
[CN, PS, R, V] A4. Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.
[C, CN, PS, R, T, V] What's Changed? } Note: Foundations or Pre-Calculus courses have no real "less math courses" advantage over Apprenticeship & Workplace courses! And are not nearly as relevant! } How do we advise our students? What are their interests? What kind of math do they enjoy? What kind of math are they good at? What do they want to "be when they grow up?" What about "keeping doors open?" What does that really mean?
Is the door really closed if you don't take a certain math course now? Is the door really open if you hate it and are no good at it? { We can talk to our students as a group and as individuals. But how do we educate the parents? brochures? info nights? email? New Stuff Gone Stuff Changed Stuff sequences & series (entire unit)
rational expressions (entire unit)
linear equations: partial & direct variation
cosine/sine laws
trig with angles >90
polynomial division
coordinate geometry: distance, midpoint Don't teach it! You'll ruin it for everyone! trig: 2 triangle problems in AI, not PLO
linear equations are no longer viewed through the "lens" of coordinate geometry
heavy emphasis on linear relations (a student-familiar vehicle for introducting functions and relations) measurement systems (proportional thinking and estimation)
surface area & volume
factors, GCF, LCM
systems of equations
basic trig (25%?) (50%?) Resources F&PC 10 Curriculum
http://www.bced.gov.bc.ca/irp/pdfs/mathematics/WNCPmath1012/2008math_foundations_precalc10.pdf Principles 10 Curriculum
http://www.bced.gov.bc.ca/irp/pdfs/mathematics/2006prinofmath1012.pdf BC Ed WNCP Overview
http://www.bced.gov.bc.ca/irp/pdfs/mathematics/support_materials/high_school_pathways_01122010.pdf BC Ed: Choosing a Pathway
http://www.bced.gov.bc.ca/irp/pdfs/mathematics/support_materials/choosing_high_school_pathways.pdf Yukon Math 10 Wiki
abstraction
algebra
trigonometry
combinatorics logical reasoning
financial math
measurement
geometry
applied functions
statistics
probability

The textbook matches this well! Processes of Mathematics Reasoning
Technology

Connections
Visualization
Communication
Problem Solving
Mental Mathematics & Estimation
Full transcript