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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

Tweet## James Caudle

on 29 November 2010#### 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

http://yukon-education-math-grade-10.wikispaces.com/ functions, functions, functions

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& 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

http://yukon-education-math-grade-10.wikispaces.com/ functions, functions, functions

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