Outcomes for Mathematics 12
Math for the Workplace 12 Curriculum Outcomes
Module 1
· demonstrate an understanding of the meaning and uses of accuracy and precision
· use a measuring tape to measure tactile items in both imperial and SI units
· identify the difference between length, area, and volume
· demonstrate an understanding of the meaning and uses of significant figures
· demonstrate an understanding of, and be able to solve problems using dimensional analysis
· identify, use, and convert among and between SI units and Imperial units to measure and solve measurement problems
· estimate distances by using a personal benchmark such as walking pace
· demonstrate an understanding of, and be able to solve problems using the Pythagorean Theorem
Module 2
· investigate a range of career opportunities to determine the best personal fit for their interests within the trades
· demonstrate to others what type of mathematical knowledge is required to be successful at various career choices
· demonstrate entry level competence in the mathematics associated with the specific career choice the student has made
· sketch and construct a model which will enable a student to show others some mathematics involved in a career interest
Module 3
· calculate the dimensions of actual objects using blueprints with various scales
· sketch and build representations of three-dimensional objects using a variety of materials and information about the objects
· illustrate, explain, and express ratios, fractions, decimals, and percents in alternative forms
· find and calculate rates in practical applications such as pulse rate
· estimate and calculate deductions taken from a pay stub as percent of gross earnings
· sketch enlargements and reductions of objects using various scales
· use the slope formula to solve trigonometric problems commonly found in industry
Module 4
· demonstrate to others what type of mathematical knowledge is required to be successful at their career choice
· demonstrate competence in the mathematics associated with the specific career choice the student has made
· prepare a detailed blueprint for, and construct a model which will enable a student to show others some mathematics involved in a specific career interest.
Chapter 1: Patterns
C4 demonstrate an understanding of patterns that are arithmetic, power, and geometric
C5 determine and describe patterns and use them to solve problems
C6 explore, describe, and apply the Fibonacci sequence
C7 relate arithmetic patterns to linear relations
Chapter 2: Quadratics
A3 demonstrate an understanding of the role of irrational numbers in applications
B1 operations used when solving equations
B3 apply the quadratic formula
C1 model real-world phenomena using quadratic equations
C5 determine and describe patterns and use them to solve problems
C8 describe and translate between graphical, tabular, and written representations of quadratic
relationships
B9 perform operations on algebraic expressions and equations
C1 model real-world phenomena using quadratic equations
C12 describe and apply the characteristics of quadratic relationships
C14 determine and interpret x-intercepts of quadratic functions
C21 create and analyse scatter plots and determine the equations for curves of best fit, using appropriate
technology
C23 solve problems involving quadratic equations
C29 analyse tables and graphs to distinguish between linear, quadratic, and exponential relationships
E2 describe and apply symmetry
F2 use curve-fitting to determine the equations of quadratic relationships
F4 interpolate and extrapolate to predict and solve problems
Chapter 3: Exponential Growth
A1 demonstrate an understanding of and apply zero and negative exponents
A2 develop, demonstrate an understanding of, and apply properties of exponents
A8 demonstrate an understanding of the exponential growth nature of compound interest
B5 demonstrate an understanding of and apply compound interest
B6 determine the amount and present value of annuitiesC5 determine and describe patterns and use them to solve problems
C11 describe and translate between graphical, tabular, and written representations of exponential relationships
C13 describe and apply the characteristics of exponential relationships
C21 create and analyse scatter plots and determine the equations for curves of best fit, using appropriate technology
C25 solve problems involving exponential equations
C26 solve problems involving compound interest
C29 analyse tables and graphs to distinguish between linear, quadratic, and exponential relationships
F2 use curve-fitting to determine the equations of exponential relationships
F4 interpolate and extrapolate to predict and solve problems
Chapter 4: Geometry of Design
D2 determine midpoints and the lengths of line segments using coordinate geometry
E1 perform geometric constructions and analyse the properties of the resulting figures
E2 describe and apply symmetry
E5 apply inductive reasoning to make conjectures in geometric situations
E6 explore, make conjectures about, and apply centres of circles
E7 explore, make conjectures about, and apply chord properties in circles
E8 explore, make conjectures about, and apply angle relationships in circles
E10 present informal deductive arguments
Chapter 5: Probability
A6 develop an understanding of factorial notation and apply it to calculating permutations and combinations
B7 calculate probabilities to solve problems
B8 determine probabilities using permutations and combinations
G1 develop and apply simulations to solve problems
G2 demonstrate an understanding that determining probability requires the quantifying of outcomes
G3 demonstrate an understanding of the Fundamental Counting Principle and apply it to calculate
probabilities of dependent and independent events
G4 apply area diagrams and three diagrams to interpret and determine probabilities of dependent and independent events
G6 demonstrate an understanding of the difference between probability and odds
G7 distinguish between situations that involve combinations and permutations
Chapter 1: Quadratics
A3 demonstrate an understanding of the role of irrational numbers in applications
A4 demonstrate an understanding of the nature of the roots of quadratic equations
A7 describe and interpret domains and ranges using set notations
A9 represent non-real roots of quadratic equations as complex numbers
B1 demonstrate an understanding of the relationships that exists between arithmetic operations and the operations used when solving equations
B10 derive and apply the quadratic formula
B11Adv analyse the quadratic formula to connect its components
to the graphs of quadratic functions
C1 model real-world phenomena using quadratic functions
C3 sketch graphs from descriptions, tables, and collected data
C4 demonstrate an understanding of patterns that are arithmetic, power, and geometric, and relate them to corresponding functions
C8 describe and translate between graphical, tabular, written, and symbolic representations of quadratic relationships.
C9 translate between different forms of quadratic equations
C10Adv determine the equation of a quadratic function using
finite differences
C15 relate the nature of the roots of quadratic equations and the x-intercepts of the graphs of corresponding functions
C22 solve quadratic equations
C23 solve problems involving quadratic equations
C29 analyse tables and graphs to distinguish between linear, quadratic, and exponential relationships
C31 analyse and describe the characteristics of quadratic functions
C32 demonstrate an understanding of how parameter changes affect the graphs of quadratic functions
F1 analyse scatter plots, and determine and apply the equations for curves of best fit, using appropriate technology
Chapter 2: Rate of Change
2.1 Purpose of the Section (Optional)
B4 calculate average rates of change (optional)
C16 demonstrate an understanding that slope depicts rate of change (optional)
C17 demonstrate an understanding of the concept of rate of change in a variety of situations (optional)
C30 describe and apply rates of change by analysing graphs, equations, and descriptions of linear and quadratic functions (optional)
2.2 Describing Instantaneous Rate of Change (Optional)
C16 demonstrate an understanding that slope depicts rate of change (optional)
C18 demonstrate an understanding that the slope of a line tangent to a curve at a point is the instantaneous rate of change of the curve at the point of tangency (optional)
C27 approximate and intercept slopes of tangents to curves, with points on the curves, with and without technology (optional)
C28 solve problems involving instantaneous rates of change (optional)
C30 describe and apply rates of change by analysing graphs, equations, and descriptions of linear and quadratic functions (optional)
Chapter 3: Exponential Growth
A5 demonstrate an understanding of the role of real numbers in exponential and logarithmic
expressions and equations
A7 describe and interpret domains and ranges using set notation
B1 demonstrate an understanding of relationships that exist between arithmetic operations and the operations used when solving equations
B2 demonstrate an intuitive understanding of the recursive nature of exponential growth
B12 apply real number exponents in expressions and equations
B13 demonstrate an understanding of the properties of logarithms and apply them
C2 model real-world phenomena using exponential functions
C3 sketch graphs from descriptions, tables, and collected data
C4 demonstrate an understanding of patterns that are arithmetic, power, and geometric, and relate them to corresponding functions
C11 describe and translate between graphical, tabular, written, and symbolic representations of exponential and logarithmic relationships
C19 demonstrate an understanding, algebraically and graphically, that the inverse of an exponential function is logarithmic function
C24 solve exponential and logarithmic equations
C25 solve problems involving exponential and logarithmic equations
C29 analyse tables and graphs to distinguish between linear, quadratic, and exponential relationships
C33 analyse and describe the characteristics of exponential and logarithmic functions
C34 demonstrate an understanding of how parameter changes affect the graphs of exponential functions
C35Adv write exponential functions in transformational form and
as mapping rules to visualize and sketch graphs
F1 analyse scatter plots, and determine and apply the equations that best fit, using appropriate technology
Chapter 4: Going Round in Circles/Circle Geometry
D1 develop and apply formulas for distance and midpoint
E4 apply properties of circles
E5 apply inductive reasoning to make conjectures in geometric situations
E7 investigate and make and prove conjectures associated with chord properties of circles
E11 write proofs using various axiomatic systems and assess the validity of deductive arguments
E12 demonstrate an understanding of the concept of converse
E15Adv solve problems involving the equations and
characteristics of circles and ellipses
4.3 Angles, Arcs, Tangents, and Sectors
D1 develop and apply formulas for distance and midpoint
E5 apply inductive reasoning to make conjectures in geometric situations
E8Adv investigate and make and prove conjectures associated
with angle relationships in circles
E9Adv investigate and make and prove conjectures associated
with tangent properties of circles
E11 write proofs using various axiomatic systems and assess the validity of deductive arguments
E15Adv solve problems involving the equations and
characteristics of circles and ellipses
4.4 Transforming Circles
E3 Adv write equations of circles and ellipses in transformational
form as mapping rules to visualize and sketch graphs
E4 apply properties of circles
E11 write proofs using various axiomatic systems and assess
the validity of deductive arguments
E13Adv analyse and translate between symbolic, graphic, and
written representations of circles and ellipses
E14Adv translate between different forms of equations of circles
and ellipses (optional)
E15Adv solve problems involving the equations and
characteristics of circles and ellipses
E16Adv demonstrate an understanding of transformational
relationship between a circle and an ellipse
4.5 Examining the Circle as a Trigonometric Function (Omit)
C36Adv demonstrate an understanding of the relationship
between angle rotation and the coordinates of a rotating point
C20Adv represent circles using parametric equations
C37Adv describe and apply parameter changes within parametric
equations
E15Adv solve problems involving the equations and
characteristics of circles and ellipses
Chapter 5: Probability
A6 develop an understanding of factorial notation and apply it to calculating permutations
B8 determine probabilities using permutations and combinations
G1 develop and apply simulations to solve problems
G2 demonstrate an understanding that determining probability requires the quantifying of outcomes
G3 demonstrate an understanding of the Fundamental Counting Principle and apply it to calculate probabilities of dependent and independent events
G4 apply area diagrams and tree diagrams to interpret and determine probabilities of dependent and independent events
G5Adv determine conditional probability
G7 distinguish between situations that involve combinations and permutations
G8 develop and apply formulae to evaluate permutations and combinations
5.5 Applying Probability and Combinations to the Binomial
Expansion (Optional)
G9Adv demonstrate an understanding of binomial expansion and
its connection to combinations
G10Adv connect Pascal’s triangle with combinatorial coefficients
5.6 Binomial Probabilities (Omit)
G1 develop and apply simulations to solve problems
G11Adv connect binomial expansions, combinations, and the
probability of binomial trials
G12Adv demonstrate an understanding of and solve problems
using random variables and binomial distributions