Appendix
A: Applications of Math 10 Prescribed Learning Outcomes
The organizers for Applications
of Math 10 are as follows:
Problem
Solving
Number (Number Concepts)
Number (Number Operations)
Patterns and Relations (Relations and Functions)
Shape
and Space (Measurement)
Shape and Space (3-D Objects and 2-D Shapes)
Statistics and Probability (Data Analysis)
Problem
Solving
It is expected that students
will use a variety of methods to solve real-life, practical, technical, and
theoretical problems.
It is expected that students
will:
- solve problems that
involve a specific content area such as, geometry, algebra, trigonometry,
statistics, probability, etc.
- solve problems that
involve more than one content area
- solve problems that
involve mathematics within other disciplines
- analyse problems and
identify the significant elements
- develop specific skills
in selecting and using an appropriate problem-solving strategy or combination
of strategies chosen from, but not restricted to, the following:
- guess and check
- look for a pattern
- make a systematic
list
- make and use a drawing
or model
- eliminate possibilities
- work backward
- simplify the original
problem
- develop alternative
original approaches
- analyse keywords
- demonstrate the ability
to work individually and co-operatively to solve problems
- determine that their
solutions are correct and reasonable
- clearly communicate
a solution to a problem and the process used to solve it
- use appropriate technology
to assist in problem solving
It is expected that students
will:
- use basic arithmetic
operations on real numbers to solve problems.
- describe and apply arithmetic
operations on tables to solve problems, using technology as required.
It is expected that students
will:
- communicate a set of
instructions used to solve an arithmetic problem
- perform arithmetic operations
on irrational numbers, using appropriate decimal approximations.
- create and modify tables
from both recursive and nonrecursive situations
- use and modify a spreadsheet
template to model recursive situations
- solve problems involving
combinations of tables, using:
- addition or subtraction
of two tables
- multiplication of
a table by a real number
- spreadsheet functions
and templates
It is expected that students
will:
- use basic arithmetic
operations on real
numbers to solve problems.
- describe and apply arithmetic
operations on tables to solve problems, using technology as required.
It is expected that students
will:
- communicate a set of
instructions used to solve an arithmetic problem
- perform arithmetic operations
on irrational numbers, using appropriate decimal approximations.
- create and modify tables
from both recursive and nonrecursive situations
- use and modify a spreadsheet
template to model recursive situations
- solve problems involving
combinations of tables, using:
- addition or subtraction
of two tables
- multiplication of
a table by a real number
- spreadsheet functions
and templates
It is expected that students
will:
- examine the nature of
relations with an emphasis on functions.
- represent data, using
function models.
It is expected that students
will:
- plot linear and nonlinear
data, using appropriate scales
- represent data, using
function models
- use a graphing tool
to draw the graph of a function from its equation
- describe a function
in terms of:
- ordered pairs
- a rule, in word
or equation form
- a graph
- use function notation
to evaluate and represent functions
- determine the domain
and range of a relation from its graph
- determine the following
characteristics of the graph of a linear function, given its equation:
- intercepts
- slope
- domain
- range
- use partial variation
and arithmetic sequences as applications of linear functions
It is expected that students
will:
- demonstrate an understanding
of scale factors, and their interrelationship with the dimensions of similar
shapes and objects
- solve problems involving
triangles, including those found in 3-D and 2-D applications
It is expected that students
will:
- calculate the volume
and surface area of a sphere, using formulas that are provided
- determine the relationships
among linear scale factors, areas, the surface areas and the volumes of similar
figures and objects
- solve problems involving
two right triangles
- extend the concepts
of sine and cosine for angles through to 180°
- apply the sine and cosine
laws, excluding the ambiguous case, to solve problems
- select and apply appropriate
instruments, units of measure (in SI and Imperial systems) and measurement
strategies to find lengths, areas and volumes
- analyse the limitations
of measuring instruments and measurement strategies, using the concepts of
precision and accuracy
- solve problems involving
length, area, volume, time, mass and rates derived from these
- interpret drawings,
and use the information to solve problems
It is expected that students
will solve coordinate geometry problems involving lines and line segments.
It is expected that students
will:
- solve problems involving
distances between points in the coordinate plane
- solve problems involving
midpoints of line segments
- solve problems involving
rise, run and slope of line segments
- determine the equation
of a line, given information that uniquely determines the line
- solve problems using
slopes of:
- parallel lines
- perpendicular lines
Statistics
and Probability (Data Analysis)
It is expected that students
will implement and analyse sampling procedures, and draw appropriate inferences
from the data collected.
It is expected that students
will:
- choose, justify and
apply sampling techniques that will result in an appropriate, unbiased sample
from a given population
- defend or oppose inferences
and generalizations about populations, based on data from samples
- determine the equation
of a line of best fit, using:
- estimate of slope
and one point
- least squares method
with technology
- use technological devices
to determine the correlation coefficient r
- interpret the correlation
coefficient r and its limitations for varying problem situations, using
relevant scatter plots
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2000 Copyright. All Rights Reserved. Curriculum Branch.
Maintained by: Mathematics Coordinator
Revised: November 28, 2000
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