Program of Studies: [Math 10C] [Math 10-3] [Math 10-4] [Math 20-1] [Math 20-2] [Math 20-3] [Math 20-4] [Math 30-1] [Math 30-2] [Math 30-3]

MATHEMATICS 10C

 [C] Communication
[CN] Connections
[ME] Mental Mathematics
and Estimation

[PS] Problem Solving
[R] Reasoning
[T] Technology
[V] Visualization


Measurement      Algebra & Number      Relations & Functions 1      Relations & Functions 2     Relations & Functions 3

General Outcome: Develop algebraic and graphical reasoning through the study of relations.

Specific Outcomes: It is expected that students will:

  1. Interpret and explain the relationships among data, graphs and situations.
    [C, CN, R, T, V]
    [ICT: C6–4.3, C7–4.2]

Select [ Linear and Non-Linear Data ] and/or [ Using Graphs to Represent Data ] - will need district login credentials for LearnAlberta

Select [ Reading Graphs ] to learn how to identy discreet and continuous data - will need district login credentials for LearnAlberta

1.1 Graph, with or without technology, a set of data, and determine the restrictions on the domain and range.
1.2 Explain why data points should or should not be connected on the graph for a situation.
1.3 Describe a possible situation for a given graph.
1.4 Sketch a possible graph for a given situation.
1.5 Determine, and express in a variety of ways, the domain and range of a graph, a set of ordered pairs or a table of values.

  1. Demonstrate an understanding of relations and functions.
    [C, R, V]

2.1 Explain, using examples, why some relations are not functions but all functions are relations.
2.2 Determine if a set of ordered pairs represents a function.
2.3 Sort a set of graphs as functions or non-functions.
2.4 Generalize and explain rules for determining whether graphs and sets of ordered pairs represent functions.

  1. Demonstrate an understanding of slope with respect to:

3.1 Determine the slope of a line segment by measuring or calculating the rise and run.

Calculating the Slope of a Line Segment

The slope(m) of a line containing (x1, y1) and (x2, y2) is found by:

rise

or

slope

 

Slope Interactive Activity

Select the link below to see the calculation for the slope of a segment line when the linear function in the form y = mx + b:

  • Click and drag points P and Q to change the size and location of segment PQ.
  • Watch the grey area below the graph for the updated slope formula, substitution and answer steps.

Linked Source - Ron Blond

3.2 Classify lines in a given set as having positive or negative slopes.

Describe Slope

  • A slope is positive if it rises to the right (as you look at a graph). Remember, if the slope is positive, things are "looking up".
  • A slope is negative if it falls to the right. Remember, if the slope is negative, things are "looking down".
  • If the numerical value is high, (whether positive or negative), the slope is steep.
  • If the numerical value is low, the slope is shallow (more flat).
  • If the slope is 0, then the line is flat (horizontal).

Linear Relation Interactive Activity

  • Change the slope of a line segment by clicking and dragging on one of the end points. Find examples where the slope of a segment is positive, negative, steep, vertical, shallow and horizontal. The statements on the left will be helpful.

Linked Source - Ron Blond

3.3 Explain the meaning of the slope of a horizontal or vertical line.
3.4 Explain why the slope of a line can be determined by using any two points on that line.

Calculating the Slope of a Line Segment

The slope(m) of a line containing (x1, y1) and (x2, y2) is found by:

rise

or

slope

 

Slope Interactive Activity

Select the link below to see the calculation for the slope of a segment line when the linear function in the form y = mx + b:

  • Click and drag points P and Q to change the size and location of segment PQ.
  • Watch the grey area below the graph for the updated slope formula, substitution and answer steps.

Linked Source - Ron Blond

3.5 Explain, using examples, slope as a rate of change.
3.6 Draw a line, given its slope and a point on the line.

Slope–point form

(y – y1) = m(x – x1)

  • m = slope
  • ( x1, y1) = one point on the graph

Linked Source - Ron Blond

3.7 Determine another point on a line, given the slope and a point on the line.
3.8 Generalize and apply a rule for determining whether two lines are parallel or perpendicular.

Parallel

  • If two line segments are parallel, the slopes of the two line segments are the same.

Perpendicular

  • If two line segments are perpendicular, the slopes of the two lines are negative reciprocals.

Linear Relation Interactive Activity

  • Change the slope of a line segment by clicking and dragging on one of the end points. Find examples where the slope of a segment is positive, negative, steep, vertical, shallow and horizontal. The statements on the left will be helpful.

Linked Source - Ron Blond

Perpendicular Line Segments

  • If two line segments are perpendicular, the slopes of the two lines are negative reciprocals.
  • Study the lines as you turn one of them. Notice that in each postion, one line is rising and one is falling. This is the reason the slopes are negative reciprocals.
  • For example if the slope of one segment is 2, the slope of the perpendicular segment is -1/2.
  • The product of the slopes of two perpendicualr segments is -1. For the previous example:

    2 ( -1/2) = -1

Negative Reciprocal Slopes Interactive Activity

  • Change the slope of the two line segments by clicking and dragging on one of the end points. Study the slopes and product of the two slopes provided in the display area..

Linked Source - Ron Blond

3.9 Solve a contextual problem involving slope.

 

March, 2008 http://www.education.alberta.ca/media/655889/math10to12.pdf

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf

Authorized Resources: http://www.education.alberta.ca/teachers/program/math/educator/resources.aspx