Grades 9/10/11 Linear Relations and Analytic Geometry
Linear and non-linear relations. Solving linear equations and linear systems. Analytic geometry and statistics.
This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.
The alternative formats for some lessons are currently under construction. These will be completed in the coming months.
Unit 1: Linear Equations
This lesson will look at solving linear equations in application based problems. Some examples will have equations given and in others the equation will need to be developed before solving.
This lesson will solve problems algebraically involving rate, ratio, proportion, and percent using cross-multiplication.
Unit 2: Characteristics of Linear Relations
In this lesson, we will explore characteristics of a linear relationship between two variables using patterns, tables of values, and graphs. A variable is identified as being independent or dependent and comparisons are made between linear and non-linear relations.
In this lesson, we will continue to identify properties of a linear relation. We will define rate of change and initial value. We will then determine the rate of change and initial value from tables and graphs and use these values to develop a corresponding linear equation. In addition, we will calculate first differences in a table of values and use this to identify a relation as linear or non-linear.
In this lesson, we will define the terms direct variation and partial variation. We will use these definitions to identify which of the two variations a linear relationship represents.
Unit 3: Connecting Various Representations of Linear Relations
In this lesson, we will use the properties of a linear relation to help us solve for unknown values in various representations of the relation.
In this lesson, we will look at connecting various representations of a linear relation.
In this lesson, we will look at changing the conditions of a linear situation represented by a graph and explore how the changes affect the graph and equation of the line.
Unit 4: Properties of Slope
Unit 5: Equations of Linear Relations and Problem Solving
In this lesson, we will look at various forms of a linear equation. We will rearrange the equations from one form to another and solve problems involving the different forms of a linear equation.
In this lesson, we will compare the properties of linear relations to those of non-linear relations. We will use these properties to classify a relation as linear or non-linear.
In this lesson, we will consider application problems that encompass ideas and concepts presented throughout the linear relations units. These ideas will be extended to include identifying and interpreting a point of intersection graphically and setting restrictions on variables within a given context.
Unit 6: Solving Linear Systems of Equations
In this lesson, we will begin looking at solving linear systems of two equations by graphing.
In this lesson, we will look at solving a system of equations algebraically. We will use the methods of substitution and elimination.
Unit 7: Properties of Line Segments and Using Analytic Geometry to Verify Geometric Properties
In this lesson, we will develop and use the formulas to calculate the midpoint and length of a line segment with defined endpoints on a Cartesian plane.
In this lesson, we will problem solve using the concepts of slope, length, and midpoint of a line segment. We will consider problems involving lines and then problems involving triangles.
In this lesson, we will investigate the properties and characteristics of various quadrilaterals. We will verify some of these properties using analytic geometry using a multi-step strategy where necessary.
Unit 8: Data Management and Statistics
In this lesson, we will interpret the meaning of points on scatter plots, construct scatter plots, and draw curves or lines of best fit. In addition, we will determine the equation of a line of best fit.
In this lesson, we will learn how to pose problems, identify variables associated with a problem and formulate a hypothesis. We will learn how to carry out an investigation to determine if a relationship exists between two variables.
In this lesson, we will learn about different types of data and about bias in data collection. We will also examine different sampling techniques.