Outcome #6
Lines
Embedded Files
Description
This outcome covers the following:
representing linear relationships with equations
graphing linear relationships
understanding how equations, graphs, table of values and visual representations/descriptions relate to each other
solving problems relating to linear relations
Curriculum Expectations: C3.2, C3.3, C4.3, C4.4
Emerging
Emerging
I can graph a line using technology.
I can graph a line using a table of values.
Notes/Examples:
Graph the line y = 25x + 100 using technology.
Plot the points given in a table of values and then graph the line.
Developing
Developing
For linear relations, given one representation (table, graph, equation, description), I can move to the other representations where the rate of change and initial value are integers.
Notes/Examples:
Graph the lines: y = 2x - 1 or y = -3x + 5
Describe how a linear pattern grows and determine an equation to represent it.
A landscaping company charges a flat fee of $250, plus $200 per hour of work. Determine an equation to represent the situation.
Proficient
Proficient
For linear relations, given one representation (table, graph, equation, description), I can move to the other representations where the rate of change and initial value are rational numbers.
Notes/Examples:
Graph the line: y = 2/3x - 1 or y = -5/4x + 7
Describe how a linear pattern changes and determine an equation to represent it (with a negative initial value)
A printing company charges $30 for every 20 pages printed, plus a flat fee of $10. Determine an equation to represent the situation.
Exceeding
Exceeding
I can solve problems involving a variety of linear relations including moving between the table, graph, description, and equation.
Notes/Examples:
Given an image/description/table/equation, answer a variety of questions (eg. value when x = 100, when they are equal, etc.)
Extending
Extending
I have a thorough understanding of linear relationships.
Notes/Examples:
Consider linking this level to other outcomes in the course.
Questions should require deep understanding of the outcome and may require multiple steps to solve.
Sample Assessments
(Approaching Standard)
(Approaching Standard)
(Reaching Standard)
(Reaching Standard)
(Reaching Standard -> Extending Understanding)
(Reaching Standard -> Extending Understanding)
Lesson Ideas
From Patterns to Algebra
From Patterns to Algebra
This book provides a variety of lessons to learn about linear relations using manipulatives.
This website provides lots of examples of both linear and non-linear patterns. Use them to help generate algebraic expressions.
Consider using some of these as warm up activities prior to diving into this Outcome.
(How do you see the pattern growing? What stays the same?)
Visual Patterns to Linear Relationships
Visual Patterns to Linear Relationships
This is a series of smartboard lessons to help connect visual patterns to linear relationships.
If you have colour tiles, use them with the students.
Otherwise, you can use the Mathies Colour Tiles online tool.
In this activity students will be given one linear representation and will then need to find two others that match it and then create the last representation. This can be delivered in groups or as a gallery walk.
A series of questions of different levels of difficulties for students to complete.
Linear Practice
Linear Practice
This is a short review note and series of practice questions that have students represent linear relationships in various ways given an equation, graph or table.
Practice Questions Rule of Four Equation given
The goal of this task is to have students take the three scenarios and put them into the same form so that they can accurately draw conclusions.
These four task questions can be used in pass 2 for Scientific notation.
From Illustrative Mathematics
Coding Activities
Using Code: Inequalities
Using Code: Inequalities
In this step-by-step, video we will create a program that will represent a linear inequality. We will also verify it in Desmos.
Graphing Inequalities Using Random Points
You can use this program to introduce students to inequalities first (they can just run the program and answer the questions - more advanced students might consider looking at the actual code): Completed Program
Desmos Classroom Activities
This activity could be a good activity to have students use terminology to describe different lines.
More of an advanced activity (but so much fun!)
This activity requires the use of inequalities to limit the domain of the lines.
In this activity students investigate how a linear relation can be used to predict the cost of Lego sets with varying number of pieces.
Also consider using:
In this activity the two slides generate infinite practice of...
1) Graphing Lines given equation in y = mx + b
2) Writing Equations in y = mx + b given graph of line.
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