Outcome #5
Relationships
Embedded Files
Description
This outcome covers the following:
Linear and Non-linear relationships
Initial values and rates of change
Tables of Values
Visual Representations
Inequalities
Curriculum Expectations: C3.1, C4.1, C4.2
Note: There are similarities between this outcome and the Lines Outcome. This outcome focuses more on the role of the table of values and how x and y-values relate to each other in a relationship.
Emerging
Emerging
I can distinguish between linear and non-linear relations given:
a visual representation
a table of values
a graph
Notes/Examples:
Eg. Determine if each of the following represent linear or non-linear relationships:
Developing
Developing
I can identify initial values and rate of change for linear and non-linear relations given:
a visual representation
a table of values
a graph
Notes/Examples:
Eg. Determine the initial value and rate of change of each of the following:
Proficient
Proficient
I can create a table of values given an equation representing linear and non-linear relationships and make a graph.
Notes/Examples:
Eg. Determine a table of values and graph the relationship defined by equations such as:
x + y = 12
xy = 24
x = 4
y = x2
2x – y = 8
Exceeding
Exceeding
I can graph an inequality.
Notes/Examples:
Eg. Graph the inequalities:
x + y < 12
x ≥ 4
2x – y ≤ 8
Extending
Extending
I have a thorough understanding of linear and non-linear relationships.
Notes/Examples:
Graphically understanding the significance of a POI.
Finding regions enclosed by multiple inequalities.
Sample Assessments
(Approaching Standard)
(Approaching Standard)
(Reaching Standard)
(Reaching Standard)
(Reaching Standard -> Extending Understanding)
(Reaching Standard -> Extending Understanding)
Lesson Ideas
Graphing Relationships from Equations
Graphing Relationships from Equations
This is an activity for small groups. (Recommended for pass 2 after some understanding of equations and linear/non-linear)
Linear vs Nonlinear Relations basic lesson
Linear vs Nonlinear Relations basic lesson
This is a simple lesson to guide students through exploring visual representations, tables and graphs of linear and nonlinear relations.
This lesson suggestion includes a warm-up activity, whole group lesson and then work for small groups (including extensions)
A series of questions of different levels of difficulties for students to complete.
Coding Activities
Analyze and Alter: Exploring Linear Growth Patterns
Analyze and Alter: Exploring Linear Growth Patterns
This program creates a linear growth pattern using shapes.
The intent is that students make changes and see how that affects the growth pattern.
This program lets you graph a relationship.
It is a more complicated program so you might not want to dig into the code unless your students are feeling confident with coding.
Coding: Distance, Speed, Time Activity
Coding: Distance, Speed, Time Activity
This class led activity explores the relationship between distance, speed and time.
Desmos Classroom Activities
In this activity students match cards that represent linear and nonlinear relationships. This includes equations, tables of values and graphs. Students will also create their own relationships.
In this activity students will create tables for relations, come up with the equations and then look at the graphs of simple linear and non-linear relations.
In this activity, students apply (and deepen) their knowledge of linear inequalities in two variables to "collect" as many points in the coordinate plane as they can.
This activity uses a "real" concept of managing a pet boarding business. Constraints on aspects of the business limit the total number of cats and dogs the business can board in a week.
Students should be familiar with the concept of a linear inequality.
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