Linear Functions and Linear Equations study group
SAT Score Range
•
25 sessions
•
AP
Home
About
About
Timing: Approximately 7 weeks
Linear relationships are among the most prevalent and useful relationships to mathematics and the real world. Any inequality in two variables that exhibits a constant rate of change for these variables is linear. Real-world contexts that have a constant rate of change and data sets with a nearly constant rate of change can be effectively modelled by a linear function. You will explore all aspects of linear relationships in this series: contextual problems that involve constant rate of change, lines in the coordinate plane, arithmetic sequences, and algebraic means of expressing a linear relationship between two quantities. Through this series, you will develop deep skills with linear functions and equations and an appreciation for the simplicity and power of linear functions as building blocks of all higher mathematics. Five days a week, we'll go over one topic.
ENDURING UNDERSTANDINGS
You will undrstand that ...
- A linear relationship has a constant rate of change, which can be visualised as the slope of the associated graph.
- There are many ways to algebraically represent a linear function and each form reveals different aspects of the function.
- Linear functions can be used to model contextual scenarios that involve a constant rate of change or data whose general trend is linear.
- A solution to a two-variable linear equation or inequality is an ordered pair that makes the equation or inequality true.
KEY CONCEPTS
- 1: Constant rate of change and slope
- 2: Linear functions
- 3: Linear equations
- 4: Linear models of nonlinear scenarios
- 5: Two-variable linear inequalities
Tutored by
✋ ATTENDANCE POLICY
Please do not miss more than two sessions and message the tutor if you cannot make it!
SESSION 1
1
Aug
SESSION 1
Other Topics
Other Topics
Fri 2:00 PM - 2:45 PM UTCAug 1, 2:00 PM - 2:45 PM UTC
In this session, we will determine whether two quantities vary directly given a relationship represented graphically, numerically, algebraically, or verbally.
SESSION 2
4
Aug
SESSION 2
Linear equations & graphs
Linear equations & graphs
Mon 2:00 PM - 2:45 PM UTCAug 4, 2:00 PM - 2:45 PM UTC
In this session, we will calculate the constant rate of change of a linear relationship.
SESSION 3
5
Aug
SESSION 3
Linear equations & graphs
Linear equations & graphs
Tue 2:00 PM - 2:45 PM UTCAug 5, 2:00 PM - 2:45 PM UTC
In this session, we will create a graphical or numerical representation of a linear relationship given its constant rate of change.
SESSION 4
6
Aug
SESSION 4
Linear equations & graphs
Linear equations & graphs
Wed 2:00 PM - 2:45 PM UTCAug 6, 2:00 PM - 2:45 PM UTC
In this session, we will determine whether a relationship presented graphically or numerically is linear by examining the rate of change.
SESSION 5
7
Aug
SESSION 5
Sequences
Sequences
Thu 2:00 PM - 2:45 PM UTCAug 7, 2:00 PM - 2:45 PM UTC
In this session, we will determine whether a relationship is linear or nonlinear based on a numerical sequence whose indices increase by a constant amount.
SESSION 6
8
Aug
SESSION 6
Sequences
Sequences
Fri 2:00 PM - 2:45 PM UTCAug 8, 2:00 PM - 2:45 PM UTC
In this session, we will convert a given representation of an arithmetic sequence to another representation of the arithmetic sequence.
SESSION 7
11
Aug
SESSION 7
Functions
Functions
Mon 2:00 PM - 2:45 PM UTCAug 11, 2:00 PM - 2:45 PM UTC
In this session, we wil use function notation to describe the relationship between an input-output pair of a function.
SESSION 8
12
Aug
SESSION 8
Functions
Functions
Tue 2:00 PM - 2:45 PM UTCAug 12, 2:00 PM - 2:45 PM UTC
In this session, we will convert a given representation of a linear function to another representation of the linear function.
SESSION 9
13
Aug
SESSION 9
Forms of linear equations
Forms of linear equations
Wed 2:00 PM - 2:45 PM UTCAug 13, 2:00 PM - 2:45 PM UTC
In this session, we will translate between algebraic forms of a linear function, using purposeful algebraic manipulation.
SESSION 10
14
Aug
SESSION 10
Linear equations & graphs
Linear equations & graphs
Thu 2:00 PM - 2:45 PM UTCAug 14, 2:00 PM - 2:45 PM UTC
In this session, we will model a contextual scenario with a linear function.
SESSION 11
21
Aug
SESSION 11
Other Topics
Other Topics
Thu 2:00 PM - 3:30 PM UTCAug 21, 2:00 PM - 3:30 PM UTC
In this session, we will take a timed learning checkpoint with SAT-style questions to review Sessions 1–10. Then, we will go over the learning checkpoint.
SESSION 12
25
Aug
SESSION 12
Linear equations & graphs
Linear equations & graphs
Mon 2:00 PM - 2:45 PM UTCAug 25, 2:00 PM - 2:45 PM UTC
In this session, we will convert a given representation of a linear equation to another representation of that llnear equation.
SESSION 13
26
Aug
SESSION 13
Linear equations & graphs
Linear equations & graphs
Tue 2:00 PM - 2:45 PM UTCAug 26, 2:00 PM - 2:45 PM UTC
In this session, we will interpret the solutions to a two-variable linear equation.
SESSION 14
27
Aug
SESSION 14
Forms of linear equations
Forms of linear equations
Wed 2:00 PM - 2:45 PM UTCAug 27, 2:00 PM - 2:45 PM UTC
In this session, we will rewrite a two-variable linear equation in terms of one of the variables to preserve the solution set, using purposeful algebraic manipulation.
SESSION 15
28
Aug
SESSION 15
Other Topics
Other Topics
Thu 2:00 PM - 2:45 PM UTCAug 28, 2:00 PM - 2:45 PM UTC
In this session, we will construct representations of parallel or perpendicular lines.
SESSION 16
29
Aug
SESSION 16
Absolute value & piecewise functions
Absolute value & piecewise functions
Fri 2:00 PM - 2:45 PM UTCAug 29, 2:00 PM - 2:45 PM UTC
In this session, we will interpret a graphical representation of a piecewise linear function in context.
SESSION 17
4
Sep
SESSION 17
Absolute value & piecewise functions
Absolute value & piecewise functions
Thu 2:00 PM - 2:45 PM UTCSep 4, 2:00 PM - 2:45 PM UTC
In this session, we will construct a graphical representation of a piecewise linear function to model a contextual scenario.
SESSION 18
5
Sep
SESSION 18
Other Topics
Other Topics
Fri 2:00 PM - 2:45 PM UTCSep 5, 2:00 PM - 2:45 PM UTC
In this session, we will determine whether the scatterplot of the relationship between two quantities can be reasonably modelled by a linear model.
SESSION 19
8
Sep
SESSION 19
Other Topics
Other Topics
Mon 2:00 PM - 2:45 PM UTCSep 8, 2:00 PM - 2:45 PM UTC
In this session, we will determine an equation for a trend line that describes trends in a scatterplot.
SESSION 20
9
Sep
SESSION 20
Other Topics
Other Topics
Tue 2:00 PM - 2:45 PM UTCSep 9, 2:00 PM - 2:45 PM UTC
In this session, we will use an equation for a trend line to predict values in context.
SESSION 21
10
Sep
SESSION 21
Other Topics
Other Topics
Wed 2:00 PM - 3:30 PM UTCSep 10, 2:00 PM - 3:30 PM UTC
In this session, we will take a timed learning checkpoint with SAT-style questions to review Sessions 12–20. Then, we will go over the learning checkpoint.
SESSION 22
12
Sep
SESSION 22
Inequalities (systems & graphs)
Inequalities (systems & graphs)
Fri 2:00 PM - 2:45 PM UTCSep 12, 2:00 PM - 2:45 PM UTC
In this session, we will convert a given representation of a linear inequality to another representation of the linear inequality.
SESSION 23
15
Sep
SESSION 23
Inequalities (systems & graphs)
Inequalities (systems & graphs)
Mon 2:00 PM - 2:45 PM UTCSep 15, 2:00 PM - 2:45 PM UTC
In this session, we will determine solutions to a two-variable inequality.
SESSION 24
16
Sep
SESSION 24
Inequalities (systems & graphs)
Inequalities (systems & graphs)
Tue 2:00 PM - 2:45 PM UTCSep 16, 2:00 PM - 2:45 PM UTC
In this session, we will rewrite a linear inequality in terms of one of the variables to preserve the solution set, using purposeful algebraic manipulation.
SESSION 25
17
Sep
SESSION 25
Other Topics
Other Topics
Wed 2:00 PM - 3:30 PM UTCSep 17, 2:00 PM - 3:30 PM UTC
In this session, we will take a timed performance task with SAT-style questions to review every session in this series. Then, we will go over the performance task.