These lessons will involve the students in investigating and understanding:
• That processes can generate sequences of numbers or objects
• How to investigate and discover patterns among these sequences
• How to use patterns to continue the sequence
• How to develop generalising strategies and ideas, present and interpret solutions, in the following:
o The use of tables, diagrams, graphs and formulae as tools for representing and analysing linear patterns and relations
Discuss rate of change and the y - intercept.
Consider how these relate to the context from which the relationship is derived and identify how they can appear in a table, in a graph and in a formula
Decide if two linear relations have a common value.
(Decide if two lines intersect and where the intersection occurs.)
Recognise that the distinguishing feature of a linear relationship is a constant rate of change
Recognise linear relationships as arithmetic sequences
o The use of tables, diagrams, graphs and formulae as tools for representing and analysing quadratic patterns and relations
Recognise that a distinguishing feature of quadratic relations is that the rate of change of the rate of change is constant
o The concept of a function as a relationship between a set of inputs and a set of outputs where each input is related uniquely to just one output
o Exponential relations
Recognise that a distinguishing feature of exponential relations is a constant ratio between successive outputs
Desmos Parking Lots
Project Maths
Patterns: A Relations Approach to Algebra
Students Presentation: Create a formula from a pattern
Functions without Formulae Quiz
Alison
Khan
Graphing proportional relationships
Interpreting and finding intercepts of linear functions
Understanding linear and exponential models
Comparing growth rates of exponentials and polynomials
Constructing linear and exponential functions
Rewriting and interpreting exponential functions
Modeling with exponential functions
Using logarithms to solve exponential equations
OTHER
Project Maths
Teachers
Algebra Matching Cards Exercise