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Hunting for Patterns and Rules

Stages

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1. Functions and Relations

Suggested Learning Intentions

To understand that functions describe the relationships between numbers
To understand that a relation is a set of inputs and outputs
To understand that a function is a relation with one output for each input

Sample Success Criteria

I can explain that the relationship between one number and another number is described by the functions performed on them
I can articulate that a relation is a set of inputs and outputs
I can determine the output of a number given a known input
I can demonstrate the effect of a function being performed using a variety of manipulatives

2. Exploring Patterns

Suggested Learning Intentions

To understand that a pattern is a predictable arrangement of elements
To understand that patterns are determined by the application of different functions
To understand the difference between repeated and growing patterns

Sample Success Criteria

I can identify and describe a pattern
I can model a pattern using a range of different manipulatives
I can continue a pattern using appropriate functions (operations)
I can create a pattern using a variety of functions (operations)
I can articulate what a repeated pattern is and what a growing pattern is

3. Equivalence

Suggested Learning Intentions

To understand that expressions on either side of an equal sign must be balanced
To explain that when a function on one side of an equation is performed an equal function must be performed on the other side to maintain balance

Sample Success Criteria

I can articulate that an equals sign represents a balance of the expressions on either side of it
I can create equivalent number sentences/equations
I can manipulate equations or number sentences to maintain the balance on both sides
I can model my problem solutions using a variety of manipulatives

4. Using Symbols to Recognise Unknowns

Suggested Learning Intentions

To understand that symbols (pronumerals) can be used to represent a variable or an unknown quantity in an equation
To understand that symbols can be used to represent an unknown in a pattern or a generalisation
To understand that these equations can be manipulated to determine the unknown quantity

Sample Success Criteria

I can use a symbol (pronumeral) to represent an unknown in an equation
I can use a symbol (pronumeral) to represent an unknown in a pattern
I can manipulate equations to determine the unknown (symbol/pronumeral)
I can justify my thinking using other representations of the mathematics

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