General algebraic forms for specific number properties

Maths

Checking and securing understanding of functions

Defining function notation

Finding the inverse of a function

Writing composite functions

Solving equations involving functions

Solving equations involving composite functions

Making conjectures about patterns and relationships

Proving or disproving a statement

Writing a generalised statement about specific number properties

Writing a proof

Logical arguments

Multiple approaches to logical arguments

Problem solving with functions and proof

In this future unit, pupils continue to explore composite functions, thereby building on their work from this unit. Pupils need to understand function notation from this unit as this is used in iteration.

The functions unit requires pupils to write composite functions and pupils will need to draw on their understanding of how to manipulate various algebraic expressions and equations, including algebraic fractions.

In this unit pupils will further develop their understanding of algebraic notation and graphs by learning about functions, their inverses and composite functions.

Functions and proof

Which of these expressions could be even if $$n$$ is an integer?

Which of these expressions must be even for any integer $$n$$?

Which of these expressions are always odd for any integer value of $$n$$?

It is always 3 less than a multiple of 6. 

Which of these statements are true for the expression $$6n + 3$$ when $$n$$ is an integer?

Which of these must represent 3 consecutive odd numbers when $$n$$ is an integer?

$$2n$$ and $$2n$$ where $$n$$ is an integer.

$$2n$$ and $$2n + 2$$ where $$n$$ is an integer.

$$2n$$ and $$2m$$ where $$n$$ and $$m$$ are integers and $$n \ne m$$.

$$2n$$ and $$12n$$ where $$n$$ is an integer and $$n \ne 0$$.

$$2n + 1$$ and $$2m + 3$$ where $$n$$ and $$m$$ are integers.

Which of these represent any 2 different even numbers?

A multiple is the product of a number and...

Which of these is an example of consecutive integers?

Which of these shows consecutive even integers?

General algebraic forms for specific number properties

Lesson outcome