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Happy numbers

As with perfect numbers, there is no practical application for happy numbers. This activity to create sequences of numbers to discover whether a number is a “Happy” number, requires students …

Reflecting on your professional development

Well done for reaching the final part of the course, where you’ll review your learning and record your professional development. This step focuses on your reflection grids and revisits your …

Perfect numbers

There are professional mathematicians, particularly pure mathematicians, whose jobs is to explore mathematics, find connections and make sense of how mathematics works. When mathematicians make discoveries often these discoveries have …

Square numbers

Square numbers are those whole numbers such that if that number is represented by that many dots we can arrange the dots in the shape of a square. Think of …

Triangle numbers

Triangle numbers are those whole numbers such that if that number is represented by that many dots we can arrange the dots in the shape of a triangle. Paula and …

Geometric sequences

Geometric sequences have a common ratio. To find the next term of a geometric sequence we multiply the current term by the common ratio. We have seen that arithmetic sequences …

The geometry of arithmetic sequences

When students learn about arithmetic sequences they are very often just taught the procedure for finding the position to term rule: the nth term. It can help students understand the …

Fibonacci type sequences

The Fibonacci sequence is best described using a term to term rule and is how the sequence is described in school. There is a position to term rule but it …

Arithmetic sequences

Arithmetic sequences are the most common type of sequence students meet. It is important to emphasise that there are two ways to describe arithmetic sequence: the term to term rule …

Examples of sequences

Below are some examples of number sequences, some have a mathematical rule behind them, others do not. Challenge Take a look at the following sequences. a) 3, 3, 5, 4, …

Sequences: term rules

Let’s clarify some of the terminology used to define sequences. A sequence is usually denoted using a capital letter. The sequence \(E\) is the sequence of even numbers 2,4,6,8, _, …

Number sequences

Welcome to week four of the course. Last week we explored negative numbers, saw the order in which operations should be performed and looked at how to express solutions in …

Exact answers: multiples of pi

When performing calculations that involve circles we will usually be required to use a value for \(\pi\) (pi). The exact value of pi cannot be found as it an irrational …

Exact answers: fractions

In some cases a rounded answer is not sufficient and the context of the problem requires an exact answer. When performing a calculation which requires a large number of steps …