## Sunday, 28 September 2014

## Saturday, 27 September 2014

### centred polygonal numbers

the Ancient Greeks took to exploring number patterns derived from shape arrangements - possibly pebbles in the sand

Hypsicles of Alexandria (around 170 BCE) seems to have been one of the first

followed by Theon of Smyrna, Nichomachus and (reported at least in) Plutarch (around 100CE)

this work might be used to focus on number patterns but also could involve:

these resources focus on the centred polygonal numbers

a geogebra version with sliders

pictures created by Stefan Birkner

pictures created by Claudio Rockini

Hypsicles of Alexandria (around 170 BCE) seems to have been one of the first

followed by Theon of Smyrna, Nichomachus and (reported at least in) Plutarch (around 100CE)

this work might be used to focus on number patterns but also could involve:

- developing quadratic nth terms
- solving simultaneous equations in 3 unknowns
- proof, involving triangular numbers

these resources focus on the centred polygonal numbers

a geogebra version with sliders

pictures created by Stefan Birkner

pictures created by Claudio Rockini

## Friday, 26 September 2014

### both ways - a sequel

the introduction-to-algebra task 'both ways' can be adapted to introduce quadratic expansions at some later stage

students feed in numbers and work out the differences between the two outcomes for that input number

they then try to relate the differences as a function of the input number

discussion can then focus on the reasons for these (linear) function differences

students feed in numbers and work out the differences between the two outcomes for that input number

they then try to relate the differences as a function of the input number

discussion can then focus on the reasons for these (linear) function differences

Labels:
quadratic expansions

## Monday, 22 September 2014

## Sunday, 14 September 2014

## Thursday, 14 August 2014

## Tuesday, 12 August 2014

### equations involving algebraic fractions

the initial idea for these tasks is from a question in Tony Gardiner's 'Mathematical Puzzling' book (1987)

the questions can be solved by trial and improvement but, hopefully, might encourage an application of fraction and other techniques

the questions can be solved by trial and improvement but, hopefully, might encourage an application of fraction and other techniques

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