don steward
maths teaching 10 ~ 16

Saturday, 27 September 2014

multiples of 4 as the difference of two squares

corner polygonal numbers

geogebra growing from a corner

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:
  • 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

Monday, 22 September 2014

directed number practice

David Wells: put a pattern in and you get a pattern out

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