rectangle areas

these are based on KS2 SAT (for 11 year olds) questions in England

a ppt is here

[see also the revamped 'lengths' resource, here]

involving some algebra

regular dodecagons

a new £1 coin was introduced in the UK on 28th March 2017
it's a dodecagon

thanks to David Wells, 'curious and interesting geometry' (and elsewhere)

a powerpoint exploring various aspects of regular dodecagons, mainly involving angles, is here

see how one arrangeent is adapted to give another one
use the area of the dodecagon (above) to establish why there must be six, 60, 120 degree rhombuses

see chapter 22 of Pierre van Hiele's 'structure and insight'

see youtube 'area of dodecagon' by beautiful geometry

better to use actual pattern blocks but this interactive from
the math learning centre
seems good














these videos from Idan Tal (on twitter) are helpful (thanks to Anne Watson)
the first two for the area of a dodecagon being 3r^2:

• Idan Tal 1
• Idan Tal 2
• Idan Tal 3

area doubling

students use trial and improvement to try to find values

should all be integer L,
exploring the function

area mazes

these puzzles are very similar to those produced by Naoki Inaba, a prolific puzzle composer
they were featured in the Guardian by Alex Bellos on 3rd August 2015 and in the NY Times on 17th August 2015

the puzzles can all be done using integers

once the puzzles have been done it can be interesting to use fractions to justify lengths or areas