median
don steward
mathematics teaching 10 ~ 16

Showing posts with label puzzles. Show all posts
Showing posts with label puzzles. Show all posts

Monday, 16 December 2019

find the shape puzzles

these are based on an idea by Naoki Inaba
he produced the 'area mazes' as well as many other puzzles
he appears to refer to these shape tasks as Zukei puzzles (42 of them)

there are translations into the English/American names for shapes, done by Sarah Carter (who introduced them to a wider audience via her Math = Love blog)
she posted her translation from Japanese on Sat Dec 17th, 2016
one version of these is here

for those with tablet/laptop availability, Desmos have an activity builder (tool) that can be used when looking for the shapes in the original (Naoki Inaba) tasks, here
students can either construct lines or draw freehand and these steps can be reversed, or erased

many thanks to all of the above people

for my versions, there almost certainly needs to be a presentation/reminder about how you know lengths are the same - using the same or rotated vectors (or by involving pythagoras)
and how you can tell that lines are parallel or perpendicular
this is highly likely to involve vectors (maybe calling it a journey between two points)

join four dots to make a shape, as specified for a particular row
other dots are there to create the puzzle
some of the shapes are tilted

I've tried to create puzzles that have just one solution but I may well have overlooked some options...
(please let me know via the email address, bottom right)

for my shapes, in this task I have chosen not to involve special examples of e.g. a parallelogram should be a general example rather than a rhombus, rectangle or square

a ppt is here





Wednesday, 19 July 2017

maths jigsaw

the shapes fit together to make a square (on the 5 by 5 dotty grid)

I'm fairly confident that you just need to rotate some of the shapes (mentally or otherwise) to fit them together i.e. you do not need to reflect/flip them





a related task:
fill up a 7 by 7 grid with the shapes indicated
the whole area should be covered

students could be asked to find alternatives

some of the questions have a few possibilities
e.g. for question 5 (there may well be more...) :




Monday, 21 November 2016

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






Sunday, 31 July 2016

number puzzles

it may be helpful to have numbers (e.g. on card) to move around

there is an added dimension/extension of proving various statements, usually connected to the sum of the numbers used and those numbers that are in more than one line

Graeme Brown did some Excel versions of four of these puzzles (the first three and hollow triangle (i))
these can be found at nrich 5512





Friday, 5 December 2014

number braids

an article by Richard Bennett appeared in the June 1976 edition (075) of Mathematics Teaching, published by the ATM

he called them 'number plaits' rather than braids




the 'triangle totals' must be in smallest to largest order going from left to right

a variety of 'triangle totals' are (usually) possible




why is there no variety of 'triangle totals' for the 1 to 6 case?














and of course you could carry on...

6 totals occur due to the braids...

Sunday, 13 July 2014

river crossing

some puzzles with a long history, variations appearing in many cultures

there are phone aps for several of these















a flash version of this at onlybestflash


 see wikipedia article

 NRICH 5916 goes full screen




Tuesday, 4 March 2014

Friday, 14 June 2013

puzzles that you could use algebra to solve

a variety of old puzzles, with thanks to David Wells and other puzzle collectors
a ppt is here







Saturday, 11 August 2012

square cuts

 some of the squares are tilted