don steward
mathematics teaching 10 ~ 16

Monday, 5 December 2016


the powerpoint gives one 'play' needs to be against someone else

Yohaku fraction addition puzzles

brought to my attention by one of Ed Southall's tweets (thanks) @solvemymaths

the name is created by Michael Jacobs who has many Yohakus,
for integers, decimals and directed numbers as well as fractions,
with multiplication as well as addition
2 by 2 up to 4 by 4 grids
and algebriac expression multiplication

the powerpoint suggests a way to tackle these puzzles (Egyptian fractions)

most reflex angles inside a polygon

most acute angles inside a polygon

the maximum number of acute angles inside a polygon is closely related to the maximum number of right angles
see the right angles powerpoint
the powerpoint for most acute angles is here

Sunday, 4 December 2016

quadrilaterals with 3 acute angles

the initial question is from a KS2 test paper (2016)
the tasks are good practice in using areas of triangles
the powerpoint is here

Saturday, 3 December 2016


quiz 1

quiz 2
longer questions

the powerpoints need to be downloaded for the animations to work

Tuesday, 22 November 2016

squares inside rectangles (1) numbers

number work practice - addition and subtraction, hopefully without a calculator
the powerpoint is here

some tasks involve simple simultaneous equations (e.g. two numbers sum to 10 with a difference of 2, what are they?)

the numbers are the lengths of the squares rather than their area
sometimes you have to find the right lengths to compare e.g. in the 7, 5, 7 resource (two) below,
having found 12 (above the 7 + 5) then 12 + 5 = ? + 7

 find the missing numbers
a 'perfectly squared' rectangle has all the squares of different sizes

an 'imperfectly squared' rectangle
what are the missing lengths?

squares inside rectangles (2) equations

forming and solving linear equations with the unknown on both sides

it can be tricky to see which lengths to compare to find expressions for the squares

the powerpoint goes through a couple of examples (that are probably necessary for students to progress)

the numbers are the (integer) lengths of the square

all of these are 'perfect rectangles' in that none of the square sizes are repeated

this work is developed from the numbers attained by Stuart Anderson on where there is a vast amount of information about squares inside rectangles and related notions

Monday, 21 November 2016

loci and regions

not too sure why this topic remains on the syllabus?
it harks back to a Euclidean tradition I guess
the tasks at sciencevsmagic are interesting and challenging, if you have IT availability

the best powerpoint is Dan Walker's
I've adjusted it but this is his (admirable) work

a powerpoint showing the constructions (click and leave, needs clicking between slides)

a loop to remind students of the loci they need to know (which could be played whilst they work: click and leave)

the questions

the geometry toolbox can be helpful, available in the 'teachers' section of Bruno Reddy's site

alternative construction for the angle bisector

these are questions from the KS3 SAT papers

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