odd and even numbers

a ppt is here

an equilateral triangle, slightly adjusted

a rectangle, slightly adjusted

re-fencing

a slightly simplified problem - because real life is too complicated

be wary of units

students could total up the cost of the rails plus the posts
this site (for example) could be used

you might want to include galvanised nails
and maybe a delivery cost

you might also ask them to create an approximate cost formula, for 'n' meters of perimeter

consecutive areas

can you find missing integer lengths so that the three triangles have areas that are consecutive numbers (not necessarily in the order given)?

same for the trapezia

Souzou

a 'Souzou' exhibition was held in 2013 at the Wellcome Collection in London
some of this exhibition could be viewed online

all the artists have received little or no tuition and produce work for the sake of creation alone, with no audience in mind

they have been diagnosed with a variety of different cognitive, behavioral or mental illnesses and attend or reside in specialist care institutions in Japan

Shota Katsube's figures are made from the twist-ties used to fasten bin liners:

Kenichi Yamazaki's drawings are like engineering schematics and are created in the confines of his hospital ward, using a compass, ordinary pens and large graph paper:

place value algebra

roof area

a GCSE question asks

you could ask students how they could work out the area of a (roof) pentagon:

then consider how the various dissections result in the given expression for the (house) pentagon

when is the roof area
(a) 3400 cm squared
(b) 198198 cm squared?

lengthy equations

forming equations from angles

show that this is an isosceles triangle

show that this is a parallelogram

length comic strips

involving lengths as unknowns can be a helpful diagrammatic device for forming equations

in this case with the unknown on both sides

find the two original lengths, 'a' and 'b'

for question 1,
a + 2 = 2(b - 2)
so, a = 2b - 6
and
a - 1 = b + 1
so, a = b + 2

2b - 6 = b + 2

1.

2.

3.

4.

front to back

you could start these tasks by exploring what happens to a 2-digit number when the front digit is put to the back and the two numbers are (a) added and (b) subtracted

and what happens with a 2-digit number if you square them first and then subtract?

establish that the result will always divide by 9 and by 11