times to add

difference between powers

a ppt is here

generalising

hidden faces

an exploration that considers surface area

a ppt is here

some square number patterns

all due to David Wells

proofs could involve expanding brackets and simplifying expressions
or use the difference of two squares equivalence
or could be considered by using diagrams

bidmas differences

one of the reasons why some people do not like to use the mnemonic 'bidmas' (or 'pemdas') is that it can lead to some students misguidedly working out division prior to multiplication (or vice versus for pemdas) and an addition prior to a subtraction

it ought perhaps to be labelled:

but this doesn't ensure a lack of confusion
















Matt Dunbar has suggested using this graphic:

it seems to be important that students have some notion of a more 'powerful' operation
as well as a need for a global convention, to avoid ambiguity

it can be interesting to look at the difference between a calculation worked out (a) using a correct priority of operations and (b) incorrectly

there are three tasks here, looking at these differences for:

1.  3 consecutive numbers
2.  where the first number is 10 times the second and the third is the second add 1
3.  where one result (incorrect version) is double that of the other (correct version)

a powerpoint is here

diagrams of the different ways that this can be worked out

as can be seen in the diagram above

as can be seen in the diagram

examples where one (incorrect) result is double the correct result

simple multiplication relationships

thanks to Marilyn Burns for the first of these
the powerpoint is here

hollow rectangles

an exploration of surrounding paths
the powerpoint is here

this work could follow on from hollow square

for hollow squares see also the approach nrich 11257

some problems involving paths around lawns
the powerpoint for these is here