sum, difference, product ratios

from a question posed by Tony Gardiner

trial and improvement is an expected strategy, initially at least, involving equivalent ratios (i.e. scaling)

one method to do these questions

rules to points 2

further work on finding integer points/pairs that fit linear relationships
then, the reverse, finding a linear rule that fits a sequence of points

a powerpoint is here

these are also of the form
ax - by = 1

rules to points 1

considering linear rules/relationships (with some simple quadratic relationships later)
finding integer points that fit rules
the powerpoint is here

sum product

a curious relationship that works for a restricted set of numbers

intended to practice many number skills

thanks to David Wells

powerpoint

work out the rule

find as many solutions as you can

find the missing number

what relationships can be found connecting the three outside numbers to th middle one?

mobiles

in good mathematical fashion you say that the weights of the bars and the string are negligible compared with the hanging weights...

(moments are ignored by having the bars suspended at their mid-points)

good practice in doubling and halving
to start with:

then an introduction of some algebraic expressions:

muddled rules and graphs

divided squares

these squares have been chopped into rectangles of equal area
what is 'n'?