three operations, expressions

an important early algebra skill is to deconstruct an expression into a sequence of operations or, in this case, the opposite

a ppt is here

which give the same output?
why?

number links

this is a more open ended task that can involve a range of numbers, fractions, decimals and negatives
overall rules can be sought (they are easy to find)
and proved

a powerpoint is here

a similar task (or an extension) is when the red numbers are the average of those either side of them
the powerpoint for this is here

first extension: find the invariant number for a particular set of 3 totals

second extension: what happens if the totals are in sequence (same difference sequences)?

du

the idea for using the two different lengths between dots ( 1 and root 2) is from a KS3 SAT question (2003, level 4 to 6, paper 2, question 19)

rectangle perimeter

perimeter change with area the same
cutting a shape in half - in two different ways

this task is based on a SAT question
(KS3, L4 to L6, year 2000, paper 1, question 14)

congruent rectangles making up a larger rectangle

in two different ways

'P' is the perimeter

find the length and width of the smaller rectangles

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:

divided squares

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

English to algebra, equations

a ppt is here

I like the idea of setting the same problems as were set many moons ago...
Robert Recorde's 'Whetstone of Witte'