two, 2-digit multiplications

four tasks with a common theme:

1.   (10n + 5) squared
2.   from a square number, go a bit more and a bit less and multiply them
3.   31 squared and 29 squared
4.   units sum to 10, in a long multiplication sum

these involve (a + b) squared, the difference of two squares and (a - b) squared

they could be a starting place for a study of these expansions

all start with number calculations (long multiplication practice) and move on to consider 

related images (an array) and then 

expanding quadratic brackets examples (which play automatically)

ppts are here:

1.  (10n + 5)^2

2.  24 x 16 

3.  31 ^ 2

4.  42 x 28

task 1

task 2

task 3

task 4

quadrilateral in a square

Chris Pritchard sets some interesting tasks in Mathematics in School Vol. 43 No.2
that involve having vertices of a quadrilateral drawn so that they divide each side in the ratio a : b (or b : a)
I have very slightly adapted his fine work

establish geometrically and also algebraically that the red quadrilateral is half of the surrounding square

show that the two red quadrilaterals sum to the initial square

try to do this geometrically and then also algebraically

Cuisenaire squares

a ppt is here

these resources focus on some algebra involved in growing squares and then a growing rectangle

you could just let students create their own growing square sequence...

Simon Gregg has developed the uses of Cuisenaire rods

he points out the availability of square trays of various sizes, available from Numicon - helpful for a study of squares made out of Cuisenaire rods