More or Less Grids

Based on an idea garnered from Dina Tirosh and Pessia Tsamir 
Perimeter & Area
The main task is to construct shapes in each of the eight parts of the grid surrounding the central one. A further challenge is to make as little change as possible from the central shape.

The applet allows you to make a copy of the central shape in each part of the grid so that you can then modify it by clicking on a cell. You can change the central shape, and set it using the buttons.
Which part of the grid is the hardest to find an example for? What principles emerged for altering area or perimeter without altering the other? Are there any shapes for the centre, for which not all of the grid can be filled in? What other shapes can you put in the centre which have the same shape and the same perimeter as the one chosen? 
LCM & HCF
What could arise is the undoing question: how to construct all pairs with a given LCM and the more particular question, what properties must a pair of numbers L and H have so that there is a pair of numbers with L as the LCM and H as the HCF?
Factor Types
The idea is to persuade learners that presenting a number as a product of (prime) factors is just as useful as its base ten presentation in some circumstances.
The idea is to provoke exploration of how the period and frequency are related, and how summing sine waves affects these.
Function Domain & Range
Here the grid has changed somewhat, so that two qualities are specified, and what is sought are formulae or sketches of functions whose maximal domain in the reals is as specified, and whose range is also specified.
Watch how you fill in cells: sometimes an attempt to create an example in one cell ends up belonging in another!
Watch how you fill in cells: sometimes an attempt to create an example in one cell ends up belonging in another!