![AMGM](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six4-icon.gif?itok=mFgf3mKb)
Conjecturing and generalising
![AMGM](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six4-icon.gif?itok=mFgf3mKb)
![Enclosing Squares](/sites/default/files/styles/medium/public/thumbnails/content-01-03-six2-icon.jpg?itok=rhwU1bq9)
![2001 Spatial Oddity](/sites/default/files/styles/medium/public/thumbnails/content-01-01-six6-icon.gif?itok=XGSVq18_)
problem
2001 Spatial Oddity
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
![Adding in Rows](/sites/default/files/styles/medium/public/thumbnails/content-01-01-six3-icon.png?itok=9BXboIyX)
problem
Adding in Rows
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
![Where can we visit?](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six3-icon.jpg?itok=fnQnUDU6)
problem
Where can we visit?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
![Why 24?](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six2-icon.png?itok=IDw_MNsq)
problem
Why 24?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
![What's Possible?](/sites/default/files/styles/medium/public/thumbnails/content-00-11-six5-icon.png?itok=Y1vBIzcp)
problem
What's Possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
![Oddly](/sites/default/files/styles/medium/public/thumbnails/content-00-11-six1-icon.gif?itok=2MAubuM_)
![Cut it Out](/sites/default/files/styles/medium/public/thumbnails/content-00-07-six1-icon.jpg?itok=Q_VPBD-2)
problem
Cut it Out
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
![Quick Times](/sites/default/files/styles/medium/public/thumbnails/content-00-05-six2-icon.jpg?itok=C7R95IrU)
problem
Quick Times
32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50
x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if
possible.