![Hollow Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-11257-icon.png?itok=aH4Q0l2T)
Difference of two squares
![Hollow Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-11257-icon.png?itok=aH4Q0l2T)
![Difference of Two Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-11120-icon.png?itok=I6siiML4)
problem
Difference of Two Squares
What is special about the difference between squares of numbers adjacent to multiples of three?
![Particularly general](/sites/default/files/styles/medium/public/thumbnails/content-id-7962-icon.png?itok=Sukq8O6Z)
problem
Particularly general
By proving these particular identities, prove the existence of general cases.
![Square Product](/sites/default/files/styles/medium/public/thumbnails/content-id-7158-icon.png?itok=L_RYaxWt)
![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?
![Plus Minus](/sites/default/files/styles/medium/public/thumbnails/content-99-07-six5-icon.jpg?itok=1D4JwE3e)
problem
Plus Minus
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
![Odd Differences](/sites/default/files/styles/medium/public/thumbnails/content-97-12-six2-icon.jpg?itok=0jU8HGYd)
problem
Odd Differences
The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
![2-Digit Square](/sites/default/files/styles/medium/public/thumbnails/content-97-07-six2-icon.jpg?itok=jK3kWII9)
problem
2-Digit Square
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
![DOTS Division](/sites/default/files/styles/medium/public/thumbnails/content-01-06-15plus2-icon.jpg?itok=lhIT7p-b)
problem
DOTS Division
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.