![AMGM](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six4-icon.gif?itok=mFgf3mKb)
Creating and manipulating expressions and formulae
![AMGM](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six4-icon.gif?itok=mFgf3mKb)
![Hot Pursuit](/sites/default/files/styles/medium/public/thumbnails/content-01-04-six3-icon.gif?itok=tGkRxYnE)
problem
Hot Pursuit
I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...
![Look before you leap](/sites/default/files/styles/medium/public/thumbnails/content-01-03-six1-icon.jpg?itok=sbTY0qAV)
![Around and Back](/sites/default/files/styles/medium/public/thumbnails/content-01-02-six4-icon.png?itok=oq5MALOB)
problem
Around and Back
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.
![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?
![Little and Large](/sites/default/files/styles/medium/public/thumbnails/content-00-12-six4-icon.jpg?itok=X_SaF6ul)
problem
Little and Large
A point moves around inside a rectangle. What are the least and the
greatest values of the sum of the squares of the distances from the
vertices?
![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?
![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.
![Fair Shares?](/sites/default/files/styles/medium/public/thumbnails/content-00-05-six1-icon.png?itok=CBro7NhK)
problem
Fair Shares?
A mother wants to share a sum of money by giving each of her
children in turn a lump sum plus a fraction of the remainder. How
can she do this in order to share the money out equally?