![Multiplication Square Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-6057-icon.png?itok=wNKOM7xa)
![Pair Products Poster](/sites/default/files/styles/medium/public/thumbnails/content-id-5978-icon.png?itok=m5XnUNVH)
![Pair Products](/sites/default/files/styles/medium/public/thumbnails/content-id-2278-icon.png?itok=CPRkwgjz)
problem
Pair Products
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
![Finding factors](/sites/default/files/styles/medium/public/thumbnails/content-id-7452-icon.jpg?itok=9Tp5nWdV)
problem
Finding factors
Can you find the hidden factors which multiply together to produce each quadratic expression?
![Factorising with Multilink](/sites/default/files/styles/medium/public/thumbnails/content-id-7490-icon.png?itok=JmNdK-Pw)
problem
Factorising with Multilink
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
![Hollow Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-11257-icon.png?itok=aH4Q0l2T)
![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?
![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?
![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.
![Always Perfect](/sites/default/files/styles/medium/public/thumbnails/content-04-01-six5-icon.gif?itok=u0FO5nhz)
problem
Always Perfect
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
![Perfectly Square](/sites/default/files/styles/medium/public/thumbnails/content-id-2286-icon.png?itok=kkvW1YaN)
problem
Perfectly Square
The sums of the squares of three related numbers is also a perfect square - can you explain why?
![Multiplication square](/sites/default/files/styles/medium/public/thumbnails/content-id-2821-icon.png?itok=kRl_Y7G2)
problem
Multiplication square
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
![Pythagoras Perimeters](/sites/default/files/styles/medium/public/thumbnails/content-id-11106-icon.png?itok=jFc2rZXQ)
problem
Pythagoras Perimeters
If you know the perimeter of a right angled triangle, what can you say about the area?
![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?
![Square Number Surprises](/sites/default/files/styles/medium/public/thumbnails/content-id-11194-icon.jpg?itok=dQ07kz3Y)
![Puzzling Place Value](/sites/default/files/styles/medium/public/thumbnails/content-id-11215-icon.jpg?itok=W_Wbj9nq)
![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?
![Harmonic Triangle](/sites/default/files/styles/medium/public/thumbnails/content-id-4716-icon.png?itok=naPq2egZ)
problem
Harmonic Triangle
Can you see how to build a harmonic triangle? Can you work out the next two rows?
Image
![Creating and Manipulating Linear and Quadratic Expressions - Stage 4 STEM footer Creating and Manipulating Linear and Quadratic Expressions - Stage 4 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13483-STEMlogo.png?itok=ul78mz1c)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.