Pick a square within a multiplication square and add the numbers on
each diagonal. What do you notice?
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
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?
Think of a number and follow my instructions. Tell me your answer,
and I'll tell you what you started with! Can you explain how I
Imagine starting with one yellow cube and covering it all over with
a single layer of red cubes, and then covering that cube with a
layer of blue cubes. How many red and blue cubes would you need?
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
Jo has three numbers which she adds together in pairs. When she
does this she has three different totals: 11, 17 and 22 What are
the three numbers Jo had to start with?”
A task which depends on members of the group noticing the needs of
others and responding.
Create some shapes by combining two or more rectangles. What can
you say about the areas and perimeters of the shapes you can make?
How to build your own magic squares.
Account of an investigation which starts from the area of an
annulus and leads to the formula for the difference of two squares.
There is a particular value of x, and a value of y to go with it,
which make all five expressions equal in value, can you find that
x, y pair ?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at
100°C (212°Fahrenheit). Is there a temperature at which
Celsius and Fahrenheit readings are the same?