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Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Can you find the values at the vertices when you know the values on the edges?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Can you match these calculations in Standard Index Form with their answers?
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
What do you notice about these families of recurring decimals?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
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?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?