Creating and manipulating expressions and formulae

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 find a way of counting the spheres in these arrangements?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Is there a temperature at which Celsius and Fahrenheit readings are the same?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Can you explain how this card trick works?