Creating and manipulating expressions and formulae

problem
Steel cables

Age

14 to 16

Challenge level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
problem
Finding 3D stacks

Age

7 to 11

Challenge level

Can you find a way of counting the spheres in these arrangements?
problem
Summing consecutive numbers

Age

11 to 14

Challenge level

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?
problem
Attractive tablecloths

Age

14 to 16

Challenge level

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?
problem
Can they be equal?

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Number pyramids

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
problem
Card trick 1

Age

11 to 14

Challenge level

Can you explain how this card trick works?