Creating and manipulating expressions and formulae

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

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

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

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

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?

Can you figure out how sequences of beach huts are generated?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?