Visualising and representing

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Place a red counter in the top left corner of a 4×4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

A 3×8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Watch the video to see how Charlie works out the sum. Can you adapt his method?