Challenge Of The Week

1) By first working out 30², try and evaluate the following multiplications WITHOUT working them out.

31x29, 32 x 28, 33 x 27, 34 x 26, 35 x 25, 36 x 24, 37 x 23, 38 x 22, etc.

HINT: If you need to, work out the first few and try to identify a patten.

2) Without working out any of the answers, and justifying your answer fully, put the following calculations in order from smallest to largest answer:

23 x 21, 20 x 24, 22.5 x 21.5, 20.5 x 23.5

Based on an activity by the wonderful, late Don Steward - his activities can be found here.

3) Use algebra to justify/explain your findings for the above.