COTW Archive | MathEVmatics

A teacher gives his class the sequence 1, 2, 5, ... and asks them to work out the next number.

Alan says, "The answer is 14." Betty says, "You're wrong! I think it is 15." Carl says, "Nah, you're both wrong - I make it 26."

1) All three of their answers are valid - try to work out what they each did to reach their answer using a valid sequence.

2) Can you find three more possible sequences which give different values to the ones above? Explain your pattern for each sequence.

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.