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These two group activities use mathematical reasoning - one is numerical, one geometric. Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules. Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Rod Measures

Rod Measures

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this? For example with rods of lengths $3, 4,$ and $9$ the measurements are:

$4-3,$ $9-4-3,$ $3,$ $4,$ $9-3,$ $9-4,$ $3+4,$ $9+3-4,$ $9,$ $9+4-3,$

Using 3 rods of ANY integer lengths, what is the greatest length N for which you can measure all lengths from 1 to N units inclusive? Can you beat 10 units? Can you beat the highest value of N submitted to date?

Why do this problem?

This excellent problem is so very good for number awareness, and reinforcement of addition and subtraction rules.

Possible approach

Starting off in a very practical way with suitable rods would be ideal in many circumstances.

Key questions

How did you get to this solution?
I see you've not got a (suppose - 9 when using 2,3 & 5) can you explain that?

Possible extension

What about four rods?
Which combinations work/do not work and why?