This term we are starting to use conjectures in our math programme. We have been looking at fractions, so we considered this:
My conjecture: Any number divided by twice itself equals 1/2, except 0.
We started off with looking at 5 divided by 10 equals a half. We asked, "is this true and how can we prove or disprove it?"
We looked at materials we could use and soon realised that we couldn't cut up cuisenaire rods to equal share them. So we moved to paper - we folded our paper to make 5 equal size shapes. We coloured each shape a different colour. Then we cut our shapes so we could equal share our 5 pieces into 10 groups. We discovered we have to cut them in half and when we had put them into 10 groups, each group contained a half.
This conjecture was proven so far, but would this work with other numbers...?
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