The treasure of maths is discoveries which often involves proving or disproving conjectures. Our exploration through the Isles of What If…? is all about locating, revealing and unlocking treasure.

Locked treasure chest - a conjecture

When a conjecture is made, it is akin to locating the site of a treasure chest. An ‘x’ that marks the spot. The investigative work that is carried out to validate that treasure is digging up the locked treasure chest. Whilst there is still doubt in the classroom about the conjecture, it remains locked. Through validating a conjecture and convincing everyone that it is true or false, a treasure chest is unlocked. It is really important to emphasise that a conjecture proved false is just as important as a conjecture proven true. We still know more about the island. Both are treasure.

Whenever a conjecture is made, it is always named. I usually use the name of the person and a few words describing it. For example, ‘Mr Merrill’s always odd conjecture’. This ownership is a statement of recognition and through explicit announcing of them and writing them down, children are quickly motivated to make more. They will likely at some points, mostly early on, make conjectures that are inherently true – ‘Sam’s 2+2=4 conjecture’. I always point out that the greatest treasure isn’t something that is immediately available to everyone but requires searching for. If the treasure chest was already unlocked, the treasure wouldn’t still be there! We want that element of doubt.

It can be really nice to talk about the size and type of the treasure. The more of the island and ‘what if…?’ questions that the treasure describes, the more bountiful a treasure chest is. This can be a really good reflection point with the children in terms of what they have discovered. Often, it can encourage the modification of conjectures to make them more general and apply to more cases.

The size of treasure - how bountiful does a conjecture prove to be?

In terms of the type of treasure, you could have hidden treasure that was hard to find or unlock, wondrous or magical treasure that provided a moment of awe, strange treasure that really surprises the class, beautiful treasure that is aesthetically pleasing or some other kind that you or the children come up with. It is reflective of the efforts the children made in discovering it.

Magical treasure

Strange treasure

Beautiful treasure