This week I used a fantastic open-ended investigation with my top-set Year 9 class. The problem was taken from the NRich Maths website and was called Painted Cube. It is based around the idea that a large cube (made up from smaller cubes) is dipped into a pot of paint, removed and the paint left to dry. You then dismantle the big cube (pulling the smaller cubes apart) and investigate the following questions:

How many small cubes have paint on their faces?

Will they all look the same?

Now imagine doing the same with other cubes made up from small red cubes.

What can you say about the number of small cubes with yellow paint on?

Many of the Year 9s really got stuck into this problem and did come up with some formulas for calculating how many painted mini-cubes you get based on the size of the big cube. They then submitted their findings online and may get published on the website next month.

I really enjoy lessons based on these open-ended types of activity as they really promote independent thought and creativity. I do find that some of the kids find it hard to engage with the work because we traditionally teach them through much more closed, spoon-feeding teaching styles and when presented with a task so open they find it a difficult thing to comprehend.

Nonetheless, with practice they do improve quickly. I fully stand by teaching through these methods because these types of problems are very like those you have to solve in the real world of work. In the real world you are not always given all the information you need to solve a problem and sometimes not even a starting point.

Einstein said “The important thing is to not stop questioning”. To solve these problems I think the real key is in the questions that you ask yourself.

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