Here are two tasks where having good ways to sort and organize can be very helpful. Young children often find working in a systematic way very difficult. These problems provide a real context and an opportunity to record thinking, which leads to the very beginnings of a proof.
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BUTTON-UP
Max has a shirt with 4 different buttons: blue, red, purple and yellow
Sometimes, Max buttons them up starting with the top button. Sometimes, he starts somewhere else.
How many ways can you find to button up Max’s shirt?
Draw a diagram to show how many ways you find.
Do you think you found all the ways? How do you know?
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INSIDE TRIANGLES
Max has a piece of four by four dotty grid paper.
He wants to figure out how many triangles he can draw with one dot in the middle of each triangles.
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He has joined three dots on the grid to make a triangle which has one dot inside it…
How many different triangles with one dot in the middle can Max draw?
Help Max find all the triangles.