Reasoning is fundamental to knowing and doing mathematics. Some would call it systematic thinking. Reasoning enables children to make use of all their other mathematical skills. Reasoning could be thought of as the “glue” which helps mathematics makes sense.

******************************************** This might be an opportunity for teamwork. Partner with your children as they attempt this first task.

CHAIN OF CHANGES

Here is a set of shapes. For this problem we will call them pieces.

Each of these pieces is either a different color or a different shape from all the others.

These problems ask you to arrange the pieces in a line so that you change either color or shape in the next piece along. If you start with a blue triangle, the next shape has to be either another triangle or another blue shape. You may want to print and cut out a set of shapes from the attached pdf.

1. The first puzzle is to arrange all the shapes in such a line starting with the blue triangle and ending with the red circle. There are lots of different ways of doing it!

2. The second problem is to arrange the pieces in the same way, starting with the blue triangle and ending with the red circle, but to change first color, then shape or vice-versa.

If you put a yellow triangle after the blue one and so change the color, next you must put another yellow piece and so change the shape.

You will not be able to use all the pieces in this way but the problem is to see how many you can use.

Parents…….this problem is useful for recalling and learning all the pairs of numbers with a total of 10 and working out the corresponding subtraction facts.

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Here are nine triangles. Each one has three numbers on it.

Your challenge is to arrange these triangles to make one big triangle, so the numbers that touch add up to 10.