Answer:

This problem solving unit is suitable for Level 5 (or Level 6) students.

In this problem solving unit, we look at numbers that fit into a triangular arrangement of circles. The point of this unit is to give students a chance to

see how mathematicians operate

display ingenuity and creativity

practice arithmetic in context

learn what generalisations, extensions, conjectures, theorems, and proofs are

work through a completely novel situation and try to develop a mathematical theory around it

Specific Learning Outcomes

Solve a mathematical problem.

See how to generalise and extend a problem.

Understand why and how mathematical statements may be justified.

Work with others to solve a problem and generate ideas.

Description of Mathematics

Like all of the Problem Solving units, this one aims to introduce students to the underlying ideas of mathematics through a problem. The problem here requires only a simple knowledge of arithmetic but the process we go through demands a considerable use of ingenuity and creativity. In this unit we see how a mathematical theory might develop through experimentation, conjecturing, proving, generalising and extending. We also see that some proofs are ‘nicer’ than others.

Step-by-step explanation:

Basic Problem (The Six Circle Problem): Is it possible to put the numbers 1, 2, 3, 4, 5, 6 in the circles so that the sums of the three numbers on either side of the triangle are the same?

sixcircles.

Before you take the problem to the class it’s worth giving it a bit of thought. There are a few things that need to be considered.