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It turns out that we can currently prove very little about the Diamonds problem. But here is the proof that we can give. Theorem: If there are an odd number of slots, A will win. Proof: This mirrors the result of the 5 and 7 slot games. If the number of slots is odd, then A should take the centre slot. Whatever B does next will either give A the chance to put 3 in a row or it will not. If it does A will win.
Level Five
Number and Algebra
Units of Work
This unit uses a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. This same catalyst is also used for the unit: Babylonian Mathematics 1. Areas under enlargement are discussed in the present unit, and lying behind the various...
Level Five
Number and Algebra
Units of Work
Here we look for patterns in some number problems and see how far we can extend two basic ideas. The main point of this unit is to produce conjectures although we will spend a little time on proofs.
No strand
Units of Work
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...
No strand
Units of Work
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 V-arrangement of circles. The point of this unit is to give students a chance to see how mathematicians operate display ingenuity and creativity practice...
Level Six
Integrated
Units of Work
This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Cosine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. We note that the Cosine Rule is a generalisation of Pythagoras’ Theorem. Note that this...
No strand
Units of Work
This problem solving unit is suitable for Level 5 (or Level 6) students.
Level Six
Number and Algebra
Problem solving activities
No strand
Units of Work
This problem solving unit is suitable for Level 5 (or Level 6) students. In this problem solving unit, we look at the way numbers can be written as the sum of consecutive strings of whole numbers. The point of this unit is to give students a chance to: see how mathematicians operate display...
Level Five
Number and Algebra
Units of Work
This unit looks at simple rules that will decide when any number has the factors 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12. It also looks at how we can quickly tell what remainder a number has when it is divided by 3 or 9. We also give the proofs of these rules. These ideas are tested by word problems.