Te Kete Ipurangi
Communities
Schools

# proofs

## Discovery

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.

## Jackson's Consecutive Numbers

Describe a rule for the general term.

Devise and use problem solving strategies to explore situations mathematically (be systematic).

## Poppy Meets Pythagoras

Find connections between numbers in a table

Use Pythagoras’ theorem in a general algebraic form

Measure accurately from a scale drawing.

devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

## Pythagoras' Theorem

This unit is an introduction to Pythagoras’ Theorem, including history, proofs, and practise in application of the theorem.

## The Power of Algebra

Here we look for patterns in number problems and use algebra as an efficient means of solving general problems.

## Fibonacci I

In this unit we look at Fibonacci numbers and how they occur in nature. We also look at what factors Fibonacci numbers can have.

## Arithmagons

In this unit students explore patterns and relationships among the circle numbers and box numbers that form different arithmagons. In the early sessions there are opportunities for students to suggest and try out several different rules based on numerical patterns that can be used to solve firstly triangular arithmagons and then square arithmagons. Later, students use simple linear algebra to solve triangular arithmagons and then in the final session, students establish and prove algebraically the general rules for solving arithmagons.

## Cosine Rule

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 unit may contain more material than you need for some classes. You may want to choose from parts of this unit if you have not allotted 5 sessions on the Cosine Rule to your class.