# Sample Problems

### What is this?

This unit presents a series of problems that can be used in the classroom, providing opportunities for pupils to use and apply geometrical reasoning while working towards a deeper understanding of proof.

The problems are organised in three sections.

Section 1: Problems based on diagrams presented to pupils

These problems:

- give pupils the opportunity to find solutions by applying the skills developed in the visualisation exercises and build-ups

- require pupils to formalise and justify the reasoning leading to their solutions.

Section 2: Problems requiring pupils to construct appropriate diagrams of their own

These problems:

- require pupils to draw their own diagrams, based on written descriptions

- provide support through alternate wording, which presents a more structured approach to drawing the required diagram and solving the problem.

Section 3: Problems requiring more extended investigation

These problems:

- require a more extended investigation of situations involving geometrical reasoning

- provide opportunities for pupils to demonstrate independence, where the teacher gives appropriate levels of support.

### What does this do?

The materials provide an opportunity for pupils to develop independent problem-solving skills as they work through sets of questions with decreasing structure and increasing challenge.### Why use this?

Use this resource to help pupils to:- develop confidence and skills in geometric proof

- structure, justify and communicate geometric reasoning

- generate solutions to geometrical problems in a more rigorous way

- develop reasoning through planned talk.

### What do I do now?

Download the problem sets and associated resources:Problem Set 1: Problems based on diagrams presented to pupils

Dynamic geometry resources to use with the problems in Set 1, available in three versions:

Problem Set 2: Problems requiring pupils to construct appropriate diagrams of their own

Problem Set 3: Problems requiring more extended investigation

Dynamic geometry resources to use with the problems in Set 3, available in three versions: