Resources by Centre for Research in Mathematics Education (CRME)

Propane tanks

This task is designed to assess how well students understand:

• Calculating the volume of a cylinder
• Calculating the volume of a hemisphere

The task looks at designing a Propane tank. The tanks are made in the shape of a cylinder, with a hemisphere at each end. The cylindrical part...

Proving Pythagoras’ theorem

This lesson develops the concept of producing and evaluating geometrical proofs. In particular students work on:

• Interpreting diagrams
• Identifying mathematical knowledge relevant to an argument
• Linking visual and algebraic representations
• Producing and evaluating mathematical...

Pythagorean triples

This task is designed to assess how well students understand Pythagorean Triples.

In the initial task students are given the Pythagorean Triples

(3, 4, 5), (5, 12, 13), (7, 24, 25) and (9, 40, 41)

They investigate the relationships between the lengths of the sides of the triangles that belong...

Ratios and proportional relationships

This series of short tasks is designed to assess how well students understand proportional reasoning in practical contexts. The contexts featured include:

• Relating a photograph to its negative
• Water used by a washing machine
• Coffee powder and cups of coffee made
• Stamp...

Representing 3D objects in 2D

This lesson develops the concept of visualising two-dimensional cross-sections of representations of 3-dimensional objects.

The lesson begins by considering two cylindrical containers placed so that they make a right angle. Water flows from one cylinder to the other. Students consider the top view of the...

Representing and combining transformations

This lesson develops the concept of combining transformations. In particular students will:

• Recognise and visualise transformations of 2D shapes
• Translate, reflect and rotate shapes, and combine these transformations
• Discuss some common misconceptions about transformations
...

Representing the laws of arithmetic

This lesson develops the concept of using diagrammatic representations of calculations. Attention is paid to order of operations, along with the distributive and commutative properties.

An introductory activity considers areas of rectangles in relation to calculations, what is often termed ‘the grid method...

Representing trigonometric functions

This lesson develops the concept of using trigonometry to model a real-world situation. In particular students will:

• Model a periodic situation, the hight of a person on a Ferris wheel using trigonometric functions
• Interpret the constants a, b, c in the formula h = a + b cos ct in terms of the...

Roman mosaic

This task is designed to assess how well students understand:

• Symmetry
• Names of shapes
• Describing angles

A representation is shown of a Roman mosaic floor that was uncovered in Spain. The task is to describe the complete pattern as precisely as possible, so that someone...

Sale

This task is designed to assess how well students understand value for money and relating this to a graph.

A graph is presented with six points. The graph plots price against weight for different bags of sugar. Students answer various questions relating the weight and price of bags. They must then determine...