Resources by Centre for Research in Mathematics Education (CRME)

100 People

This task is designed to assess how well students understand applying proportional reasoning to humanitarian statistics.

In the 1990s researchers calculated that if there were just 100 people in the world

• There would be 20 children
• 25 people would not have food and shelter
• 17...

25% sale

This task is designed to assess how well students understand repeated percentage reduction.

The task begins with reducing the price of a jacket by 25%. The sale price of the jacket reduces by 25% on a further three occasions. A statement is made that ‘four reductions of 25% must mean the jacket is then free...

A golden crown

This task is designed to assess how well students understand using density.

The task is set in the context of determining if a crown is made from pure gold. Figures are given for the volume and mass of the crown. Information is also presented for the density of gold and silver.

Examples are given of...

A million dollars

This task is designed to assess how well students understand proportional reasoning.

The task is centred around burgers costing $3.50 and $1 000 000. Students must calculate various quantities related to the two initial figures. As an example, one question asks;

‘How many years does it take to earn...

Aaron’s designs

This task is designed to assess how well students understand drawing and recognising transformations.

There are a range of tasks that involve reflecting, translating, and rotating shapes to create designs for greetings cards. A final task presents a completed design and students must identify the...

Adding and subtracting directed numbers

This lesson develops the concept of adding and subtracting directed numbers. The activities address common misconceptions about the addition and subtraction of directed numbers. Students explain their reasoning using diagrams.

The activities use the ‘charge’ model of directed numbers. For example, a diagram...

Applying angle theorems

This lesson develops the concept of using geometric properties to solve problems. Particular attention is paid to interior and exterior angles of polygons.

The lesson starts by considering four regular pentagons arranged so that the ‘gap’ between them is a rhombus. Students must calculate the angles in the...

Applying properties of exponents

This lesson develops the concept of using the properties of exponents. In particular students will:

• Recall and use the properties of exponents to generate equivalent numeric expressions.
• Identify the appropriate property to use and apply it correctly.
• Check the numerical value of an...

Best-size cans

This task is designed to assess how well students understand calculating the volume and surface area of a cylinder.

The task involves finding the height and radius of a cylindrical can which holds 200 cm³ of liquid and uses the smallest amount of aluminium.

This task is from the Mathematics...

Calculating arcs and areas of sectors in circles

This lesson develops the concept of finding areas of sectors. In particular students will:

• Find perimeters, areas, and arc lengths of sectors using formulas
• Find the relationships between arc lengths, and areas of sectors after scaling
• Using radians

The initial challenge...