Resources by Centre for Research in Mathematics Education (CRME)

Calculating volumes of compound objects

This lesson develops the concept of calculating the volume of compound objects. In particular, students enhance their understanding of:

• Computing measurements using formulas.
• Decomposing compound shapes into simpler ones.
• Using right triangles and their properties to solve real-world...

Candle box

This task is designed to assess how well students understand using a description to draw the net of a shape.

A hexagonal prism is to be used as a box for a candle. A design featuring a candle is to be placed on each face of the box. The task is to use isometric paper to draw a net for the box.

This...

Circle pattern

This task is designed to assess how well students understand

The initial problems shows a black circle with radius 2r, inside of who two smaller circles of radius r are drawn. Students must show that the fraction of the diagram that is black is equal to a half.

The initial problem is altered with four...

Circles and squares

This task is designed to assess how well students understand ratio and areas.

A diagram is shows a circle with one square inside and one square outside, both just touching the circle. The first task is to work out the ratio of the areas of the two squares.

A circle is then inscribed inside of the...

Classifying proportional and non-proportional situations

This lesson develops the concept of identifying when two quantities vary in direct proportion to each other. Students enhance their ability to:

• Distinguish between direct proportion and other functional relationships
• Solve proportionality problems using efficient methods

The...

Classifying rational and irrational numbers

This lesson develops the concept of distinguishing between rational and irrational numbers. In particular, students will enhance their ability in:

• Classifying numbers as rational or irrational.
• Moving between different representations of rational and irrational numbers.

 An...

Comparing strategies for proportion problems

This lesson develops the concept of direct proportion and its application to problems. The works addresses the following problems that students might have:

• Use of inappropriate additive strategies in scaling problems.
• Inefficient strategies such as not using a single multiplier for solving...

Comparing value for money: baseball jerseys

This is a problem solving lesson, designed to help you assess how well students are able to:

• Interpret a situation and represent the variables mathematically
• Interpret and evaluate the data generated and identify the break-even point

The problem is set in the context of the cost...

Cross-totals

This task is designed to assess how well students understand addition, working methodically, and giving a proof.

A cross is given that uses two squares on each arm around a central square to give nine squares in total. The numbers from 1 to 9 must be placed in the squares so that the vertical and horizontal...

Describing and defining quadrilaterals

This lesson develops the concept of naming and classifying quadrilaterals according to their properties. Students identify the minimal information required to define a quadrilateral. They sketch quadrilaterals with given conditions.

During the first part of the lesson students choose from the words ‘all’, ‘...