Resources by Centre for Research in Mathematics Education (CRME)

Evaluating statements about length and area

This lesson develops the concepts of length and area. Particular attention is given to proving why two areas are or are not equal.

The lesson begins with three questions regarding area that students must classify as ‘sometimes, always, or never true’. An example is ‘if you join the midpoints of the opposite...

Evaluating statements about radicals

This lesson develops concepts relating to radicals. In particular, students will enhance their understanding of:

• Use the properties of exponents, including rational exponents and manipulate algebraic statements involving radicals.
• Discriminate between equations and identities.
  In this...

Evaluating statements about rational and irrational numbers

This lesson develops the concept of reasoning about the properties of rational and irrational numbers. In particular, students will enhance their understanding of:

• Finding irrational and rational numbers to exemplify general statements.
• Reasoning with properties of rational and irrational...

Evaluating statements about rational and irrational numbers

This lesson develops the concept of reasoning about the properties of rational and irrational numbers. In particular, students will enhance their understanding of:

• Finding irrational and rational numbers to exemplify general statements.
• Reasoning with properties of rational and irrational...

Fearless frames

This task is designed to assess how well students understand maximising a volume.

The task looks at designs for freight containers made using metal frames. For the first task, 60 metres of metal tubing is available and students must design a container in the shape of a cuboid that maximises the volume of the...

Finding areas of circles

This lesson develops the concept of area of a circle. In particular students will:

• Sketch and construct loci involving arcs of circles
• Calculate the area of a circle, given its radius
• Calculate the radius of a circle, given its area

The opening question is about a goat...

Finding factors and multiples

This lesson develops the concept of ‘Greatest Common Factor’ (GCF) and ‘Least Common Multiple’ (LCM). The central theme is to separate out the two concepts.

There is an introductory ‘guess my numbers’ activity. The GCF and LCM of a pair of numbers is given and students must work out what the numbers are,...

Floor pattern

This task is designed to assess how well students understand:

• Angles in quadrilaterals
• Rotation
• Geometric reasoning and proof

The task examines a floor pattern. The first example shows two overlapping squares, both with the same centre, but with one rotated through 45...

Fruit boxes

This task is designed to assess how well students understand nets of 3D objects, calculating length and volume.

The task shows the net of a box used for a fruit box. The net includes flaps for joining the sides together. The first task is to calculate the volume of the box. There is an extension task in...

Fun-size cans

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

A drinks company is designing a can for a new drink that is to be sold in 200 ml cans. Students consider the effects of using different values for the radius of the can. They then go on to...