Resources by Centre for Research in Mathematics Education (CRME)

Matchsticks

This task is designed to assess how well students understand:

• Using the formula for the volume of a cone
• Converting between measurements

For this task, a tree trunk is thought of as being approximated by a cone. Students are given the formula for a cone, and the dimensions of a...

Maximizing area: gold rush

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

• Interpret a situation and represent the variables mathematically
• Explore the effects on a rectangle’s area of systematically varying the dimensions whilst keeping the perimeter constant.

...

Modelling linear and exponential growth

This lesson develops the concept of modelling linear and exponential growth. In particular students will enhance their understanding of:

• Translating between descriptive, algebraic, tabular, and graphical representation of the functions.
• Recognizing how and why a quantity changes per unit...

Modelling making matchsticks

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.
• Select appropriate mathematical methods.
• Interpret and evaluate the data generated.

The problem is set in the...

Modelling population growth: having kittens

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

This lesson unit is intended to help you assess how well students are able to:

• Interpret a situation and represent the constraints and variables mathematically
• Select appropriate mathematical...

Octagon tile

This task is designed to assess how well students understand symmetry, shape and angles.

Eight squares are places so that they each touch a vertex of an octagon. Students evaluate properties of the resulting pattern, including ideas about lines of symmetry and calculating angles between pairs of squares and...

Optimizing coverage: security cameras

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

• Construct lines of sight for the visibility of a camera
• Find and compare the areas of triangles and quadrilaterals
• Calculate and compare percentages and/or fractions of areas

The...

Photographs

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

The task shows a large photograph with its width and height marked. Two arrangements are shown for printing the large photograph together with two smaller copies:

• Two smaller photographs are placed with their...

Ponzi pyramid schemes

The task is set in the context of a Ponzi scheme. A letter describes the following scheme:

“Do you want to get rich quick? Just follow the instructions carefully below and you may never need to work again:

1. At the bottom of this email there are 8 names and addresses. Send $5 to the name at the top...

Proofs of the Pythagorean theorem

This task is designed to assess how well students understand geometrical proofs.

The task presents three attempts to prove Pythagoras’ theorem. Students must look carefully at each attempt and determine which is the best ‘proof’. They must explain their reasoning as fully as possible.

This task is...