Resources by Centre for Research in Mathematics Education (CRME)

Describing and defining triangles

This lesson develops the concept of constructing triangles with given conditions. In particular students will:

• Recall and apply triangle properties
• Determine whether a set of given conditions for the measures of angle and/or sides of a triangle describe a unique triangle, more than one...

Designing 3D products: candy cartons

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

• Select appropriate mathematical methods to use for an unstructured problem
• Interpret a problem situation, identifying constraints and variables and specify assumptions.
• Work with 2- and 3-...

Designing a 3D product in 2D: A sports bag

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

• Recognize and use common 2D representations of 3D objects
• Identify and use the appropriate formula for finding the circumference of a circle

The initial problem to solve is calculating the...

Discovering the Pythagorean theorem

This lesson develops the concept of Pythagoras’ theorem. In particular students will:

• Use the area of right triangles to deduce the areas of other shapes
• Use dissection methods for finding areas
• Organise an investigation to systematically collect data
• Deduce a generalizable...

Discovering the shortest route across a school yard

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

• Select appropriate mathematics to solve a problem
• Compare and evaluate different methods for solving a problem and make generalizations about the appropriateness of different approaches
• ...

Division

This task is designed to assess how well students understand working with recurring decimals in practical situations.

The task gives students the information that when you calculate 100 ÷ 6 using a calculator, the result is 16. 666666667

They use this information to arrive at answers to a series of...

Drawing to scale: a garden

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

• Interpret and use scale drawings
• Use proportional reasoning
• Work with metric units

The initial problem is to construct and conversion graph to convert between measurements in the...

Estimating length using scientific notation

This lesson develops the concepts of estimating the lengths of everyday objects, and converting between decimal and scientific notation.

An introductory activity looks at converting between decimal and scientific notation.

The main activity involves a collaborative exercise centred around picture...

Estimating volume: the Money Munchers

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

• Model a situation.
• Make sensible, realistic assumptions and estimates.
• Use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.

This...

Evaluating statements about enlargements

This lesson develops the concepts of:

• Finding perimeters, areas, and volumes using formulas.
• Finding relationships between perimeters, areas, and volumes of shapes after scaling.

There are three initial questions to consider that deal with:

• The perimeter of a circle...