Resources by Centre for Research in Mathematics Education (CRME)

Sampling and estimating how many jellybeans

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

• Model a situation mathematically, justifying any assumptions made.
• Estimate unknown values/missing information when solving a problem.
• Calculate volumes of three-dimensional objects.
• ...

Security camera

This task is 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

A shop owner has...

Sharing costs equitably: travelling to school

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

• Solve a real world modelling problem
• Apply proportional reasoning

The problem is set in the context of a journey to school. Here are the features of the problem:

• Each day...

Shelves

This task is designed to assess how well students understand proportional reasoning and how it relates to graphs.

The task is set in the context of making shelves by using planks of wood supported by three bricks at each end. Students investigate both the materials and costs involved for making different...

Smoothie box

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

Top and side views are shown of a smoothie bottle. The task is to design a package that will hold twelve of the bottles. The bottles must be held so that they do not rattle about. All of the...

Solving problems with circles and triangles

This lesson develops the concept of using geometric properties to solve problems. In particular students develop their ability in:

• Solving problems by determining the lengths of the sides in right triangles using trigonometry
• Finding the measurements of shapes by decomposing complex shapes...

Sorting equations of circles 1

This lesson develops the concept of using Pythagoras’ theorem to derive the equation of a circle and translating between the geometric features of circles and their equations.

The initial activity involves looking at a circle with end points of the diameter at (6, 0) and (–6, 0). Questions relate to...

Sorting equations of circles 2

This lesson develops the concept of using the equation of a circle. In particular students develop their knowledge of how to:

• Translate between the equations of circles and their geometric features
• Sketch a circle from its equation

In the introductory activity a circle has been...

Sports bag

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

The task is to draw the net of a sports bag with the following features:

• The length of the bag will be 60 cm.
• The bag will have circular ends of diameter 25 cm.
• The main...

Square

This task is designed to assess how well students understand applying Pythagoras’ theorem to finding the gradient of a slope.

The task looks at points plotted on a set of axes. The points are joined to make a quadrilateral. The first task is to calculate the length and slope of each side. Students must then...