Resources by Centre for Research in Mathematics Education (CRME)

Geometry

There a series of short tasks designed to assess how well students understand a range of geometric concepts, including Pythagoras’ theorem.

• Other topics covered comprise:
• Circumference of a circle
• Area of a rectangle
• Angle measure
• Angles at a point

This...

Giantburgers

This task is designed to assess how well students understand calculating in scientific notation.

The task is set in the context of a newspaper headline that claims: ‘Everyday 7% of Americans eat at a Giantburger restaurant.’

The following information is presented:

• There are about 8 x 10^3...

Glasses

This task is designed to assess how well students understand finding the volume of a sphere, cylinder and cone.

The task involves finding the volume of liquid that three different glasses can hold. There is also work in finding the height of a cone given its slant height and base radius.

This task is...

Historic bicycle

This task is designed to assess how well students understand calculating the circumference of a circle, working with imperial units.

The task features a ‘Penny Farthing’ bicycle with a big wheel of diameter 52 inches and a small wheel of diameter 18 inches.

Tasks comprise:

• Calculating the...

Hopewell geometry

This task is designed to assess how well students understand similar triangles, using Pythagoras’ theorem, and using trigonometry to find angles.

The Hopewell people were Native Americans whose constructed earthworks using right triangles. The task shows eight right triangles.

The first tasks are to...

Hot under the collar

This task is designed to assess how well students understand using approximations for temperature conversions, and assessing their accuracy.

The following methods are given for converting from degrees Celsius to degrees Fahrenheit:

Method 1: multiply the Celsius...

Identifying similar triangles

This lesson develops the concept of identifying similar triangles. In particular students will:

• Use facts about the angle sum and exterior angles of triangles to calculate missing angles
• Apply angle theorems to parallel lines cut by a transversal
• Interpret geometrical diagrams using...

Increasing and decreasing quantities by a percent

This lesson develops the concept of percentage increase and decrease. In particular students will develop their understanding of:

• Translating between percentages, decimals, and fractions.
• Representing percent increase and decrease as multiplication.
• Recognizing the relationship...

Inscribing and circumscribing right triangles

This is a concept development lesson that develops thinking on decomposing complex shapes into simpler ones in order to solve a problem. There is work on bringing together several geometric concepts to solve a problem. Students also find the relationship between radii of inscribed and circumscribed circles of right...

Interpreting multiplication and division

This lesson develops the concept of interpreting multiplication and division. This includes working with calculations that involve non-integers. An outcome of the lesson is that students will be better able to select the correct operation to perform when solving word problems.

An initial activity has five...