Resources by Centre for Research in Mathematics Education (CRME)

T-shirt sale

This task is designed to assess how well students understand percentage calculations and special offers.

The task shows three T-shirts with different prices. A special offer states that all three may be purchased together for a discounted price. There are various tasks to complete, including calculating the...

Table tiling

This task is designed to assess how well students understand tessellation, area, and patterns.

A square table top is to be tiled using three types of tile:

• Square
• Half a square (cut along the diagonal)
• Quarter of a square (half of a ‘half’ tile)

A design is shown...

Taxi cabs

This task is designed to assess how well students understand calculations in a practical context.

The task is set in the context of organising a trip for 75 people, where two types of taxi are available:
A small taxi costs $40 for the trip and holds up to 4 people.
A large taxi costs $63 for the...

Temple geometry

This task is designed to assess how well students understand applying Pythagoras’ theorem in an unfamiliar situation and calculating areas of circles.

During the Edo period (1603-1897) of Japanese history, geometrical puzzles were hung in the holy temples as offerings to the gods and as challenges to...

The number system

This task is designed to assess how well students understand various aspects of the number system.

There are a series of short tasks on using a calculator, working with fractions, directed numbers, and extending a multiplication fact.

As an example:

12345679 x 27 = 333 333 333

and...

The real number system

These short tasks are designed to assess how well students understand working with scientific notation combined with numbers written in ordinary form. There are also questions on working with surds.

This task is from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the...

Transforming 2D figures

This lesson develops the concept of transformations. In particular students will:

• Describe in words the transformation that maps an object to a transformed image
• Given a geometric figure and a transformation, draw the transformed figure
• Describe transformations as algebraic functions...

Translating between fractions, decimals, and percents

This lesson develops the concept of converting between and ordering fractions, decimals, and percentages. The lesson uses area and linear models of fractions, decimals, and percentages to understand equivalence.

The main activity is a collaborative exercise. Students must collect together cards that show a...

Translating between repeating decimals and fractions

This lesson develops the concept of translating between decimal and fraction notation, particularly when decimals are repeating. This is achieved by

• Creating and solving simple liner equations to find the fractional equivalent of a repeating decimal
• Understanding the effect of multiplying a...

Trigonometric functions

This short task contains two questions on applying trigonometry.

The topics covered are:

• Linking sine, cosine and tangent
• Using Pythagoras to determine a length in a triangle and then give the tangent of an angle in surd form
• Using the Pythagorean identity sin2(x) + cos2(x) = 1...