There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

This article outlines an extension exercise that is based on the elementary geometrical constructions in the National Curriculum. The challenge for students is to organise and execute an extended construction. The hidden, parallel agenda is proof, for the teacher's role is to convince students that they "must" succeed and that doing so is a…

In this article, the author describes what his students are doing following the ATM Easter conference in Telford, where he was inspired by a workshop entitled "Vitamin D Maths," conducted by Jocelyn D'Arcy. He describes an activity that allows his Year 11 students to walk through angles drawn on the floors. This topic will now literally…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

The author discusses how she made up some dice problems for a child's birthday. She presents some activities that can be used with younger and older children based on dice. (Contains 4 figures.)

In the first part to this article, the author described three stages that he believes are effective starting points for translating familiar classroom activities into mathematics-with-information and communications technology (ICT) lessons that exploit the power of variation to focus student attention. In this second part, the author continues to…

The authors explore the teaching of trigonometry using a method developed by Jeremy Burke of Kings College. A series of lessons was planned using an approach which looks at moving from a mathematical description of the topic, to a sequence plan, to a set of activities, which students can use to help them come to understand the topic. This is…

This final article focuses in particular on the engagement of year 8 students who were taught trigonometry using dynamic geometry software ("Geometer's SketchPad"), as outlined in "MT214" and with resources from the ATM website. The project was implemented in three different classrooms in two different, multiracial,…

Activities that are helpful for teachers and pupils alike in getting the feel for how big a million really is are suggested. (DT)

As an alternative to the usual method of counting squares to find the area of a plane shape, a method of counting lattice points (determined by vertices of a unit square) is proposed. Activities using this method are suggested. (DT)

A description is given of a game used to give a continuous review of multiplication facts and illustrate certain properties. (MP)

An alternative approach is described for presenting the idea of the derivative through the use of chords of a graph. (MP)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

One of the major characteristics of mathematics is that one can derive new information from old information with logical certainty. The fancy word for deriving information is inference. The elementary school and secondary school years are the time for the construction of logical operations and the development of tactics and skills which are at…

An activity providing practice with whole number addition and subtraction, as well as enlarging on the idea of numeration systems, is described. (DT)