Thinking Through Mathematics

These resources, produced by The National Centre for Excellence in the Teaching of Mathematics (NCETM), have been designed to encourage distinctive ways of thinking and learning as part of the NCETM professional development package.

Analysing reasoning and solutions sets a number of problems about proportion and percentages and gives a range of student responses to each problem. The examples provide inspiration for further discussion about student misconceptions.

Classifying contains a number of cards each containing a different shapes. Students are asked to place the cards into categories. The task is inspiration for teachers to discuss how the teacher should proceed with the activity. The second activity, classifying using two-way tables, requires students to place the cards into a two-way table according to the shape’s properties.

Creating and solving problems explains the ‘doing’ and ‘undoing’ processes in mathematics giving three examples of a problem poser where a closed problem is posed and the problem solver where the problem is posed in a more open format.

Evaluating mathematical statements gives a number of examples for which it has to be decided whether the statement is always true, sometimes true or never true. A further example is given in which each statement has to be categorised as true, false or unsure.

Interpreting multiple representations contains an example of an activity in which students are asked to take it in turns to match up cards. One set of cards contain decimal numbers, one set contain diagrams of shaded squares and one set contains arrows on a number line.

As part of the NCETM course teachers were asked to make a similar activity for another area of mathematics.

Show health and safety information

Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.

5 Files

You might also like

Resource collection
Resource collection
Resource collection
Resource collection

Published by


Share this resource



Appears as though the card sort from the last piece is missing

Steve Lyon

Thanks for your comment.

The resources were produced as part of a NCETM professional development package.

Rather than produce the finished activity, the interpreting multiple representations resource is designed to inspire teachers to make similar resources of their own in other areas of mathematics.

I have altered the description to make this clear.