– Adding and Subtracting Positive and Negative Numbers – Adding and Subtracting Positive and Negative Numbers.

Here’s a superb idea for showing why subtracting a negative number works the way it does.  Many students know how to add or subtract integers, but they don’t always know why subtracting negative five becomes add five!

Addition and Subtraction of Integers (directed numbers)

This is an excellent starter if you have an interactive whiteboard. Students have to drag the correct answer for each question and drop it in the right place.  The activity is also timed, so students have to think quickly!

Marking Books – views and research

Here are some interesting views, ideas and opinions about marking students’ books in mathematics.

“Marking for mathematics teachers is like occupational therapy; it stops them doing more important things.”

2. A useful document entitled “ASSESSMENT FOR ACTION – Marking and Feedback –Manageable and effective ways of marking and providing feedback to pupils” can be found at

3. Some tips on marking from TEACHERS TV at

4. Practical guidelines as well as Steps to achieving effective comment marking from

5. Laura Doggett, Head of Modern Foreign Languages at Berkhamsted School in Hertfordshire makes some interesting points on her blog at

6. Some examples of maths work that has been marked are illustrated in a document called “How to mark books effectively”

7. Here is an extract from a book called “Assessing higher order thinking in Mathematics

New Directions for
Mathematics Assessment


The nation’s attention has recently been
directed to the finding that many students have
a great deal of difficulty in solving the simplest
mathematics problems that require thinking
beyond the retrieval of practiced algorithms
Dossey et al., 1988 McKnight et al., 1987 ).
The narrow focus on “back to basics” and the
nearly unanimous decision by states and school
districts in the late 1970’s to settle for minimal
competency in mathematics resulted in exactly
the results that might have been expected. Stu-
dents have learned how to do numerical com-
putation at the expense of learning how to think
and solve problems.

A byproduct of an era of competency-
based education and accountability has been a
focus on, if not an obsession with, testing. Fall-
ing SAT scores, poor showings in comparison
with Japan and other developed countries,
and failures on competency tests have resulted
in even more tests at state and district levels.
Tests are becoming the primary and widely
accepted means for determining entry to,
progress through, and exit from educational
program of all types and levels. Satisfactory
performance on tests is becoming the sole in-
dicator of the “value added” by education.

If you need some ideas and resources that you can begin using immediately in your maths classroom to assess students, then go straight to

If you like using RUBRICS, then this is the place to go: (What is a rubric? Go here )

For information about types / purposes of assessment in mathematics, click here (See below)

The three purposes of assessment are as follows.

Formative assessment.
The purpose of formative assessment is to support and inform students’ learning. This feedback could be qualitative, eg written or oral comments. Such comments could be detailed and tailored to what the student has written, or brief indications of where students’ written work departs from model solutions.

Summative assessment.
The purpose of summative assessment is to establish the achievement of the student. In mathematics, summative feedback is most often quantitative, either a mark or a percentage. An examination provides the majority of the summative assessment in undergraduate mathematics.

Evaluative assessment.
The purpose of evaluative assessment is to measure the effectiveness of the teaching or the assessment of students. Such assessments could have quality enhancement or quality audit functions. For example, student feedback questionnaires. Examination statistics sometimes have a minor evaluative function.


Dear Maths Teachers of the World,

I am sure that you have also got to the point where there are so many websites out there these days, that you simply can’t remember which one was the best or which one had those fantastic worksheets you were looking for last week. Well, at last I am ready to take on the virtual mathematics playground and present it in a way that is useful to you as a teacher.

I have used computers in my classroom since 1995, and I didn’t ever expect to get to the point where there were just too many resources available. I have searched the internet for years, always finding new websites and checking for updates on old favourites. Sometimes, websites I have loved and used have shut down or changed to commercial websites, but it has never stopped me from finding more than I needed for any lesson without having to pay for the resources. I have to admit though, there are one or two (such as “mymaths” and “supermathsworld”) that are part of my toolkit because they are excellent, and come at a very reasonable price. I have spent the last 6 years finding PowerPoint presentations, worksheets, lesson plans, schemes of work, videos, flash animations, interactive whiteboard tools, Promethean flipcharts, Smart notebook files, templates, printable graph paper, posters, blogs and hundreds of other resources designed especially for mathematics teachers and learners. But it takes plenty of time and a lot of fine tuned discernment to get the best out of all the stuff available. Well that’s what I have done for you! So with the beginning of 2011, let me begin to share and show you all the excellent resources that are available to you right now with just a few clicks.

Firstly, I’d like you to vote for your favourite websites that you use for planning, teaching or learning. There are some that you may not have heard of before, and there may be some I have omitted on my first list of best websites (I have tried to narrow it down from hundreds to just 25). I have taught in South Africa, the USA and the UK, so this list is not intended to be only for UK teachers, but at first I will start with the UK in order to get things up and running. Come back and visit for the results as well as my final list of the best maths resources on the internet for 2011. Have fun and please vote or leave a short comment! MrWilliamsmaths.

Mathematical, Motivational & Memorable |

Mathematical, Motivational & Memorable |

cre8ate maths was a CPD project for Yorkshire and Humber teachers of mathematics.  It ran from April 2007 to March 2010. The end result was these new curriculum materials for KS3 created by teachers from 18 schools.  Materials are complementary to those of the Bowland Trust, and require less IT in most cases.  The materials are also designed to address the functional maths agenda.