What is the smallest number to contain the letter ‘a’? Is a square a rectangle? What is the hardest multiplication fact to recall? John Tranter reveals the answers in a new maths resource available free on line for use in your lessons!
Maths games get lessons off to a great start!
After more than 30 years of teaching Maths I have now retired and spend a great deal of my time collating and developing the excellent ideas I have collected from courses, colleagues and classes during that time. The result is a collection, which I call “Starter Of The Day”.
Lesson starters for every day of the year!
Since I first found myself involved in the launch of the UK’s Numeracy initiative in the 1990s I have been convinced that beginning a Maths lesson with an engaging puzzle, question or challenge is a great way to get things going! I have seen in many schools how a “starter” can settle a class very quickly as they arrive and set the tone for the rest of the lesson. I have also seen how pupils can get quite excited when the lesson starter is well presented and pitched at the right level.
In my collection there are now 366 different starters, one for each day of the year, and many of them will be different each time they are loaded thanks to the random number generating code behind the display. Each starter also has a related pupil activity so that a teacher can choose to extend the starter into a more substantial part of the lesson. These pupil activities include self-marking exercises, games puzzles and investigations.
Watching maths worldwide
It is interesting to see from the logs (Google Analytics) which particular parts of the site are most popular and from where they are being accessed. During my morning (Thai time) I can see Australia and New Zealand light up on the map of the world as schools there are well into the school day.
By the afternoon the UK comes into its own as the teachers switch on their projectors and pupils begin their Maths lessons. The starters are clearly the most frequently viewed pages but the times tablesactivities come a close second.
Times tables games – some surprises!
On completion of an activity pupils can claim virtual trophies that they can collect in a virtual trophy cabinet. If pupils choose to record their performance (anonymously) the time it took them to answer each of the questions is stored on the server. This provides important data!
After collecting this information from over two hundred thousand timed tests, I can reveal that the times table test that takes longer to complete than any of the others is the five times table. It takes on average 59 seconds to answer twenty questions compared to easier tables such as the eleven times table which takes only 38 seconds.
This is a surprising result as most people would think the five times table is easier than the six, seven or eight times tables.
More recently I started collecting data about the time taken to answer each individual question in order to find which multiplication facts were proving to be the hardest. The data shows that 7 × 12 takes more thinking time (3.07 seconds) to work out than the others.
The easiest multiplication fact is 11 × 2 which took on average 1.45 seconds thinking time.
Stages in learning multiplication
There are three stages to learning multiplication facts. The first stage involves figuring out the fact for yourself and understanding the concept. Stage two involves being able to recall the facts based on relationships with other facts or by employing quick mental calculations. The final stage is achieving ‘automaticity’ which is the ability to know the answers immediately just as one would know that grass is green. A variety of drills, games and activities have been provided on the site to help move pupils through the stages until that have that instant recall that demonstrates knowledge.
Find out more
The task of curating this collection has been a labour of love and it has been great to receive feedback from Maths teachers around the globe – this has been inspiring me to keep going! All the Maths starters are available to anyone at www.transum.org
If you would like to know more about my project there is a monthly update and podcast available on the site summarising the new and updated content.
Did you get the right answer?
The smallest number to contain the letter ‘a’ is either one hundred and one or one thousand depending on the version of English you speak (see discussion on the October 7th Starter page). A square is a rectangle but that fact only makes this paradox puzzling!
John has a background of over thirty years of teaching Mathematics in the UK and abroad and most recently has worked for fifteen years as an Assistant Principal at one of the largest British International schools in South-East Asia. His roles have also included Head of Mathematics at three different schools and Senior Teacher Consultant (Mathematics) for Birmingham Local Education Authority.
This article was first published here.