Thursday, 1 June 2017

Learn Times Tables in 90min!

Multiplication chart
Times tables are the cornerstone of mathematics and are a lifetime investment for every one. We used to learn them since the early years in primary school. Still I am always surprised to see so many children (and adults...) not mastering this very basic knowledge.

There is a common misunderstanding in considering the times tables as a long list of multiplications difficult to memorise. Well, this is wrong. Actually, there are only 36 unique combinations to learn, and most of them can be deduced from the easiest ones. For example, if you know 2×5=10, you definitely know 8×5 which is simply 4×(2×5)=4×10=40. And if you know 8×5, you know 5×8 as well by symmetry. Additionally, most people know already the times tables up to 5×5 - this is 25% of all times tables - without even noticing!

Convinced? Let's have a look at the multiplication chart above. The numbers in the top row and the left column are called factors. All the others numbers are the products of the multiplication of these factors. You can easily notice that the shaded numbers are symmetric to the coloured ones. Because of this multiplication fact: a×b=b×a. It means you need to learn only haft of the times tables. If you don't know a×b, just try b×a. The 36 unique combinations I mentioned before are represented by the coloured area in the chart.

Lesson plan
Now, the question is: 36 combinations, are they to much to memorise? You must believe in the extraordinary capacity of the brain. Do you know that children from grade 3 onward learn 2000-3000 new words a year (ref. Biemiller; Nagy & Anderson)? That is 6-8 new words a day in average. By comparison, if you learn 36 combinations in 9 days, it is like learning 4 new words a day. By practising 10min a day for 9 days, you can master all the times tables in 90min. How easy it is!

You can find the full lesson plan in the illustration. Times tables are arranged by difficulty level to optimise their memorisation. They are incremental, i.e. only a few new combinations are introduced in each one: no wasting time with the symmetric forms that will be assimilated naturally by practising the daily worksheets.

The full method package including a complete set of daily worksheets to practise at home or at school is available for download.

MathEngines Founder

Tuesday, 25 April 2017

Smartest Math Generator

Xsmart Math Generator™ is a state-of-the-art tool developed by MathEngines, a start-up based in Sydney, to create dynamic worksheets on demand. For parents and teachers, this incredibly powerful generator is capable of producing the finest quality papers in mathematics that they may dream of for primary school students. This generator is the result of many years of research and development, especially focused on the user friendliness and the content adaptability. Certainly, the Xsmart Math Generator™ is second to none, simply unique of its kind, with years ahead.

Powered by Xsmart Engines™

It is in its core that the revolution started. The generator is powered by various smart exercise units, called Xsmart Engines™. Imagine the engines as logical blocs, like the computer processors, each one implementing a generic type of exercise, for instance Addition, Roman Numerals, Equivalent Fractions, etc. When tuned with their small set of dedicated parameters and plugged into the generator, they are able to generate exercises that match any student levels and needs.

Along with the generator, MathEngines also released a large library of engines, covering the essentials of the primary curriculum in mathematics, and many more already planned to come soon, especially a rich problem solving database currently in active development.


One of the most interesting features of the Xsmart Generator™ is its high adaptability. This reflects not only in the possibility to customise the engines to any requirements, but also in the ability to mix the engines of your choice. Because the children develop their skills at different rhythms, the learning process must be tailored individually in order to release their full potential. When confronted with problems that match their level of understanding, they feel more comfortable and confident to solve them effectively. In this regard, the generator adaptability differentiates to meet the needs of each individual, which is of great importance in education.


Cleverly built with a minimalistic design, every single detail of the interface has been made user friendly first. But this apparent simplicity never compromises on the generator quality and capability. In three quick and easy steps, you are able to create the finest quality worksheets in PDF format ready for downloading or printing. Additionally, there is a very intelligent suggestion feature to assist you in automatically customising the engines with the most appropriate parameters, that you can base on for a more personal customisation should you wish to.


At the end, only the results count. Undeniably, the produced worksheets are purely sublime. With a professional typography, an attractive design, the output papers are really eye-catching, engaging, a pleasure to work with for all students. 

Give the Xsmart Generator™ a try to be amazed, for free. Because education matters.

MathEngines Founder