Times tables - a new way to learn

“Order and simplification are the first steps towards mastery of a subject” -Thomas Mann.

Our website introduces an innovative way to learn times tables. PDF downloads are free and feedback is welcome. The focus is on a 9×9 number pattern. And with good reason. Position holds the key. If the multiples of a number are always in the same position, then the values in that position will always  be multiples of that number.

See how it works or read further for a short introduction.

It gives reason to argue that x 10, x 11 and x 12 should only be learnt later.

 

“The most dangerous phrase in the language is, ‘We’ve always done it this way.’” -Grace Hopper 

Order and Structure
Learn by Location

Memorising information

Below are two lists with the same set of 9 words. If you were asked to memorise the words in order, which list would be easier to remember?

 

candle

swan

heart

boat

snake

cherry

flag

snowman

balloon 

Structure - Sets of three

Regrouping the information into a 3×3 layout with 9 positions, can make it easier to learn and recall. It is similar to creating 9 imaginary rooms as described in the memory system referred to as the method of loci [1].

Equally, 9 positions  of 9 specific colours, can further assist memory. For example, here the word “balloon” is in the colour PINK. Hence, if we know that the colour pink is always at the BOTTOM RIGHT, we can visualise a pink balloon.

Position holds the key! If we always put something in the same place, we always remember where to find it.

Then, why not apply these concepts to numbers in times tables? 

For example, if the number 81 is in the colour PINK and if we know that the colour PINK is always a multiple of 9 which is also always at the BOTTOM RIGHT, we can remember that 9×9=81.

This 3×3 format yields a number set that is perfectly organised. So each number/multiplier holds a specific position, colour and image throughout. 

Multiplier structure within identical Structure
Multipliers - fixed order and colour - 3x3 within same 3x3 structure
Image and colour associated with each number
Images - fixed order and colour

Order of data

Times tables are sorted by column ↓. The transposed alternative would be to order the numbers by row →. The same concepts apply.

List sorted by Columns
Sorted by column
List sorted by Rows
Sorted by row

Symmetry and geometry

Both methods of sorting the times tables result in square number symmetry.

Students learn by number, position and colour. Symmetry can later be introduced as a mathematical surprise.

Times tables - symmetry
Symmetry - square operations

How to learn

We learn one set of multiplication tables at a time.

Not only will we eventually know the entire structure, but we will also associate numbers according to position, colour and image.

visual multiplication
9x9 structure

The picture within each table is identical to the overall big picture. Both consist of 9 positions, 9 colours and 9 images.

a x b = b x a

The answer can only be in the colour that is associated with “times a” or “times b”.

For example the colour that we associate with x7 is blue while the colour associated with x3 is red.

3x7 = 21 blue, position and colour associated with x7 within 3x table

7x3 = 21 red, position and colour associated with x3 within 7x table

9x9 structure with images in each 3x3 structure

References

[1] McCabe, Jennifer A. – Teaching of Psychology, (2015) – journals.sagepub.com – Location, Location, Location! Demonstrating the Mnemonic Benefit of the Method of Loci.   

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