A few years ago, I came across a method for writing out the answers to the 7-times tables – without counting in sevens. It used a grid identical to the one we use in the game Tic Tac Toe (also known as ‘noughts and crosses’ or ‘exee-ozees’).
After seeing success with this strategy in my tuition classes, it got me wondering if other times-tables could be written using the Tic Tac Toe method. I quickly discovered that the 3-times tables could be done easily this way, after which it became clear that the answers to the 4s, 6s, 8s and 9s could also be successfully written by a child – each one in under 20 seconds.
The Tic Tac Toe Tables
Before getting your child to try this method, give it a go yourself. This should give you the confidence to demonstrate it at speed (in other words, impress your child with the trick) then do it slowly (so as to reveal the simple secret behind the trick). In many cases, this will create an urge in your child to mimic the trick and a desire to impress friends and relatives. The video below first shows them done at speed, then breaks it down in more detail.
The 3-times Tables
Draw the four lines of the Tic Tac Toe grid, then start at the bottom-left square. From bottom to top, write the numbers from 1 to 9.
Across the centre row, add a 1 before each digit. Across the bottom row add a 2. Voila! The first nine answers to the 3-times tables.
Now, reading from top-left to right, recognise the number of each square. The square with a 3 is square number one and is therefore the answer to 3 times 1. The square with a 6 is square number 2 and is therefore the answer to 3 times 2. And so on. The bottom-right square (the one with 27 in it) is the ninth square, which means it’s the answer to 3 times 9.
But what about x10, x11 and x12?
It’s assumed that, by this stage, most kids will be familiar with the answers to the 10-times tables and will also have recognised a simple pattern in the 11-times tables (at least, up to the number 99) so this isn’t really a problem. The vast majority of kids will already know that 3x10 is 30 and 3x11 is 33. However, the 12-times tables aren’t so simple and many schools expect their students to memorise the first twelve answers to each table.
The good news is that the Tic Tac Toe does reveal the answer to 3x12. Simply combine the first two answers (3 and 6) as if they are tens and units: 36. This will also work with the 4-times tables and, with a bit of tweaking, will also work with the 6s right through to the 9s.
The 4-times Tables
Draw the Tic Tac Toe grid again and, this time, start at the top-right square. You are going to move in the opposite direction to the 3-times tables: downwards.
There is one other important factor to consider: 4 is an even number. We can’t write the numbers from 1 to 9 because this would create an odd digit for the units in many of our answers. The simple solution is to only write even digits: 2, 4, 6, 8 and then… 0. The centre square should not be a 10 – we are only writing single digits. So, the pattern is this: 2, 4, 6, 8, 0, 2, 4, 6, 8.
You should be able to see now that the first two answers to the 4-times tables (4 and 8) are in the correct squares. Now we must add tens-digits to the other squares. This is easily done by using the following rule: when the units get smaller, increase the tens by one. For example, the third square says ‘2’, which is smaller than the square before it. You must add a tens digit, so write a 1 to convert the 2 into a 12. The next square says 6, which is not larger than the 2 so stick with just writing a 1: the number becomes 16. The next square is a zero, which is smaller than the 6 in the square before it: increase the tens digit by writing a 2: the zero becomes 20. And so on…
The 6-times Tables
The 6s use a combination of what we learned from the 3s and 4s. 6 is double 3 and just happens to move in the same direction as the Tic Tac Toe method for the 3s (from the bottom-left upwards). But 6 is an even number, so we must use the 2,4,6,8,0 digit pattern from the 4s.
You will know that you’ve done it properly if the 6 is in the top-left square. Now all you have to do is add the tens digits. Remember, if the units digit decreases then make the tens digit one greater than before.
But how does this help kids memorise answers?
Writing the tables using the Tic Tac Toe method will only work if you insist on asking the kids questions from the tables once they have written it out.
The way I use this method in my tuition classes is as follow:
· Demonstrate one of the Tic Tac Toe tables
· Get the student to write it slowly (at first, literally telling them what to write)
· Make sure the student repeatedly writes it (you’ll need lots of paper) until they do so almost by instinct
· Time the student – once they do it in under 20 seconds get ready for the next stage
· Ask rapid, random questions from the relevant times table and insist that they look at their grid for answers (e.g. 6x7 then 6x2 then 6x9 then 6x6…).
After a while, they will have visualised where the answer is on the grid, which is priceless for long-term memorisation, particularly if you repeat this challenge on a regular basis (say, once per week or per fortnight).
The 7-times Tables
The 7-times tables start in the same place and move in the same direction as the 4-times tables: moving downwards from top-right to bottom-left. As 7 is an odd number we will count in ones.
There is a memorable pattern for adding the tens digits: nothing, 1, 2 on the top row; repeat the 2 then 3, 4 on the middle row; repeat the 4, then 5, 6 on the bottom row.
All of a sudden, the trickiest of the times-tables becomes one of the easiest to write out!
The 8-times Tables
The 8s and 9s both start on the bottom-right square and go backwards (right to left).
8 is an even number so use the even digits again: 2,4,6,8,0…
The tens digits are pretty easy to add. From the second square onwards, you will be counting in ones – except that you will write the digit 4 twice (this is simple to remember because two 4s make 8).
The 9-times Tables
The easiest of them all! From the bottom-right square, and moving right to left, count in ones.
Then, when adding the tens digits, count in ones again from the second square. You should also show your child that each answer has digits that add up to make 9.
Yes, but what about those x12 answers?
Fair enough, the 6s, 7s, 8s, and 9s grids don’t reveal the x12 answers in the way that the 3s and 4s grids did. But the first two answers on each grid will still help. For example, on the 6s grid, the first two answers were 6 and 12. Combine the 6 and the 1 to make a 7, then put this before the 2 to make 72. On the 7s grid, the first two answers were 7 and 14. Combine the 7 and the 1 to make an 8, then put this before the 4 to make 84. It won’t take long for kids to work out this pattern.
Isn’t this cheating?
If being able to automatically answer a times-table without counting in 3s, 4s, 6s, etc. is cheating then hopefully we’re all cheats! The point of learning the tables is instant recall, not constant calculations. The point is not to keep counting in sevens if someone asks us the answer to 7x4. We want kids to give the correct answer instinctively. If the Tic Tac Toe tables help us get there faster, then good!
How does my kid use this strategy at school?
There are many possible answers to this question. If your child is asked to answer a times-table question mentally, and at speed, then they won’t likely have the chance to grab pencil and paper and draw a Tic Tac Toe grid! But, if they’ve practised it enough with you at home, they may have already visualised the answer. In other words, this strategy is a stepping stone towards instant recall of answers.
But even while your child is learning each table, the Tic Tac Toe strategy could be extremely useful. Perhaps they get weekly tests at school on the tables. Sometimes the teacher calls the questions out. Maybe they’ll get a chance, as the teacher asks the first question, to quickly scribble the Tic Tac Toe for the relevant times-table. Of course, this depends upon the teacher’s discretion but one thing they can certainly do is scribble out the relevant Tic Tac Toes when presented with longer multiplications (or divisions) when solving word problems during lesson-time.
Tic Tac Toe & Hit the Button
I have found the Tic Tac Toe method to be very useful alongside the online kids’ Maths website, Hit the Button. Among the many one-minute challenges on this site, there are high-speed times-tables challenges for each of the tables.
At Catapult, I challenge the kids to reach a target of 20 correct answers in under one minute. This can prove too challenging and daunting at first, so my initial challenge to these students is to write out the relevant Tic Tac Toe grid and hold it in front of them as they answer each ‘Hit the Button’ question. I do this until they score somewhere around 20-25 within a minute.
By this stage, they should have hopefully become familiar with the answers and are then ready to try to score 20 without looking at the grid. Repetition is key. Even if the student is successful, they will likely need to revisit this challenge a week or two later, then a month or two later.
Rewards are key too – they need to know what’s in it for them!
Using Tic Tac Toe Tables for other Maths challenges
As suggested already, the Tic Tac Toe tables can help kids solve a wider range of problems than just getting a good score in times-tables tests. Long written multiplication depends upon knowledge of the tables. So does creating equivalent fractions. The same counts for solving word problems, and so on.
Indeed, it works perfectly well with division. If your child needs to give an answer to 51÷8 they can draw out the Tic Tac Toe table for the 8s, after which they’ll discover that they can only go as far as square number six (the one with 48 written in it). So, they know that the answer is 6… but they must also give a remainder. All they’ll have to do is count from 48 to 51 to discover that the remainder is 3.
Target Practice
Book number 1 in my Target Practice series provides other suggestions for memorising the tables, so the Tic Tac Toe strategy is just one of many. The key is to answer them quickly and instinctively, hence the time limits, target scores and repeat activities within the workbook.