Top Tips

PLYT Top Tips

Counting beyond 12

If a child is just doing number recognition, they can start to “count on” from the square they are currently on to encourage counting up to 112. For example if a child is on square 47 and they throw a 6 they can start counting at 47, and count on another 6 by using their fingers to get to square 53.

Number Bonds

One of the easiest ways to learn number bonds is for children to use their fingers – hold them out so they can see all 10 fingers. Then, if for example they throw a 6, they can put down six fingers and see how many are still upright – 4. This works for numbers up to 9. For 10.11 & 12 get your child to hold their hands up twice, so the first time is 10 and the second time put down either 0, 1 or 2 and they will get the answer 10. 9 or 8 making the number bond up to 20.

Addition

Don’t forget to teach your child that it doesn’t matter which order they add the numbers – they are looking for the easiest way to add the numbers together. (This is known as the commutative law and it means that a + b is the same as b + a From your child’s perspective it is whichever is the easiest way to add the numbers together).

For Example - when adding two numbers, always start with the biggest number and add on (even using fingers) from there. E.g. 4+12 = 12 +4 It’s much easier to start at 12 and add on another 4, even on fingers, than the other way round.

If they are adding 3 or more numbers they may want to consider which ones to add together first. For example if they throw 12, 7 and 3, from doing number bonds they know that adding 7+3 =10 and they can then add that onto the 12.

 

 

Addition

Don’t forget to teach your child that it doesn’t matter which order they add the numbers – they are looking for the easiest way to add the numbers together. (This is known as the commutative law and it means that a + b is the same as b + a From your child’s perspective it is whichever is the easiest way for them to add the numbers together).

For example if they are adding 3 or more numbers they may want to consider which ones to add together first. For example if they throw 8, 6, 11, 4, from doing number bonds they know that adding 4+6 =10 , so they can then add on the biggest number - the 11 to get to 21 and finally add on the 8 to give 29.

Your child may do it a different way and there is no right or wrong way to add them – you just want to point out where they could make it easier for themselves to add the numbers together.

Fixed Dice Multiplication

If your child is just learning to multiply, start off by fixing one dice and just throwing the master dice.

Start on 2′s as these are easy to work out. You child can do this by counting and missing out every other number. Once you have mastered the 2′s, move on to numbers that are a function of 2′s, for example try 4′s as these are just like doing 2′s but again missing a number each time, then move onto 8′s again missing a number.

The same process applies to the sequence of 3, 6, 9 and 12. Start off with 3 and then once you’ve mastered that, move onto 6 and so on. (also see tips on rounding below, for 9 and 12)

5′s and 10′s are probably the easiest of the lot as children learn to count in 5’s and 10’s.

Remember if you’re multiplying 5′s by an even number it will always end in a zero and if it’s an odd number it will end in a 5.

Multiplying by 10′s is easy as you just add a zero to the end of the number you are multiplying by eg. 6×10 = 60. (Note that this can be controversial as we're not talking about place value but in PLYT we only use whole numbers so it works fine.) 

That just leaves 11′s and 7′s. To multiply 11′s, you just need to repeat the number you are multiplying by twice
•e.g. 3 x 11 = 33 (ie: the multiplyer 3, twice).

This works up to 9 (9×11=99) and then for 10 you add a zero to the end of the 11 (10×11 = 110) as described above and for 11 and 12. I would say the easiest thing is to work out 10 (110) and get your child to add one or two more 11′s
• e.g. 11 x 11 = (10 x 11)+(1 x 11)=110+11 = 121
•e.g. 12 x 11 = (10 x 11)+(2 x 11)= 110+22 = 132.

Unfortunately 7′s is a hard one but once your child has mastered all the other times tables, the only one of the 7′s that they are missing is 7 x 7 =49 and the easiest thing is to learn this one off by heart. All other calculations in the 7′s can simply be turned around and they are within the known times tables – it doesn’t matter which way you multiply the 2 numbers as the answer is still the same. This is a great discovery for children and can really help with all times tables and especially when children move on to using 3 dice.
•e.g. 5 x 7 = 7 x 5 = 35.
•e.g. 12 x 7 = 7 x 12 = 84.

To practice 7′s, fix one dice on 7 and keep throwing the master dice and try to answer – the more you practice, the more the answers will stick in your child’s head.

Multiplication with 2 dice

Remember that you can turn the times table around and still get the same answer – eg 5 x 7 = 7 x 5 , so you may not know your 7 times tables but you can do this if you know your 5’s. This is called the commutative law.

Multiplying by 10 – add a zero on the end (as we are only using whole numbers)

Multiplying by 5 – an even number multiplied by a 5 will always end in zero, an odd number and a 5 ends in 5

Round up or down:

If you have a 12 as one dice, first times it by 10 then add two times the original sum on
•Eg. 12 x 8, first multiply by 10 so 10 x 8 =80
Then add two times the original sum on 80 + (2 x 8) = 80 +16 =96

If you have a 9 as one dice, first times it by 10 and then take one times the original sum away
•Eg 9 x 4, first multiply by 10 so 10 x 4 =40
Then take one times the original sum away 40 – (1x4) =40-4 = 36

 

 

 

Chunking Opportunities

Break down the numbers into easy to manage chunks (chunking)

e.g. if you throw 3 dice – 4, 7, 8

First multiply 2 of the numbers together 7 x 8 = 56 before multiplying by the final dice, 4

To work out 56 x 4, break 56 down to 50+6 and then multiply each by 4 before adding the totals back together again

So you have 50 x 4 (=200) plus 6 x 4 (=24)

The final total is therefore 200 + 24 = 224

Great – practising multiplying and addition in one! 🙂

Easy Combinations

Even numbers and 5’s – If you throw a 5 as one of your dice, try to pair it with an even number (if you have one) to give you a number ending in zero

· e.g. if you throw 3 dice – 8, 7, 5

First multiply the even number by the 5 : 8 x 5 = 40

The 40 is the same as 4 x 10

So you have 4 x 7 = 28 and then multiply that up by the ten (add a zero on the end) 28 x 10 = 280

Multiply dice together where you can, to keep numbers in known times tables

· e.g. if you throw 4 dice – 2, 4, 6, 3

Firstly combine 2 x 6 =12 and also combine 3 x 4 = 12

You can then multiply 12 x 12 = 144

Rounding Up or Down


•If you have a 9 as one of your dice, first multiply by 10 and then take 1 (times the original sum) away at the end,

e.g. if you throw 3 dice 12, 4, 9

Firstly multiply 12 x 4 = 48 then multiply up by 10: 48 x 10 = 480

Then take away 1 x 48

Which is 480 – 48 = 432

This really works on your mental maths – here you are multiplying and subtracting in one go!


•If you have an 11 as one of your dice, multiply by 10 and add one (times the original sum) on at the end.

e.g. if you throw 3 dice 6, 7, 11

Firstly multiply 6 x 7 = 42

Then times the answer by 10: 42 x 10 = 420

Finally add on 42 x 1

= 420 + 42 = 462

In this calculation you are using multiplication and addition – great!


Create “Round-able” numbers - If you throw more than 2 dice, you may be able to multiply 2 dice together and then round up/down your first answer before multiplying by the final dice

e.g. if you throw 3 dice 11, 6, 9

Firstly multiply 9 x 11 = 99

Then round this up to 100 (by adding 1) before multiplying by the last dice

ie:- 6 x 100 = 600

Finally take away 1 x the final dice from the answer

600 – (6 x 1) = 594

You can do this for much bigger numbers too, where you are throwing even more dice, such as 108 x 99, which when rounded up gives 10,800 and then you just have to remember that you have to take away one lot of 108 (as you have 99 of them and not 100). The answer would therefore be 10,692 (10,800-108) – not an easy calculation but easier than doing a long multiplication in your head!

Halve and Double

If you have an even number either as one of the dice or a multiple of the dice, then you can use the halve & double technique

e.g. if you throw 4 dice - 8, 7, 6, 3 - multiply the 8 x 6 = 48 and 7 x 3 = 21 to leave you with 48 x 21


Now that seems like quite a difficult calculation so the aim is to reduce one of the numbers to something easier. So we're looking to keep halving the even number as far as we can whilst doubling the other number as follows:

48 x 21 = 24 x 42 = 12 x 84 = 6 x 168 = 3 x 336  = 1008

e.g. if you throw 3 dice - 4, 8, 12 - multiply the 8 x 4 = 32 to leave you with 32 x 12


You could use some of the earlier tips but you can also use the halve & double technique as follows:

32 x 12 = 64 x 6 = 128 x 3 = 384

Or alternatively you can do it this way:

32 x 12 = 16 x 24 = 8 x 48 = 4 x 96 = 2 x 192 = 384

Multiplying by 11

There is a simple way to multiply bigger numbers by 11 and we don’t really like this as it is a trick to learn rather than a multiplication method, but we’ll tell you anyway.

Take the multiplier and separate the two numbers out, then add them both together and put the sum of the two between the original numbers – best explained in an example:-

· e.g. 54 x 11

Firstly split the 54 so you have 5 ” – ” 4

Then add the 5 and the 4 together to get 9

Finally insert that new number in between the 2 original numbers to give the final answer = 594

· e.g. 96 x 11

Again split the 96 so you have 9 ” – ” 6

Then add the 9 and 6 together to get 15

Insert that in between the originals but because we’re inserting a number greater than 9, the 1 from the 10 is added to the first number, the 9 and the units number (5) is placed between the originals

10(9+1)56 = 1056

· Just check it works by trying another example:-

88 x 11 would be 8 ” – ” 8 and the sum of the 8 + 8 = 16,

Add the 1 to the first 8 and put the 6 in between to give

9(8+1)68 = 968

Great – you’ve got it!

 

 

Say it Out Loud!

The best way to learn how to multiply quickly is to listen to others working it out!


So .......... if you are trying to help someone become more confident with numbers, rather than doing your calculations in your head, do them out loud - tell the other players which of the tips above are you using as you multiply the dice - chunking, rounding, easy combinations first etc.

We have found this to be one of the best tools for teaching our children how to multiply quickly - if you verbally demonstrate how you use the quick tips and get the answer correct, they are more likely to do the same when it's their turn!  Not only that, but if you encourage young Plyters to also say it out loud you can discreetly check their methodology and if and where they are making any mistakes. 

It might seem strange at first, as we assume all mental maths should only be done in our heads, but it really does work!