When to start teaching children times tables by rote

[Happysummer]

My DD is year 4 and I was speaking to a friend about how she is learning all her times tables as they need to know up to x12 by the end of year 4. Her DD is at a different school, in Y1, and quite frankly she scoffed and said her daughter is learning them at home now, and any parent who doesn't do this is lazy.

I'm personally not convinced of the merits of rote learning. My DD is quite able in maths and I would have thought having a good grasp of bonds, addition, subtraction, fractions etc is a good foundation before moving on to all the times tables.

I'm curious, is there a benefit to teaching by rote? Would doing so at home be beneficial from year 1? I assume as this isn't a requirement until year 4, you're asking the child to run before they can walk. But I may be wrong!

I absolutely agree irvineoneohone that the rote recall of 7 x8 is important. It's usually fairly easy to tell if kids understand multiplication by their use of it in problems. For example I have 3 bags of 8 chocolate bars, how many do I have all together? Here is a grid with 5 rows of 7 dots - how many dots are there? Do they recognise that they need to use multiplication?

It's pointless to recall that 3 x 8 = 24 if you have no idea what this fact means, it also puts children off maths because you're forcing them to learn a set of facts that doesn't relate to any concept or have any immediate use. Ideally you learn your times tables as you begin to use them more, this way the rote learning gets reinforced and it actually gets linked to the relevant reasoning skills.

The fact that you know your times tables by rote also aids in the ability to tackle more complex reasoning problems as it reduces the number of steps required to solve a problem. For example I have 8 bags of 4 sweets and give a sweet out each to students in my class (in my class we have 6 tables of 5 students) how many do I have left for myself. For a young student this can seem like quite a lot of information but if they can immediately pass 8 x 4 = 32 and 5 x 6 = 30 it makes things a lot easier, they'll immediately know I have 32 sweets give 30 out oh ok I have 2 left.

I used to teach dd by doing one sum a day. It only took a few seconds several times throughout the day. Then we just go over them once a week about and make any she had forgotten another sum of the day.
With the tricks for the 5, 9, 10 and 11 tables, there are not that many left to actually learn.

I think she was in year 2 or 3 when she learnt them, but I never really looked on it as essential for her learning things in maths; useful, but not essential.

I'm not convinced that they need they by year 4

Look at the year 5 curriculum and you’ll see that they really are needed by end y4. Equivalent fractions, multiplication, division - all the year 5 end of year expectations are very hard to meet without quick recall of tables.

HopeClearwater I've not said that, maybe that was someone else.

I fully understand they need them by the end of Y4. It's my friend who wants her 5/6 year old to learn them all by rote by the end of year 1 I'm questioning. I wondered if this is beneficial.

National curriculum in England is 2, 5, 10 by end of KS1. Then it's 3,4 and 8 in Y3 and up to 12 X 12 by end Y4. Obviously by the time you've learned 2-5, 8 and 10 you know much of 6,7,8,9,11 anyway. Surprised by schools teaching beyond 2, 5, 10 in KS1 - it's just not necessary and there's plenty of other things in the curriculum to focus on.

We are in Ireland and everything is much different here. They do the addition tables at the equivalent of year1/2/3 and then multiplication tables in equivalent of year 3/4/5. Everything is at a slower pace here I feel, schools are much more relaxed here. The day is shorter 9.00-1.40 for first two years and then 9.00 - 2.40 (although my dd’s school starts at 8.40 and finishes at 1.20 for rec/year 1 and the rest finish at 2.20. They focus on the basics for way longer and then build from there. Understanding is the key!!

I think, HappySummer, it could be beneficial to a child that wants to learn tables and understands the numbers and how they can be used. If it’s just chanting and the child has no idea of what 4x4 means or looks like, then the child might be better off learning a poem!

Some children grasp number concepts early but even doing fractions is greatly enhanced if you know your tables! 1/2 of 8 is?? 2 x 4 is 8 etc.

I think your friend is just boasting really.

I fully understand they need them by the end of Y4. It's my friend who wants her 5/6 year old to learn them all by rote by the end of year 1 I'm questioning. I wondered if this is beneficial.

I see what you mean. For me, maths is all about puzzles, patterns and ideas. I would be concerned that rote learning arithmetic might put some children off.

I agree with user1471468296; there is so much more in the curriculum to focus on.

For instance, to teach equivalent fractions to my child I would actually draw circles and colour in quarters and eighths so she could see 1/4=2/8 and that doubling the number a section a circle is divided into, doubles the number of sections in the shaded bit. If you triple it, the shaded bit also triples. Children understand this better easier than "What you do to the denominator you must also do to the numerator" and they do not need their times tables to grasp the concept.

Obviously they will need them for their tests and when they move on to not drawing out equivalent fractions, but they should not be a barrier to finding out how fun maths is.

I have dyscalculia, and really struggle with numbers and can easily get things wrong even with a calculator. However, I learned my times tables by rote, back in the dark ages of the 1970s and can still do them now. I never mastered long division and my life has not suffered with this lack. Learning by rote does mean that the facts are there at your fingertips, which comes in very useful.

For those sneering about learning by rote, it was done for generations and general knowledge was much better overall. Spelling was better, because you did spelling tests daily and weekly and you were taught the rules of grammar. There is far too much emphasis on the stupid SATS tests far too young. Luckily, my DC are adults, so I didn't have to worry about this, but I would have made sure than they were not in school to take these tests, because there is no need. If teachers were allowed to actually teach kids and listen to reading etc, they would know how the child is doing and not require another useless, time-consuming test.

Surprised at some of the responses here - my DS is still working on his in Yr5 and that's fine by me. We got some done the previous year, but found that doing too many and once was confusing

Learning number facts for easy recall, which is what learning times tables is, is essential but nota substitute for mathematical understanding.

LittleCandle - I don't see people sneering at learn-by-rote. Just talking about whether it's valuable to do them all in Y1 or spreading them out over first 4 years.

I am close to 50 and was never taught grammar!

I don’t understand why you wouldn’t. DS is in p2 (y1) and has been learning his 2 and 5 this term, after learning his 10 times table last year in p1. The earlier the better in my view, because it makes it easier to do a gradual introduction to the more difficult 7/8/9 times tables later on.

I never learnt my 9 times table. I still just take one away for the tens and add whatever makes it add to 9 in the units. Also, a few years back, times tables only went up to 10x10. It has not held dd back. There were less than 30 sums to actually learn.

As regards learning sums by heart, for secondary, much more useful has been learning 2,3 and 4 times 25, 2 to the power of up to 10, 3 to the power of up to 4 and square numbers up to 16.

Why there has been this return to learning the 11 and 12 times table, other than the old fashioned idea of maths being all about arithmetic, I do not know.

I never learnt my 9 times table. I still just take one away for the tens and add whatever makes it add to 9 in the units.

This works fine if you're multiplying but there are occasions when it's useful to be able to look at for example 63 and know that it has a factor of 9. For example what is the remainder when 6363631 is divided by 9? Straight away I can see it will be 1. Or what is 27/63 simplified. Immediately I know both 27 and 63 have a factor of 9 and I can write 3/7. Or for example one bus leaves every 27 minutes another every 36 both leave at 11:00am when will they next both leave together? Knowing that 27 = 93 and 36 = 94 I can say well they'll next both leave after 934 minutes = 108 minutes so 12:48pm. This makes it much quicker than having to run through all the possible factors. Not having to even think about the multiplication also massively aids solving more difficult reasoning problems as any multiplications are passed immediately.

To find the remainder of any number when divided by 9, I would add the digits together.

Adding the digits also works for dividing by 3 to find the remainder.

Also, rather than teaching the 5 times table by rote, you can halve the number and times by 10 if it is even. If it is odd, do this with the even number below it and add on 5 at the end. With this any number can be multiplied by 5, without having to learn the whole table by rote.

To find the remainder of any number when divided by 9, I would add the digits together.

Yes but that would take much longer and only work for 9 (or 3)

Your methods of calculation are definitely good in many ways - they demonstrate an understanding of numbers that can be applied in other situations (e.g. to find 808 * 2.5 I could divide by 4 then times by 10) BUT as a PP pointed out they don't help when you have to factorise. For increased fluency in maths you have to just know your times tables so I can see 35 and know instantly it's factors are 5 and 7. This is not the same as being able to quickly multiply 5 and 7.

If I want to add the fractions 11/14 + 19/35. It's useful to see immediately that there's a common factor of 7 then i can quickly find the lowest common multiple and choose the denominator 70 as opposed to multiplying 14 and 35 or going through all the possible factors until I find a common one. Likewise when they go on to factorising it's vital that I can see 27x + 63 and note immediately both have a factor of 9 and then I can rewrite as 9(3x +7). If you didn't know your times tables it would take you a long time to run through all the possible common factors. It has been firmly established that this is useful.

I hate learning by rote and I love finding more efficient methods of calculation if you have to multiply 27 by 5 then yes of course multiply by 10 then half it but the simple fact is knowing times tables by rote is incredibly useful as you move up through the maths syllabus.

IME a child learns times tables easier by being told the tricks than being told to repeat 12 sums until they remember them. "Look at this pattern," is a lot more appealing than, "Say this list until it sinks in."

I agree that knowing the tables by heart is good, but being able to grasp new concepts and finding maths fun is a lot more beneficial.

Our school did:
Y1 - x2 x5 x10
Y2 - x3 x4 x6 x8 x9 (patterns between 3,6 9 and 2,4,8)
Y3 - x7 x11 x12

Y4 was spent reinforcing them every week, Y5 and Y6 have then been mixing them up so quick fire recall and being able to use these to get bigger numbers e.g. 4 x 16 would be the same as 8 x 8, or 14 x 8 would be 10x8 plus 4x8

If an able child has cracked 2,5,10 in yr1 by rote, then absolutely worth introducing 4 and 8 and spotting the pattern with 2x. And so on.

JustRichmal

Absolutely my way of teaching them by heart would be to encourage them to use various tricks to figure them out. Eventually they won't need the tricks as they'll just remember.