# Introduction to Ten Frames for Teaching Numbers to 10 or 20

So let me just explain what a ten frame is

and why they’re so useful and why I think you should be using them with your students

assuming that you’re teaching young students in primary school, elementary school. So the

ten frame, it’s one of the simplest resources to produce, I just print these on a computer

they’re so easy, you just make a table with 10 square cells in it, give it some boarders

you know, so that you can see it, and then we simply use counters and if you’ve got magnetic

counters then of course you can use a white board like I am with your students and we

just put the counters on the ten frame like that. Now let me make a point here, some teachers

I’ve heard write numbers in the squares, you don’t need to do that, we don’t need the numbers

there, that’s not the point, in fact rather the opposite, we don’t want the numbers written

down, what we want is for the students to visually recognise how many counters there

are without counting and without any other queues, if you write the symbols in here then

they’ll be, if you like distracted by the symbols or you know it will be a sort of a

short cut to save them having to think and that sort of thing, we don’t want that at

all, we just want to say, “Here’s some counters then me how many there are?” and of course

the skill that we’re developing in our students and there are two ways to spell that, so I

better put both of them, is “Subitizing” with an “S” or a “Z”. And that of course, you possibly

perhaps, sorry, I’m not going to make any assumptions, you may remember this from your

studies at University because it’s not a word you choose with your students very often it’s

the skill of being able to count a group of objects by just looking at them, so it’s effectively

not really counting its recognising how many there are and just go, “That’s 4”. So an adult

can look at that easily and go “That’s 4”, you don’t have to apply a numeral to each

one and go “1, 2, 3, 4” if I put 20 of them on there, you’d have to count them, unless

they’re in some ordered arrangement, because there are too many, but with small numbers

you could subitize. Alright, so our students will get used, they can subitize small numbers

anyway, but we want to stretch it beyond the small numbers cause subitizing usually goes

to about 4 or 5, but we can carry that much further, and say for example, “How many are

there now?” once the students are familiar with the basic numbers it won’t be hard for

them to see that that is the number 7, because there are 4 here and 3 there. There other

arrangement I recommend is to fill one line of 5 first and then the other 2, so the others

I should say, so that would be an alternative arrangement for the 7, and again you can easily

see its 7, providing you know how a little bit of maths that you know that, you know

5 and 2 makes 7. So every number that we represent with a ten frame can be easily subitized.

So we can go all the way to 9, we can go all the way to 10, there’s no difficult numbers

there, they’re all easy, there all easy to, once you, you know, once the student gets

their head around the numbers up to ten, so they’re familiar with the numbers, the names

the symbols and that sort of thing, they will quickly get used to the idea that when it’s

all full, it’s 10 and if you take one away that must be 1 less than 10, so that’s 9,

if we have 2 lines of 4 that’s 8, and so on and so on and so on. And so as the students

become familiar with using the ten frame and become familiar with the numbers, they’re

developing a knowledge of the numbers that I believe would be almost intuitive, just

like for you and I, when we glance at that, if I said to you, “Explain to me how you know

that’s 8?” you probably have to stop for a minute and go, “What are you talking about,

of course it’s 8, I can see it’s 8” it’s so easy I can’t even work out, you know how to

make it more complicated, because you sort of intuitively feel that’s 8, because you

are very very familiar it. I believe students will be able to do the same thing, that with

practice over time, having used ten frames a lot, they will develop such a knowledge

of the numbers up to 10, that they effectively become easy and they become intuitive, and

I think that quite honestly, my firm belief is that if you were to apply this with very

young children early on in their schooling you almost wouldn’t need to teach a whole

lot of number fact strategies for addition and subtraction, because the students would

just go, “Oh that’s easy, I do that with a ten frame”. So they will know for example,

going back to the arrangement for 7, that “4 + 3 is 7”, and they’ll just know that because

they’ve seen it so many times with a ten frame, or they’ll know that “5 and 2 is 7” and they

won’t need to use the count on strategy, to start with 5 and then count in their head

6, 7 and say “7”, they’ll just know its 7 because they’ve used the ten frame. So, you

can tell from what I’m saying, I think ten frames are outstanding, I wish I’d used them

when I was a younger teacher in my classes because they’re just so powerful, so useful,

all these mathematical ideas are almost brisling with mathematical ideas. I know the numbers

are small, it’s not going very far, but it lays such good foundations for the young students

that I think it should be just used as a matter of course. Let me go one step further and

put up the double ten frame, so again we can easily fit this on to a single sheet of photo

copied paper, now we can use this to show numbers that go obviously beyond 10, so let’s

have a look at one, let’s have a look at that arrangement. Now, just one little point, on

the orientation of the ten frames, it’s perfectly fine to have these rotated the other way,

so the long axis is horizontal, but for double ten frames, particularly for dealing with

numbers beyond 10 , I like to have it in this orientation, simply because it matches the

notation for the teen numbers. So if a number like, this “13”, if we fill up the ten frame

on the left, we can then put a 1 and explain to students that is one collection of 10 and

that’s what the 1 means and then the one on the write has the left of the ones that make

up the rest of the number. Just have a think for a moment, about the number 13 and how

complicated it is, now again we grew up as children ourselves we’ve learned that 13 came

after 12 and say write it down and all sort of thing. But, and I’m sure you’re aware of

these things, that these difficulties with teen numbers, they all share them, they’re

backwards and what I mean by that is, we say the teen last, we say this number first, know

I could have started with an easy one like fourteen, we say the four first as you know

and if you’ve taught to very young children you’ll know that they often write the wrong

way around, and I don’t think it’s because they’re dyslexic, although that could be a

problem for some students, it’s because of the way we say it. If you say to a child,

“I want you to write down the number 14” before you even say the teen they probably written

the 4 already. Thirteen is difficult, because it doesn’t say “Three”, it would be helpful

if it was called “Threeteen”, but of course it’s not, it’s thirteen, so a child has to

associate the “Thir” part of the name with the number 3. It’s a bit like the number one

third, or the third in a sequence, so there’s a bit of a link there, we don’t say, “Ten”

we say “Teen” instead of ten, you know. So all this difficulties, so ten frames would

be very very useful to help our students develop a familiarity with the numbers between 10

and 12 and help them deal with all those challenges that the teen numbers post to them. Now, we

could go further with this, we can do all the number facts of course, up to 20, so we

could do a number fact like “9 + 4” quite easily with an arrangement like that, we could

even use more ten frames, but that’s a story for another day, but you could multiply this

and do multiplication strategies and so on, with that as well. Ok this video is a bit

long this week, I hope it’s been useful and I look forward to talking to you next time.