So we've got two resources that we're going
to use for this strategy, as we do pretty
well for all addition and subtraction number
facts, and that's Ten Frames and Number lines.
So let's look at the Ten Frames for a start,
a ten frame is a really really good device
for helping students to recognise the numbers
up to ten, in what we call "Subitizable Patterns",
which means they can recognise the number
without actually counting the counters. So
you'll be able to look at that and see straight
away there are 5 counters, we want children
to recognise that in the same way, and by
saying "They're not counting", what I mean
by that is they're not saying "One, Two, Three,
Four, Five" so they're not using the sequence
of number names, they're simply glancing at
it and seeing. Ok, this isn't really about
ten frames, but that's a quick introduction
to that, and the other part of using ten frames
is we have a couple of choices so we can either
start them as they were, just there in pairs
and have odd and even numbers as we go up
to ten, or we can fill up one row, one at
a time up to 5 and then the second row. So
let's continue with it like that since the
numbers 5 it's going to be quite convenient
and we're counting on 1, 2, or 3. So the question
for the students will be "What is 5 + 1?"
"What is 5 + 2 or 5 + 3?" or the turn arounds
for those, so we could say, "What is 3 + 5,
2 + 5, or 1 + 5?" Realizing of course that
we want the student's to count on the small
increment and the increments only go up to
3, so we're never going to count on 4 or above,
we're only counting on 1, 2, or 3 and if we
have another number with 1, 2, or 3 where
we start with that number, start with a large
one and count on the small amount. Alright,
so the question might be "What's 5 and 1 more?"
we want the students to recognise that the
answer is going to be "6", but we don't want
to use the ten frame as a sort of physical
calculator, were you put the counters on and
then say, "How many do you have now? Let's
count them" or something like that or even
"Let's Subitize them". We're not using the
ten frame to find out what the answer is,
we're using the ten frame to help the students
imagine it, and visualise it and picture it
in their minds, that sort of thing, so rather
than put the counter on straight away, we
might say, "What number is this on the ten
frame?" "How many will there be if we add
one more?" "Can you picture it in your mind?"
"What will it look like?" that sort of thing,
so we want the students to visualise that,
and we could use the same colour or a different
colour I don't particularly mind, but this
emphasises "5 + 1", similarly, "5 + 2, 5 +
3". So we're asking the students, as I've
said, to picture it in their mind and think
what the answer will be, before we actually
show it with the counters, so we'll probably
show the 5 to start with, but the sum the
5 plus something else, we want them to picture
it first, obviously some students won't be
ready for that when they're very young, so
they may need the counters to support that
level of thinking, but that's where we're
going with this, and of course ultimately
we want to stop using the ten frame all together
and say, "What's 5 + 2?" and we want the students
to think of those numbers, and a ten frame
gives them a visual model on with to base
that sort of thinking. Alright, using the
number line is not really, I was going to
say, is much the same thing, it's the sort
of principle that we want the students to
visualise and think in their heads and again,
and not use this as a calculating device,
but it does represent the numbers differently,
for a start there are no counters there, so
there are no objects that are being countered
or the numbers are not being represented by
physical objects, but rather by the symbols
or the written numerals from 0 to 10, and
of course they're written in sequence from
0 to 10, so what we're looking at is the sequence
of counting numbers. So were as, if we were
doing another number fact like, "4 + 5" we
could do that on a number line but it's slow
and cumbersome and it's you know, when the
numbers get larger the number lines not all
that useful, we can use it but ten frame are
going to be more useful for a lot of those
examples, but for counting on 1, 2, or 3 the
number line actually emphasizes what we want,
which is the counting on aspect. So if we
were to say, "What is 6 + 2?" and we would
use other language, I meant to say that before,
so we could say, "6 and 2, or 6 and 2 more,
or 2 more than 6" you know, any language that's
similar to that, that encapsulates the addition
operation will be fine. So "6 + 2" use the
number line to visualise the answer, again
we're not necessarily or especially when the
students are able to do it without actually
recording it on the number line, we're not
going to say, "Alright, find the 6 count on
2 more, what number do you get to?" that's
ok when the students are just learning it,
but what ultimately we want them to do is
to be able to look at the number line and
see what the answer is or work it out in their
head and then of course do it without the
number line, but obviously at the learning
phase the students can see that there are
2 jumps if we're starting from the 6 we're
moving on 2, then we get to 8 and so on. We
can talk about the fact that if you start
with an even number you'll get to an even
number, if we add 2, if you start with an
odd number you get to an odd number, there
are all sorts of patterns and so on that can
be seen here, you've got the whole set to
work with, starting with any number from 0
all the way up to 10, to add on 1, 2, or 3,
some are going to be really easy, some are
going to be harder than others, there'll be
a whole lot of things that you can talk to
students about, so I just want to say this,
although when you look at the worksheet, it's
just a plane set of practice exercises, our
intention here is not just to give the students
busy work, we're not just saying, "Here do
a page of these and be quiet" we're using
this as a vehicle to help them practise thinking,
so the most important thing, cause I think
when we look at these, it would be easy to
look at that and go, "Well, these are too
easy, you know, I can't see any grade intellectual
challenge here". The challenge is getting
it in your head, so for the children, we want
them to be able to visualise, think about
the numbers in their head, in the case of
the number line, think of the sequence of
numbers in their head. So another way to do
this just on that particular point using the
sequence is not to use any resources at all
and say something like, "Think about the number
8, in your head, I want you to count on 2
more and tell me what you get to?" so ask
them to count silently without even whispering,
..10, you know so they can think in their
head 9, 10. So that's the aim of all number
facts strategies is to help students to think
about it in their head reach the answer accordingly.
