This particular strategy is for "Counting
on 2 within 10" or up to 10, so none of the
number beyond that. The worksheets include
examples of two different resources that we
recommend for these facts and that is as you
can see, the number one and the ten frame,
and the questions come at variety of forms
and then we talk about this four types briefly
now. So if we are adding "5 + 2", of course
quite simply with the number line we would
start from the 5, make two more hops "What
number to we get to?" With the second example,
"2 + 7" of course we're not going to from
the 2 and then count on 7. There is no count
on 7 strategy, so we would teach our students
for counting on small amounts and our recommendation
is to go only up to 3, so count on 1, 2 or
3. Start with a larger number, so start from
the 7 again count on 2. Early on you'll have
the students draw the lines and the arrows,
you know mark the numbers that they get to
but as they become more familiar with it what
they want them to do is to look at the number
line and if you like mentally imagine the
jumps or you know trace with their eyes where
the jumps would be. So you could say, "Look
at the seven, where will we get to if we can
on another two?" "I'm not going to show you,
you look at it and tell me where you get to".
Ultimately, and we do the same sort of thing
with the ten frame, we put out the counters
to start with, but later on we won't put the
counters out and ask if they can picture it?
Ultimately we want them to, as if were, see
the numbers with their minds eye and be able
to do the addition in their head. So with
the ten frame let's look at that -so if we have "5
+ 2" the same example using the ten frame
we put out five counters and to start with
we would say right now put out another two
counters, "How many do we have now?" The ten
frames are a wonderful source for helping students
develop their understanding of their numbers
up to 10 and then of course you can have another
frame for numbers up to 20, and it works so
well because it's an ordered structure that
allows you to "Subitize" or recognize the
numbers without actually counting them. So
they should able to see that's 5 once they
are familiar with ten frames and they'll be
able to see that that's 7. Again, after a
while as I've said before we might put out
some of the counters and say put out five
and say "Imagine the other two, what number
would we get to?" There's also another arrangement,
we could fill one row to start with so that
would be 5 "Where would the other 2 go?" "What
number would we make there?" And then after
a while not put any counters out and say "Can
you picture five counters?" now picture another
two, "What number would that be?" and so on.
With the latter two questions, these are missing
addend questions, of course where one of the
two numbers being added is missing and we
have the sum of the two numbers. Going back
to the number line, this question that would
say, "We finish at four we have two hops from
this side of course, where do we start from?"
So it's more complex, we're asking the children
to imagine a sort of backwards motion. This
is not subtraction as such, so were not going
to say "Simply turn this around and subtract"
but it's preparing the students for subtraction,
so I would probably say we'll, "If we have
two hops like this where did we start from?",
that makes it obvious and then after while
of course they can work for that for themselves
with other examples. As similarly 2 plus something
equals 8 using the ten frame to show this
one, we would need to put out the 8, probably
all with one color. Actually we could do it
this way, with two of them in another color
and say "2 plus what equals 8?" "What's the
other number when we added 2, to it?" Ok so
reasonable straight forward, but it's important
that the students to develop this ability
to picture the numbers in their head and ultimately
be able to think and recall their number facts
independently of the resources.
