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G'day, I'm Dr Peter Price of Classroom Professor. In this video I'm going to talk about some
"Addition and Subtraction Number Facts" and the topic and the strategy is "Doubling and
Halving". So this will be for students as it says on the screen, roughly in Grade 2,
Year 2 in the UK, Year 3 in Australia. So we're dealing with number facts where the
two numbers being added together are the same, some of these are nice and easy, some you
can picture in your mind's eye, you can Subitize counters if you see them, I'm thinking of
examples like "double 1, double 2, double 3" those are the really really easy ones and
students as I've said in other videos in the past they're familiar with examples from everyday
life, like the legs on a chair, there's 2 on each side, or the legs on a horse, again,
2 on each side or 2 at the front, 2 at the back. So adding pairs of 2, you know we're
not going to find that difficult and adding pairs of 3, that's not too hard either. So
a lot these are not going to be difficult students shouldn't find any trouble at all.
Let's take a harder one though; we are again using the Ten Frames as a good way to help
the students to visualize the numbers, so I'm going to use a couple of approaches to
this in this video, so using the ten frame as one approach we have 7 on each side and
we want to be able to say what the result is. Now the 2 strategies are these, one I've
already mentioned and that is to think of an everyday example, so again the smaller
ones are easy, we've got things like egg cartons, double 6 is a nice straight forward one if
you know that a dozen eggs comes together in an egg carton. Some of the larger ones
harder, I don't have a great example for double 8, so you can make something up that works,
I talked to about in one of my blog post, the edges on 2 Octagons, so it works but it's
not particularly straight forward. For sevens interestingly enough there is another example
and that is the word we use in many English speaking countries for two weeks, a week of
course has seven days, two weeks has 2 lots of seven days or "7 + 7 or double 7" and we
call it a "Fortnight" which just happens to be a little bit similar to the word "Fourteen"
and the word "Nights". So a fortnight is "14 nights" so there's a nice, if you like a Cultural/Historical
connection that will work as well. Let's go back to the ten frames though; if we were
doing this with the ten frames and we put each of the numbers on one of the ten frames,
put them next to each other and then say, "What can we see?" we would want the students
to think about the numbers, we're not going to dive in and say, "Right, start moving the
counters, what's the answer?" "Hurry up; we've got work to do". But rather say, "I want you
to look at this arrangement and see if you can tell what the total is without counting
them" as I've said last week, "And without moving the counters even, can you picture
what it will be like if you were to move them?" That's a more challenging question, if you
just say, "Move the counters now, count them up" that's easy, and a student who doesn't
understand the Mathematics at all can follow that procedure and get the answer, but not,
they're not really thinking about it. So this is a much better thinking question, "Here's
7; here's 7, what will this be if we add them all together to make one number?" "What will
it look like?" "Can you imagine it in your mind?" hopefully the students the better students
especially will see, there are 3 empty spaces up here, and of course if they didn't you'd
point it out, so would ask leading questions like, "How many are?" "What would happen if
we move?" So but better soon, I'm hoping that we'll be able to pick this up themselves and
go, "Well I can imagine there are 3 here, if I take the top 3 from the right hand ten
frame, that will fill out that space, how much will be left?" and be able to picture
it and of course see that the answer will be "1 ten, and 4 ones" and they'll know that's
"14". So obviously we will move the counters, this is quite similar to last weeks' video,
and we can validate that answer and you know, confirm that we we're right. But again basically
I would do a series of these questions using ten frames, using stories about familiar objects,
where we have pairs of numbers being added together that are the same. The halving questions
of course are the reverse of these or the inverse if you like of these questions, so
for this particular example, that would be a question like, "14 - 7=_" now if you just
give students a whole, you know, a whole page full of questions that are halving questions
after a while they'll recognize none of them are difficult because it's always the same
number as this one, so if that's 7, that's 7, you know "6 - 3 is 3, 10 - 5 is 5", so
basically you want to jumble them up a bit, and not make them too predictable. So that's
it for this week, I hope your students enjoy the worksheets, and I'll talk to you next
week.