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G'day, I'm Dr Peter Price of Classroom Professor. Welcome to this video in which I will talk
about identifying numbers that are "Multiples of 2 or Multiples of 4". This comes from our
e-Book called "10 Minutes a Day Level 3 Book number 4: Multiples and Factors". So this
comes from a series for students in grade 4 or year 5 and it helps them to recognize
numbers right through numbers with 3 or 4-digits and beyond, which are multiples of the single-digit,
multipliers up to 10 and 11 and 12 as well. So this is from the first set of worksheets
from that book looking at multiples of 2 and 4, the two easiest examples I'm sure you'll
agree. So let's start with a 10 frame, it's quite easy to show a connection between even
numbers and the way they are arranged on a ten frame. So looking at the arrangement of
8 counters we can see that it's an even number, simply because the arrangement of counters
is even, there's no extra ones on the end. So the single-digit are numbers up to 10 are
simple, of course we can continue that further once we've got 10 we can continue and look
at 12 and 14 and so on, but what we can point out here is, that 10 is already covered and
effectively we don't have to look at the 10 because 10 itself is an even number. And we
could back this up and have more tens, we can have 2 tens or 3 tens or you know 128
tens, all the tens are even numbers all we really have to look at is this last set or
of course the last digit the ones digit in a number. So we can show our students quite
easily, that we could have a whole lot of odd numbers, maybe 3,574, that's an even number
simply because of the 4, so the test for divisibility by 2, the test to see if a number is a multiple
of 2, same thing is looked at the ones digit. Of course we're not looking at decimal fraction
so we're not you know, it's got nothing to do with fractions this is just integers, the
last digit if it's a multiple of 2 if it's an even number, including 0 of course then
the whole number is a multiple of 2, so that's quite straight forward. Let's look at 4 now;
looking at the multiples of 4, it will be nice if we could look at the digit again but
of course we can't because, here we have "4, 8, 2, 6, 0, 4, 8, 2" it's all the even numbers
again, but we also have other numbers between them that are not multiples of 4, like these
here, and they also end with those digits, we've got "6, 0, 4, 8, 2, 6" so clearly we
can't just look at the last digit. The test of course and sure you're aware of this, is
that we can look at 100, I'm not going to draw all the squares here but imagine this
has 100, of course we can divide 100 into four equal pieces, we could do it that way
and of course there are 25 in each piece, students can recognize that by this stage
and so 100 itself is a multiple of 4. So much like multiples of 2 where we only have to
test the ones digit, in multiples of 4 we only have to test the last 2-digits, the tens
and the ones, so again if we have, let's put some columns here, if we have thousands and
hundreds and tens and ones, we could have 9 and 7, 8, 0. That's a nice, that's a fairly
easy example, we can see this is a multiple of 4 simply because ignoring the digits that
come before the last 2, the 8-0 the 80 is a multiple of 4 so the entire number is a
multiple of 4. We could use more materials, we could put out some base 10 blocks maybe,
to show hundreds and reinforce the understanding for students by letting them see it for themselves
that every hundred block is made up of 25 fours, or a multiple of 4, 25 times. And so
we don't have to consider them, so we can have a very very long number and all we have
to look at is the last 2-digits. Now that in itself is a bit of a challenge so let's
spend a bit of time looking at that, here are the multiples of 4 up to 48, now if your
students are learning up to 10x number facts then they'll stop at 40 as looking at, sorry,
considering the numbers that the students have learned in their number facts they should
be familiar with multiples of 4 up to 40 or 48, depending whether you got a 10x or 12x
when you teach it, beyond that we have to look at another method so let me suggest a
couple. So we have a number like "74", at first glance a student may not know if that's
a multiple of 4 or not, so let's do a test, the first strategy here is to simply divide
by 4. We're not going to use a calculator that would the defeat the purpose of the whole
program which is to develop mental strategies and develop fluency of understanding, so we're
not going for an easy you know, technological solution. We're just going to try a quick
division "Can we divide this by 4?" 7 divided by 4 is 1 with 3 left, 34 is not a multiple
of 4 so 74 is not a multiple of 4. An alternative let's take a different number, so I'll go
for "62". "Is this a multiple of 4?" let's try halving it twice, because if we double
a number twice, we're multiplying a number by 4 we should be able to reverse the process,
divide that by 2 or take half of it, it's 31. "Can we get half of 31 as a whole number?"
No we can't, so that's not a multiple of 4 either, let's take one that is a multiple
of 4, let's say "64" halve that we get 32, halve that we get 16, that's an even number,
we could halve it twice and so 64 must be a multiple of 4. So that's the strategy it
is more advance its for older students who've learned their number facts, but I'm pretty
sure they're going to enjoy this, it's a fairly simple way of testing for divisibility by
2 or 4. So that's the end of the video, I hope it's been useful and I'll talk to you
next time.