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G’day everyone, it’s Dr Peter Price of Classroom Professor. In this week’s video
I’m going to talk to you about “Factors and Multiples of 3 and 9”. This comes from
this e-book “10 Minutes a Day Level 3, book number 4: Factors and Multiples”. So were
going to be looking at teaching our students how to determine whether a number has 3 or
9 as a factor, or the other way round of saying that, “Is it a multiple of 3 or 9?” Now
with any divisibility test, one way simple to divide and see what happens, and you know
go through the steps and see if you get the answer. But clearly we’re looking for something
a bit faster than that, and so here’s a collection of numbers and we want to test
which of these are divisible by 3. Now the method that we can use which is really neat,
I remember being quite excited when I heard about this, is that if you add the individual
digits together, if the sum of the digits is a multiple of 3 then the entire number
is a multiple of 3, which I think you’ll agree is pretty neat. So we can start with
a number like 24 and see clearly that it is a multiple of 3 because “2 + 4 equals 6”,
now of course we also know that “24, is 3 x 8”. So if we recognize any of these
just from knowing number facts that’s going to be even faster and you don’t have to
write it up. Another method of course is to look a number like “93”, that’s a multiple
of 3 also, because each of the digits is a multiple of 3, so the students by this age
will hopefully know, the division algorithm, they’ll know what happens when you divide
by a single digit and so they should be able to see that one straight away. Let’s look
at the others “4 + 6 is 10”, so that’s not a multiple of 3, “6 and 2 is 8”, no
neither is that, “5 and 1 is 6”, so that’s good that is a multiple of 3. If you know
that one you don’t need to check 52 because that 51 plus 1 more so that can’t be a multiple,
“7 + 8 is 15, 8 + 4 is 12”, there’s two more multiples. So it is relatively easy
to do, I think it’s one that the students will enjoy, because it’s so easy, and you
know you can have fun of it. Now we’re only doing two digit numbers here but it works
for any size number, so you know, you can easily extend this to other questions for
students. Let’s look at some other numbers, so we’re looking for multiples of 9 this
time, let’s see what we’ve got, now all of these are fairly easy if we only use 2-digit
numbers so let’s add some harder ones, so we’ll have, okay and we might throw in that
one, ok. Now the method for multiples of 9 is almost exactly the same, if you add the
digits together, if the sum of the digits is 9 or a multiple of 9, then the number is
divisible by 9. Now the students probably already know that, having learned the 9 times
table, well before their tables before they get to here, they know that the some of the
pairs of digits is always 9 and so some of these are going to be really easy, that one,
that one, and that one straight away, and this one, the sum of the digits is 9. So as
I said the 2-digits ones are pretty easy, 3-digits we got to actually think about it.
108 if they know up to “12 x 9”, that’s it we’ve got that one, “1 + 0 + 8 is 9”.
“1 + 6 + 1 is only 8” that can’t be a multiple of 9, “4 + 3 is 5, plus 2 that’s
only 7”, “2 + 5 + 2 is 9” so that is a multiple of “9”. So the approach as
I said is fairly straight forward, student should be able to do this quite easily, and
we’re finished so I’ll talk to you next time.