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G'day everyone, I'm Dr Peter Price of Classroom Professor. Welcome to week "39" in the Free
Math Worksheet Series. This set of worksheets; this is for the second school week of 2013,
if you are in the northern hemisphere and so it's another revision week. So this time
we're looking at "Multiplication and Revision" and the worksheets this week come from the
"10 Minutes a Day Level 2 Book: Multiplication and Division Revision" and it's actually the
last set of worksheets. So there isn't a particular strategy to focus on this week, because it
will include all the strategies, so once again as last week's revision set, I mentioned then,
for this week this would be another good revision worksheet set obviously, but you could also
use it as a form of a check-up, to see how your students are going in learning all of
their multiplication and division number facts, so quite a useful set. Just to quickly go
over the strategies that a part of our scheme if you like or the scheme that we recommend,
we have "Doubles", so 2x number facts and of course for each one these there's the division
inverse facts as well, so dividing by 2. "Multiplying by 5 and 10" base on a place value strategy,
"Multiplying by 3", where we say "Start with a double of a number and then add one more",
"Multiplying by 4", which is double and then double again, "Special cases of 0 and square
numbers", "Multiplying by 9" with all the patterns that we can find there and then the
last 3 sets, the most difficult number facts the "Sixes, Eights, and Sevens", for the sixes
we build up from known facts, so build from 5x or from 3x and then double, for the eights
we can do double, double, double and the sevens, there isn't a simple strategy for the sevens
but again we build from known facts. And of course in the cases of the sixes, eights and
sevens, if you leave those to the end then you'll have already done the multiples of
those numbers by all the other numbers, so for example, you'll have done the 6 nines
when you've done the 9x, 6 fives with the fives and so on. So all that's left at the
end there, because we've already done squares as well is "6 x 8, 6 x 7 and 8 x 7", so there's
not a lot left over. I just thought I talk briefly about some basic ideas for a sort
of over view lesson of number facts and sort of generic strategies that we can use, or
our students can learn to use themselves in learning these number facts. Once again I've
got the magnetic tiles I've put up, and again this is an exercise you could do with students,
that you give them material like this or just cards with numbers on or so on and ask them
to find the number fact families, the groups of facts that go together. Again we've got
this cloud with associated numbers in it, in this case it's "3, 6 and 18" because we're
looking at multiplication and division. And once again those three numbers in a sense
belong together for this number fact, so if a child, a student can learn to associate
those 3 for these 2 operations then they should be able to come up with the 4 number facts,
"3 x 6, 6 x 3, 18 / 3 and 18 / 6". And so the numbers are effectively recycled or reused
over and over again, and so we think that's a help for students to see yet again, connections
between number facts and how they belong together. Let's look at some material as well and these
counters well of course are arranged in an array, in rows and columns and that's a highly
recommended arrangement for multiplication and division, just on that point we shouldn't
just scatter the facts around, the counters rather, or even just you know, put them in
groups because visually it's not very helpful, it's ok when the numbers are small, so if
you did 2 x 6 and you see a cluster of 6 and another cluster of 6, that's going to be fine,
but if you do 7 x 6 and you make 7 clusters of 6, nobody can see what that number is,
those arrangements are simply unhelpful. Whereas an array you can do other things with it,
For example, this array of course is 3 in this vertical dimension and 6 horizontally,
and we're multiplying those two together we can see that if we took those counters and
just rotated them 90 degrees, we would then have 6 x 3, so we can see the commutative
property of multiplication and the inverse facts, sorry, not the inverse, the turnaround
facts for each other the "3 x 6 and the 6 x 3". Another one which was taught to me at
University and I thought is a very clever idea is to make this into a division question
and say, "Well if we're dividing by 3, here's the number that we're dividing, what will
the answer be?" and of course the answer is 6. So that's a sort of combination of the
written algorithm and the visual representation and again of course we could turn that around
and have 6 here and 3 there. So the students can see that interaction between the three
numbers in this particular fact family, and you could do similar things with other facts.
Just on this particular one I mentioned before, teaching the 6x number fact, here's an illustration
of that, that we're multiplying by 6, we could say, "Well do you know what 3 x 5 is?" because
the fives are easier, let's add another 3, or we could split this in half, "And that's
not done very neatly" so we can say, "Here's 3 x 3, here's another 3 x 3", 6 threes is
the same as 3 threes doubled and of course 3 threes a 9. Ok so there's some ideas, I'm
sure you've got plenty of your own and I hope the worksheets are really useful to you, and
this video is at an end and so I'll talk to you next time.