And now we are talking about place value. And specifically, tens and ones, and what
that means and we'll use a variety of materials to show the numbers. But the patterns themselves
are interesting, because we are using increments of 10 or 20 or decrements going in the other
direction. Of course the ones will remain the same, so we could start with base 10 materials
and ask them to put out the blocks to show the number "6", and then ask them to show
the number "16" which is a difficult number, because we say "Six" first, but we write the
"One" first and they really have to think about what 16 really means, but they'll you
know, they'll remember they have to put in a 10 there, then do "26, do 36, do 46", write
them down on the white board in a sequence and ask the students "What the difference
is?" "What is changing as we move in to the next number in the pattern and what do you
notice?" "What is the same?" "What is different?" and with the base 10 materials they'll see
of course that the ones material is unchanged, there's, in that example, there's 6 every
time, there's 6 ones, there's 6 ones, there's 6 ones, but the number tens changes and "How
does that affect the number?" And talk about how we say those numbers and how we write
them down. Using a "Grid, a Hundred board" and you got two options with one of these,
either start from "0" or start from "1", and it will finish at 99 or 100, I don't particularly
have a preference one way or the other. But if you lay the numbers out in their standard
locations, the sequence that we're talking about here, the sequences, in tens and twenties
will all form vertical columns of course. So I've got some of these magnetic numbers
and you can see quite clearly, we've got 18, Sorry, "8, 18, 28, 38" all the eights are
in a line because that's 8 ones, and just the tens are changing. We could ask the students
again, obviously "What do you notice?", but ask them to explain "Why?" And that's quite
a challenging question because, you as the teacher set-up the sequence, set-up this quite
obvious pattern, but to ask the child to explain the pattern is far more conceptually challenging,
so it's a good question to ask, I like that sort question to challenge the students in
their thinking. And a student who's up for that challenge, for whom that challenge is
within their capabilities, will recognise that there are 10 in each row, and if we count
along and we count up another 10 we'll end up in a vertical line. It is quite challenging
but I think it's worth, as I've said, challenging the students to reach that. Of course we're
looking at sequences of 20 as well, so we would ask a similar question and say, "We'll
if we start at 18 and we add 20, what number will we get to?" We might even count along
the lines, now I haven't drawn the whole grid up here for the sake of time, but if we started
here and went "19, 20, 21, 22" and counted up 20, it's a bit laborious, but of course
we find out what directly under the 18, but two rows below, "Why is it two rows?" because
it's two tens and so on. To further extend this, we could ask the students about the
numbers that are around this pattern, so these are all the numbers that we have, we could
say, "What number is here?" "What number is there?" What number is there?" and so on.
And ask the students to think about the numbers in relation to each other on the hundred grid.
Lastly, we've got a number line, again number lines are really useful for certain maths
topics, or math topics, I wouldn't want to use a number line for every mathematics topic,
I think they can be over used and often base 10 materials or 10 frames and so on are better,
but for skip counting they're just really useful, and so of course we can a nice, neat
pattern, neater than my drawing, of tens here. Because of the way this number line is drawn,
we've actually got another pattern in-between those, of fives, so we could perhaps say,
"What pattern is this?" "What is this sequence of numbers?" "What do we know about it?" so
we'd have "35, and 45, and 55, and 65". And so there are other questions, other activities
that you could do with a number line. In all these examples it would be good for the students
if they have their own materials if possible, or work in small groups, with a hundred board
or you know, that sort of thing. To really challenge the students to think for themselves,
and also of course to construct their understanding of what their seeing, so it's not just listening
to us as the teacher, it's not just begin a series of instructions to follow, although
that's part of it, but more than that it's being asked to explain what they seen to recognise,
and observe, and analyse and you know, basically use those higher order thinking skills even
among these are quite young students.