Let’s explore 1

OK mathematicians, let's explore.

So one of the strategies that we are shared was counting back in 10s and ones to solve 23 - 19.

Now some of you might know this as the split strategy and the jump strategy.

We're using a combination of them.

Some of you also know that what we're actually doing here is partitioning the numbers into chunks of 10s and ones so using knowledge of place about you too.

And knowledge of the backward count.

So let's have a look at how many steps at talk to solve this problem.

So here's the 2 tens and three representing 23.

And here's a number line underneath to help us keep track of the number of steps that we're taking.

So the first thing that we did was to take away a big chunk of 10.

And we can record that here and so that means we've taken one step.

Then what happened was to remove the other 9.

9 ones.

So this is what that looks like.

Yeah, and that's now the second step and we take away a block.

We do the jump.

That's the third step, another block, another jump.

That's the 4th step, and so we keep going on until

Yes, we removed all nine ones.

And that's what it looks like.

So that was one strategy, counting back in 10s and ones.

Let's have a look at another one that we used.

Let's explore it further.

So in this one we adjusted the numbers.

So we used our knowledge of landmark numbers as well as using known facts and some other bits and pieces of mathematical knowledge.

So so far this shows 23 and we haven't taken any steps yet.

And then what happened was we could re imagine the problem because we know that 23 - 19 is equivalent in value to 24 - 20 and so now we're going to record this on a number line 2 to show actually is little jump there to increase the quantity in our collection from 23 to 24.

So there was one step and then a giant step of removing 20 uh-huh.

And that's what that looks like on a number line.

And that was the second step taken that got us to the conclusion of four things remaining.

Yes, so adjusting the numbers only took two steps.

So now if we compare and contrast one strategy counting back in 10s and ones took us nine steps to solve the problem and adjusting the numbers.

Only took us 2 steps to solve the problem, so what's some of the mathematics here?

So what we really wanted to draw attention to today is the idea of efficiency.

So efficiency is defined by the number of steps you take to solve a problem.

It's not about speed.

It's about the number of steps you take.

In fact, sometimes a more efficient strategy takes a little bit longer to think through as you're becoming confident in using them and as you become more confident.

It does tend to make it a little bit faster for you, because it's a more efficient strategy with this less steps.

It also means that you've got much less chance of making small computational errors.

If I do 9 steps, I've got nine chances of making a small error if I do 2 steps.

I've only got two chances of making a small error.

So the other thing about efficiency though, is it's a really personal.

So how efficient a strategy is to you is based on how much you know about numbers, operations and mathematics.

You can't use strategies and knowledge that you don't know about just yet.

And three other things to be careful of.

Some strategies are pretty similar in their efficiency, so then you get to choose which one you would like to use.

And sometimes there's a difference of one or two steps, and you might think, well, I'm really confident using this strategy, so I'm OK to go ahead with it.

Sometimes a strategy is efficient in one context, but not in another, which is why it's really important that we learn lots of different strategies.

Yeah, and not just get locked into one way of thinking.

And when we are tired or stressed or not feeling our mathematical bests, we might choose to use less efficient strategies as it's the best that we can do as as a mathematician that day.

And that's OK too.

Yeah, so over to you now, mathematicians, I'd like you to reflect on the strategies you used to solve 23 - 19.

Or you might have been working on 23 - 19 or two tens and 3 ones minus 1 ten and 9 ones and identify now the most efficient strategy you used.

Yeah, how many steps did you take and do you think you could use the same strategy with other problems and note down your thinking in your workbook?

OK mathematicians, I hope that's helped you clarify some ideas about efficiency and until next time we meet have a lovely day.