Lesson video

Hi everyone, and welcome to today's lesson with me Ms. Jones.

And today we are going to be learning about tracking calculations.

But again before we begin, please make sure that you have a pen and some paper with you, and that you've turned off any distractions and you hopefully you've got a nice quiet space to work.

So pause the video to make sure you've got all of that set up before we can begin today's exciting math lesson.

Right, so hopefully you're all ready to go and begin with this lesson.

So the first thing we're going to be looking at is the try this activity.

We can see here, we've got a grid, and we've got some row numbers along the bottom, and hopefully you can see that this grid has got six columns and currently five rows, but that jagged bit at the bottom shows it can continue on.

What I would like you to do is tell me what the 10th row would look like if you can imagine that grid continuing on below, what the 10th row look like? What about the 50th or the 100th row.

Now, obviously I'm not expecting you to draw every single row until you get to the 100th row that's going to take you a really long time.

So what I want you to do is try and look for some patterns.

Now, if you think you can have a go with that straight away, pause the video here to do that now, if you want a little bit of a hint, then I'll continue with that.

So my hint for you is to have a look at this column here.

What do you notice about these numbers? What is happening to these numbers? Think back to your previous lesson, six, 12, 18, 24, 30.

How can you use that to find in this column, the 10th row? The first row's six the second row's 12, the third row's 18, the fourth row's 24, so what's the 10th row going to look like in this column? And what about the 50th number in this column or the 100th number in this column? And how can you use this column to help you with the other ones? So pause the video now to have a go at that.

So hopefully you managed to get something like this and really well done if you did, 'cause it was a hard starter to begin with, but you did really well on that.

The 10th row actually, where I'd start from it's the last number because as I was seeing this column here is going to really help us.

I know that this is the first column of six, then second column six times two is 12, six times three is 18, six multiplied by four is 24.

And to get the 10th one, the pattern is the row helps you, the row number helps you and the multiples of six helps you, so the 10th row, it's going to be six multiplied by 10 is 60.

And then every column from there has been shifted back a place, shifted by one number.

And that's how we get that number there.

For the 50th row very similar, I would look at this column first.

I know it's going to be six multiplied by 50 which is 300 and then I go back one each time, the same with the 100th row so really well done if you managed to get the 50th and the 100th that was really tricky.

Our connect task in a six column grid, the columns give us sequences that contain the multiples of six or sequences shifted from these multiples.

So we've got six columns, one, two, three, four, five, six the sixth column there is actually giving us the multiples of six.

And all of these columns have been shifted from the multiples of six.

We can use tracking calculations to help work out what the number is in any row.

So we can see this column, the tracking calculations that are six multiplied by one, six multiplied by two, six multiplied by three and so on.

This one is six multiplied by one, but it's been shifted back to so six multiplied by one subtract two.

This one is six multiplied by two, subtract two, six multiplied by three subtract two.

So the 10th one, for example, what's that going to be? And we're going to have a go with that in a second.

What tracking calculations describe the sequences in the other columns? So as one is finding the other columns and tracking sequences name, or even want to extend these further and have a think about how far they go.

So pause the video to do that now.

So well done if you managed to get something like this so all of this column should be six multiplied by one, two, three, four et cetera, but subtract three this time, so we're going back three from the multiples of six.

This one is going to be six multiplied by one, subtract four, six multiply by one, two, three, four subtract four, and this one is six, five, sorry, and this one is six multiplied by one just subtract one, we've just gone back in one space.

And these go on for as long as you want, you can find any row using these tracking calculations.

So the 10th row for this blue column might be six multiplied by 10 subtract two.

Please pause the video here to complete your independent learning task.

And your independent class looks like this.

You had a grid shown here and you had to write out the five terms of the sequences for the highlighted columns.

So hopefully you used the number of columns to help you here.

I knew that we were going to have multiples of four in one of these columns, starting with four.

So it should have looked like this for A four, eight, 12, 16, 20, for B five, nine, 13, 17, 21, because this B column has just been shifted one place up.

So you just had to add one to each of those.

If we think about the tracking calculations that actually might have been something that you did first to help you get this answers.

We've got four rows of one, four rows of two, four rows of three all down the A column to the multiples of A and for the B columns, you would just, in fact, that's not quite right we were just adding one four to each of the B columns.

So they should say.

Well done if you spotted my mistake.

For question two, you were given the sequence 12, 19 26, et cetera.

You had to put that into a grid where that sequence lies within economy.

You could have picked any column within your grid, but the important thing is that your grid, you should have recognised it's going up in sevens.

So your grid needed to have seven columns like this, as an example, one, two, three, four, five, six, seven.

Now I put my grid, my sequence in this column, but you could have put it in any column it was up to you.

So it should have looked something like this.

Then you needed to replace the sequence with tracking calculations.

So my 12, 19, 26, 33, 40, got me seven rows of one, add five, seven rows of two, add five seven rows of three add five and et cetera, as you go down the column, because we know that it's multiples of seven because it's going up in seven.

So my grid needed to have seven columns every time going up in seven.

So multiples of seven, and then it's just shifted from your multiples of seven.

Really well done if you managed to get those ones, fantastic job.

Well for your explore task.

Image here shows part of the number grid.

In how many ways can you place the numbers here nine, five, 14 and negative two within the orange squares? So for this one, you might want to use a bit of logic, a bit of deductible thinking, but you might also want to just do a bit of trial and error.

So maybe draw out a grid on a piece of paper yourself and try and fit in the numbers.

Once you've had a go at that, how could you convince someone that the grid must have more than four columns so that's a little hint for you that it's probably going to have more than four columns, just to remind you these jagged lines here, just show you that that grid could be going on infinitely in any of those directions.

So it's not that we just have a three by four grid, actually we can move it further in those directions.

So pause the video here to have a go at that task.

This is your only option I believe, so well done if you managed to do this.

Negative to you and in the top left corner and that had to have five columns to make all of those numbers fit.

So you might have done that just by trying things out and having a go at different combinations to see which numbers would fit.

There were lots of combinations where maybe the five was outside of those orange boxes, sometimes the nine was outside of those orange boxes and the 14 you'll notice had to be, there had to be certain difference between as you go down each column to make 14 fit.

And actually that's how you could convince someone the grid must have more than four columns.

The difference between negative two and 14 is 60 I hope you got that.

And so we needed to have a certain amount of difference between each of the numbers in those columns.

And actually we needed three different sets, 16 divided by three is four with a remainder.

So we needed more than four columns because we needed a difference of larger than four to make that 14 fit in there.

Absolutely excellent job if you've got those, that was just a bit of trial and error so really well done.

And if you managed to convince somebody of this last question then that's outstanding work, 'cause that's quite tricky, that's quite hard reasoning so really, really well done.

This brings us to the end of our lesson.

And again, I'd love to see your work.

So if you just share your work with Oak National, so by sending it to your teachers, and if you'd like to please ask your parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNation and #LearnwithOak so that I can see some of your work too.

That would make me very happy.

Really, really well done again and I'll see you next time.