﻿Hi, everybody. I'm Ms. Jones and I'm really excited to start working with you today. But before we can get started and begin, what you need to do for me is make sure that you have a pen and some paper ready to go, as well as making sure that you have a quiet space to work and try and turn off any distractions like any notifications or anything like that. So before we can make a start on our maths today on number grid sequences, pause the video to make sure you have all of that ready. Okay, let's begin. So the first thing that we're going to be doing is we're going to be looking at this number grid here, okay? I would like you to describe the patterns made by sets of multiples. Hopefully we know what multiples are, but if you want to have a quick refresher of that, then have a look at this. A multiple is the result of multiplying a number by an integer. Remember, integer is whole number. That language is really important. So for example, multiples of 5 would be 5 'cause you can multiply 5 by 1, 10 'cause you can multiply 5 by 2 15 'cause you can multiply 5 by 3 and so on. So the first thing that you might be looking at is for those multiples and where you can find them in that grid. If you want a little hint, then keep watching. If you're happy to have a go, pause the video here. So if you wanted a little hint, I've outlined those multiples of five that I mentioned. So I can see multiples of five straight down. What about other multiples? Multiples of four, multiples of three, where can you see them? They might not be straight down a column, or straight along a row. You might have to look elsewhere. So pause the video to have a go at that. So hopefully you manage to see things like this. Here are the multiples of four, the multiples of three, three, six, nine. And actually, they're all linked to these multiples of five in a way, because to get the multiples of four, we've gone down one and across one, so back one. We've gone down one and back one again, down one and back one. And how does that link to the multiples of five? These were just going straight down, but this time you've got to go down and then left because actually there are five columns. So it's starting to hopefully make sense and to link, similar with the threes. Instead of going down one and left one, we now need to go down one and left two, or back two, because it's linked to those multiples of five. So now we're going to do our connect task. The number of columns in each grid determines the number sequence within each column. So let me explain. If you've got this grid here, one, two, three, four, five, six, it's got six columns, and we can see that each column, when we go down each column, we're going up in sixes. So our number sequence is increasing by six. You might want to consider how that changes here. It's still increasing by six, even though it's not technically the multiples of six. In a five-column grid, one of the columns would include the multiples of what? So we've got five columns, so the columns would include the multiples of five. You can see 5, 10, 15, 20, 25. And the other columns will have number sequences increasing by five still. Well done, brilliant. So we're still increasing by five, even though these aren't the multiples of five. You've actually just shifted the multiples of five. So for this one, this column here, 4, 9, 14, 19, 24, we've shifted the multiples of five back one. For this column here, we've shifted the multiples of five back four places. How would you describe the number sequences in each column of the grids shown? So looking at all four of these grids, how would you describe to somebody else, maybe even try describing it to somebody else, each of the number sequences in each of the columns? So think about what we've just talked about in terms of the multiples and then shifting those multiples. So pause the video here to do that. I would now like you to think about what you've worked on today and pause the video to complete your independent task, which you can find on your worksheet. So your independent task, your answers should have looked something like this. So for the first question you needed to write out the first 10 numbers in the number sequences that fall in the columns here. So I've just filled out the first five for you, but hopefully if you've got the first five, you would've got the first 10 as well. So for this one, we can see we've got two, four, five columns. So we knew we were going up in fives. And actually in our example here, it shows you we're going up in fives. We've now shifted that one space backwards. We're still going up in fives. And then for a, we've shifted that one, two, three spaces backwards. Similarly for this one, we've got 1, 2, 3, 4, 5, 6 columns. For this one, we can see we're going up in sixes. And for this column, we needed to move it two spaces to the right or two spaces up to get our column here, and then two spaces down to get our column here. So hopefully you got answers like that. For number two, we were given number sequences in a row, in a line. And what I wanted you to do is draw a grid where the sequence lies in one column, one column in your grid. So the most important thing here is that we recognise how many columns there were going to be in this grid. So for a, we are going up and we are increasing in our number sequence in sevens. So that means there needed to be seven columns, which we can see in this grid here. It didn't matter where you chose to put your column. You could have put your column at the beginning, which I'm sure a lot of you did, but actually we could have had our column as a second column. So if we got rid of this line here and had 6, 13, 20, et cetera down there, that would have been fine. There were lots of different answers. For b, we were going up in three, so we needed three columns. And again, here's another example of that. And for c, we needed four columns. And your question three was to draw a different grid for each part of question two. So you should have two grids for each. So really well done if you managed to get those. Excellent work, well done. So for our final task, our explore task, this is an opportunity for you to explore things a little bit more deeply. Some number grids have been torn into parts. Which parts belong to the same grid? So some of these parts belong to the same grid. For the parts that don't belong to that grid, that are leftover, draw a grid that they could be a part of. So pause the video here again to complete this. So hopefully you recognise that we needed to think about what these grids were going up in. So this column here was going up in fives. So we needed to be looking if it was going to be in the same grid, they would also have to be going up in fives. And we can see that actually this grid is also going up in fives down the columns. So these two grids could in fact be part of the same grid. If I were to extend that and make this a six and then a seven, remember this would have to have five columns. This 10, excuse my poor writing, 11, 12, this 13, 14, 15, 16, 17, we can see that this grid just slots in really nicely there. These two are slightly different because this one is going up in sevens, and this one. Well done if you managed to get the difference between the negatives, 'cause I know some people struggle with that, but you did really well if you did that. This one's going up in sixes. So you just needed to create that grid, extend it whichever way you wanted to, but ensuring that we had for this one seven columns and for this one, six columns with these numbers in. So well done for that if you managed to get that. So that brings us to the end of today's lesson. A massive well done again for your amazing work. And actually, it would be great if you could share that work with your teachers and even better sharing that work with Oak National so that I can see the amazing work that you've been doing, that would be brilliant. So if you'd like to, please ask your parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnWithOak. A massive well done again, because it's amazing work you've been doing on sequences and there's amazing more work to come. I'm really looking forward to working with you again soon.

The number of ______ in each grid determines the number sequence within each column.

In the following grid, what number sequence are the columns going up in?

What is the missing number in this number sequence? 1, ___, 7, 10, 13, ...

Number Grid Sequences Quiz

In this lesson, we will learn about finding sequences in number grids using multiples.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Number grid sequences

Sequences

Algebra

THEME

UNIT

Tracking Calculations

Generalising arithmetic sequences through tracking calculations

The nth term rule: Position-to-term for arithmetic sequences

Descending arithmetic sequences

Dot chain sequences

Growing pattern sequences

Finding the term-to-term rule

In a six column grid, the columns give us sequences that contain the multiples of ___.

Look at the number grid shown on the right. Write down the column and row that match the tracking calculation 5 x 3 - 1

Which column has the position-to-term rule 4n - 1?

Work out position-to-term rules for the sequence 3, 7, 11, 15, 19, ...

What do we mean if we describe a sequence as "descending"?

What is the nth term of -4, -7, -10, -13, ...?

If the tracking calculation for this 3-chain is 8 x 3 + 1, what would the tracking calculation for a 20-chain?

Which definition best describes an arithmetic sequence?

Which of the following statements is true?

How many squares does the next term in this sequence have?

Which sequences starts at 2 and has a term-term-term rule of multiply by 3?

Lesson overview:Number grid sequences

Core Content

Sequences: