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Hello everybody and welcome to today's math session.

My name is Ms. Hughes, and today we're going to be looking at identifying number patterns by skip counting in threes.

So let's get started.

For today's lesson, you are going to need a pencil and rubber, some paper, and then the last items that you need are some counters and a 100 square.

If you do not have a 100 square at home, that's fine.

Pause this video now to get the equipment that you need.

If you have not got these things already.

Brilliant, time to look at our lesson agenda then.

So we're going to start off today's lesson with some pattern seeking when counting in threes and trying to spot the pattern when we count in threes.

Then you're going to have a talk task.

After that, we're going to look at three more and three less and finding three more and three less than a number.

And finally, you're going to have your quiz, where you're going to recap everything that you've learned in today's lesson and show off everything that you have remembered.

So let's get going.

We're going to start off today's lesson by skip counting in threes and practising doing this on a counting stick.

So I've got my lovely counting stick here.

And am I going to start from zero.

So let's skip counting threes together.

Zero, three, six, nine, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60.

Brilliant.

As we were counting then were our numbers increasing or decreasing as I was counting? What do you think? Brilliant.

They are all increasing aren't they? As I'm counting up this was in counting forwards.

My numbers are getting greater and they are all getting greater by three each time because we're counting in threes.

What about if I count this way down my number stick then.

Will my numbers be increasing or decreasing? Let's find out.

60, 57, 54, 51, 48, 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, nine, six, three, zero.

Hmm.

When I count backwards on my counting sticks, I can notice that my numbers are getting smaller.

That means they are decreasing.

Let's try counting forwards in threes one more time.

Just so we've got it in our heads, zero, three, six, nine, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 40, 42, 45, 48, 51, 54, 57, 60.

Brilliant.

As I'm counting up my number line, My numbers are getting greater by three they're increasing.

And as am counting down they getting lesser and lesser by three, so they are decreasing by three each time.

We're going to play a bit of a game now.

So I'm going to start counting in threes and then I'm going to stop.

And I want you to tell me what number is going to come next.

So zero, three, six, nine, 12, hmmm.

What number is going to come after 12 when we are counting in threes? I'll give you a little bit of time to think about it, decide what you think and how you know.

This number is going to be the number 15, like this.

My numbers are getting greater when I count forward.

So I know that this number, this mystery number needs to be bigger than 12.

I also know that I'm counting in three, so my numbers are getting greater each time by three.

So I know that whatever number this was going to be, i need to be three greater than 12.

So 12 add three equals our mystery number 15.

So I had to add three to 12 to find out what number was three greater than 12.

Let's see a new one, we're going to count backwards now.

So, 60, 57, 54, 51, 48, 45, 42 39 and? the like, there's our mystery number hmm.

What is our mystery number going to be? Which number comes before 39 when we are counting in threes.

I'll give you a few seconds to decide.

Well, when I'm finding out this number, I know that we're counting backwards so my numbers are decreasing.

So I know it's got to be smaller than 39.

I also know that my numbers are decreasing by three time because we've been counting in threes.

So this number needs to be three smaller than 39.

It needs to be 39 takeaway three.

And that will give my answer.

So my answer is 36 and I can write that as an equation, 39 was the number that we had and we're trying to find three less.

So, 39 - 3 = 36.

Good job If he found that one out.

So we've thought already in today's lesson about counting forwards and backwards in threes.

Now we're going to use this knowledge of counting forwards and backwards in threes and apply it to more of a reasoning focus.

Our question that we're looking at on this slide is will I say the number eight when counting forwards in threes from one? While we're thinking about that question and I've just realised there's an equation at the bottom of my screen, i want you to ignore that for the moment then we'll come to that in a second.

So we're just focusing on this question.

Will I say the number eight when counting forwards in threes from one.

Let's put a counter on the number one so we know that's where we're starting counting from.

Okay, so counting on from one, I know that I'm not going to land on eight.

I know that because 1 + 3 = 4.

So lets pop that on there.

I know that if I was to go from four and add on another three, I would get to the number seven.

So 4 + 3 = 7, so let's put a counter on seven where I land.

And then seven if I was to count on another three, I would land on the number 10.

So I'm not going to land on the number eight.

So when I'm counting in threes from one, I would say one, four, seven, 10, I wouldn't say the number eight.

And you can see from where my counters are placed, there was not a counter on the number eight.

Eight has completely missed out.

We have a few more reasoning problems just like the last one to have a look at.

So let's look at this next one.

It says, Will i say 65 when counting backwards in threes from 74? Well, I'm going to start by putting a counter on 74 because that's where I'm starting.

And because the question says that we are counting backwards in threes.

I know that means we're counting this way along my number line and my numbers are going to be decreasing.

So they're getting smaller by three each time.

So I know that 74 take away three gets me to 71.

So one, two, three, put my counter on there, Count back another three, one, two, three.

It gets me to 68 and one, two, three gets me to 65.

Okay, so I do say the number 65 when counting backwards in threes from 74.

I could have worked that out using some of my equations.

So 74 - 3 = 71.

Then, 71 -3 = 68 and 68 - 3 = 65.

So I would have known from decreasing my numbers by three each time with an equation that I would have landed on 65.

Let's have a look at my next one.

Will I say the number 39 when counting forwards in threes from 30? Well, I know from when we were counting in threes earlier that the pattern goes zero, three, six, nine, when we're counting from zero.

So if I'm starting from 30, the pattern will go 30, 33, 36 39, it's going to follow that pattern.

So I know that I will land on 39 when I'm counting forwards in threes.

So let's put our starting counter on 30 just to double check this.

So there's my counter on 30.

I'm counting forwards which means my numbers are getting greater by three this time.

So I'm adding three each time.

So 30 add on three is 33, 33 add on three is 36 and three greater than 36 is 39.

So I do land on my number 39.

You are going to continue this exploration of number patterns, counting forwards and backwards in threes.

To complete this task, you will need some counters and a number square to 100, just like this one.

Remember, if you haven't gotten number square at home, there is a principle resource that you can download.

Shortly, you are going to see a list of different investigation questions.

Your first step is to read the question aloud and place a counter on the starting number like I showed you earlier.

Then your next step is to reason whether you think the target number is going to be reached.

So whether you think you're going to reach the number that it says that you might.

Then using counters and skip counting, I want you to see if your reasoning was correct.

Okay, you can use this sentence structure here.

I think that I will or I will not reach the target number.

Pause the video now to have a go at this task.

Let's play when you are ready to continue with the lesson.

Okay, team welcome back.

Let's go through these answers and see what you thought.

So the first one says, I will say the number 13, if I count forward in threes from the number five.

So I know that if I'm starting from the number five that I will not reach the target Number 13.

I can show this in counters, so five count on three will get me to eight, count on three will get me to 11 count on three will get me to 14.

So I'm going to miss up 13 there.

I will say the number 15 If I count backwards in threes from 23.

So this time you're counting backwards and I know that I will not reach the target number and here are my counters to prove it.

So from 23 if I'm counting backwards, I won't reach 15.

That's okay, the next one.

Will I say the number 32, if I count backwards in threes from 40? I know that I will not and I know this because I know that 10 - 3 = 7 and 7 - 3 = 4 and 4 - 3 = 1.

So if I'm counting from 40, 40 take away three is going to be 37.

37 takeaway three is going to be 34.

and 34 takeaway three is going to be 31.

So I know that I will not land on the number 32 from the number sequences I already know.

Okay, the final one, you will say the number 71 if you count forwards in threes from 62.

Let's use counter to prove it.

So we know that we are going to land on that one.

Moving on team, we're going to start off our develop learning by looking at this question.

Sally landed on 22 when she was counting in threes.

What number could she have started on? I'm going to give you about five seconds to find as many numbers Sally could have started on to have landed on 22 when counting in threes.

Off you go.

Have you got any ideas? Great, let's look through it.

Well, it's important to notice that in this question it does not say that Sally is counting forwards or backwards.

So we know that she could have started from a number that comes after 22.

She could have also started from a number that comes before 22 and counted forwards.

She may have started close to 22, so for example, she could have started on 19 which is three fewer than 22.

So she started in 19, she counted on one of three she would have reached 22.

So you could have started on 19.

She could have started on a number that comes after 22, for example, 25 which is three greater than 22.

She could have started a number even further away from 22, not a number that's just three greater or three fewer.

She actually could have started on the number four.

If I count on three each time from the number four, I would eventually get to the number 22.

So she could have started there.

We're going to take our exploration of counting in threes a bit further now to try and fill in the missing gaps in our sequence such as this one here.

I want to know what the missing number is.

So in other words, I'm looking for what number comes between 12 and 18.

So I need to identify the pattern so that I can work out what my missing number is.

So need to work out the patterns of my other numbers.

Hmm, well, I can see here that as I count forwards, my numbers are getting greater and they're getting greater by three because three add on three or six, six add on three is nine, nine count on three is 12.

If I count backwards though, my numbers are getting fewer each time.

In fact, they're decreasing by three.

So they're getting three less.

This pattern is going to help me find my missing number here.

I either need to find the number that is three greater than 12.

So counting this one needs to be three greater than 12.

Or I could find the number that is three less than 18 because counting backwards, my numbers are getting three less.

With that in mind, I know that my missing number is going to be the number 15.

It has to be 15 because I know that 12 add three is 15.

So three greater than 12 is 15 and 18 takeaway three is 15.

So three fewer than 18 is 15.

Let's look at this next problem then.

There are two missing numbers now that we are trying to find in this sequence.

So this one here and this one here.

I'm looking for the number that fits between 22 and 16.

And I'm looking for the number that goes between 13 and seven.

Hmm, i can see that if I count this way along my number line, looking at the numbers that I do have that my numbers are getting greater and they're getting greater by three.

So each number is getting three greater.

If I'm counting this way, however, and going down my number line this way, I noticed that my numbers are decreasing and they are getting three less each time.

These patterns are going to help me to find my missing numbers.

So I know that this missing number must be greater than 16 but three fewer than 22.

So because it's here, it's going to be three greater than 16 or three less than 22.

This one is going to be three greater than seven, or three fewer than 13.

The missing number here therefore must be 19.

And I know this because three greater than 16 or 16 add on three equals 19 and three less than 22 or 22 takeaway three is equal to 19.

This missing number must be 10.

I know this because seven add three, so three greater than seven is 10 and three less than 13 or 13 - 3 = 10.

So having found our patterns, we were able to find our missing numbers in our sequence.

You are going to have a go yourselves at this type of task and identify the missing numbers on each sequence.

Remember, there's a principle 100 square that you can use if you do not have your own.

This task comes in two parts, so this is the first part.

And then this is the second part for you to complete.

Pause the video now to complete your task and resume once you are finished.

Great, let's go through these answers then.

Okay, so in this sequence, you should have noticed that we're getting three greater each time.

So it goes three, six, nine, and the next missing number is 18.

In this instance, we're also getting three greater this way so this number was seven after 13 you should have had 16 and after 16 you should have had 19.

Going this way our numbers are actually decreasing.

They're getting three less so the number after 43 should have been 40 and the number after 34 should have been 31.

In this sequence we are getting three less again as we're counting down and three more going up.

So three more than 47 is 50, three less than 47 is 44.

And this number over here was 35.

Finally, in our last example we've got, our number is getting three greater, three greater than 69 is 72, three greater than 72, 75 and three greater than 78 is 81.

So there is the numbers that you should have had on those sequences.

Brilliant job team.

You've worked super hard today.

And now it is time to complete your quiz to recap everything you've learned and to show off all of the fantastic knowledge of counting threes that you can remember from today's lesson.

So good luck.

Team, you did an excellent job today with your learning.

And I just wanted to hop on here at the end to say goodbye and well done.

Hopefully, I'll see you soon in another session.