Lesson video

Hello everyone.

Welcome back to another mass lesson with me, Mrs. Potchul.

As always, I can't wait to learn lots of new things and most importantly, have lots of fun.

So let's get started.

This lesson is called "Combining and Partitioning Numbers Within 10", and it's from the unit, Solving Problems in a Range of Contexts.

By the end of this lesson, you should be able to use your knowledge of combining and partitioning numbers with intent to help you to solve some problems. Let's have a look at this lesson's key words, combine, partition, whole and part.

Let's practise them.

My turn, combine, your turn.

My turn, partition, your turn.

My turn, whole, your turn.

My turn, part, your turn.

Fantastic.

Today's lesson is going to look a little bit like this.

The first part of our learning, we are going to be looking at combining numbers within 10, and the second part of our learning, we are going to be partitioning numbers within 10.

So let's get started with the first part, combining numbers within 10.

In this lesson, you're going to meet all of our Oak children, Izzy, Laura, Lucas, Sofia, Aisha, Sam, Andeep, Jacob, Alex and Jun.

They're going to help us with our learning today.

Andeep and Sofia decide to create their own pictures using the shape tiles.

Andeep suggests that they should choose a number of shape from the bowl and create their own pictures.

Once they create their pictures, they will share them.

Andeep goes first, he selects his shapes and creates his picture.

He has picked two triangles and four rectangles, and he explains that two is a part and four is a part.

Sofia loves the idea of that stem sentence, so she records it underneath for them to use later.

Andeep creates a train with his shapes.

Let's have a look then Andeep.

Wow, that looks brilliant.

We can still see that two is a part, the two triangles and four is a part.

The four rectangles, well done Andeep, you've used all of those shapes.

Sofia now selects her shapes and creates her picture.

She has used three triangles and three rectangles.

So three is a part and three is a part.

Well done if you spotted that.

Let's see what Sofia creates.

Ah, wow, what's Sofia created? Looks to me like a rocket.

It is Andeep, well done.

She's created a rocket.

Sofia and Andeep now want to compare the number of shapes that they have used.

They use a bar model to represent their pictures so that they can find the whole.

Andeep has used two triangles, so this is a part.

He will record this on his bar model.

Two, he's used four rectangles, which is another part, so he can now record this on his bar model.

Four, two and four combine to make six.

Two plus four is equal to six.

So six is Andeep's whole.

He has used six shapes altogether.

Let's see how many Sofia has used.

She used three triangles, so three is her first part.

She used three rectangles, so this is the other part, three and three.

We know that three and three combine to make six, or we could also see this as double three.

Three plus three is equal to six.

So six is Sofia's whole.

She has used six shapes altogether, wow.

What do we notice here? They've both used the same amount of shapes, but they've used different parts.

Well done Sofia and Andeep.

Okay then, let's have a go at this.

Andeep has now created you a picture.

Can you represent this picture using a bar model and an equation.

Andeep has given us the stem sentences to help us with our learning.

Mm is a part and mm is a part, that might help you with your bar model, and mm combine to make mm, that again is going to help you to complete that bar model.

Once you've completed the bar model, can you show this as an equation? Pause this video and come on back once you've had a chance to create the bar model, say the stem sentences and create the equation.

Welcome back, I hope you enjoyed exploring Andeep's picture and using those stem sentences.

Let's see how we've got on.

There are three rectangles and four triangles, so we can say three is a part and four is a part, and we can record these on our bar model.

Three is a part, four is a part.

Now let's use that second stem sentence to help us find the whole, three and four combine to make seven.

So seven is our whole.

This bar model is then showing the equation three plus four is equal to seven.

Well done if you've got that correct and Andeep, can I just say I am very impressed with your skill at creating a butterfly from those shapes.

Okay then, over to you with task A.

It's your chance to see what you can create with rectangles and triangles.

Can you use a number of rectangles and triangles and combine these to make the whole picture? You can choose any amount, might choose this randomly, or you may select to choose these purposefully.

Remember though, your maximum whole is 10, so don't pick more than 10 shapes.

Once you have created your perfect picture, can you create a bar model to represent the number of shapes in your picture? Once you've created your first picture, you might like to challenge yourself to see how many different pictures could you create using that same whole.

Pause this video, enjoy creating, get as creative as you can and come on back once you've had a go to see how the Oak children have got on.

Welcome back, I hope you had lots of fun creating all of your weird and wonderful pictures and creations.

I'm really sad that I can't see them, but I hope you shared them with lots of people just to show how fabulous a job you have done.

Let's see what the Oak children created.

(person gasping) Andeep, I can see a beautiful plant or a flower there.

Well done, let's see how you represented it using your bar model.

We can see that he has used three triangles and four rectangles and he's used the stem sentence.

Three is a part and four is a part, and seven is the whole because when we combined three and four we get seven.

That is a beautiful bar model and a beautiful picture.

So well done Andeep, let's have a look at Sofia and I can see already what this is.

It's a fish, well done Sofia, so creative.

Let's have a look at how your picture has been made.

Sofia has used four triangles and three rectangles.

So four is a part and three is a part, four is a part and three is a part.

Sofia has worked out that four and three combine to make seven.

So seven is the whole, well done Sofia, again, a beautiful picture and a wonderful bar model.

Do you notice anything? Andeep has noticed that they both use the same parts three and four, but they represent different shapes.

So in Andeep's we can see that he has three triangles, but the three in Sofia's picture represents the rectangles.

Well done, Sofia has also noticed that because they have the same parts, they have got the same whole.

It doesn't matter which way around those parts are, that whole is still seven.

They both use seven shapes.

Well, for completing your first task, let's have a look at the next part of our learning.

Part two of our learning is to partition numbers within 10.

So let's get going.

Lucas and Izzy now explore the shape tiles.

Lucas is given eight shapes to make his picture, he's created a castle and it looks the same on both sides.

Izzy asks him, how did you know how many shapes to use on both sides? What information do you think Lucas might have used to help him create this picture that's the same on both sides? He knew that half of eight was four, so I could partition eight into four and four just like this.

You can see that there are four shapes on each side and he made them look the same.

Lucas continues to explain.

He can see that we can partition eight into two equal parts of four.

We can represent this using a bar model just like the children before, we know that eight is our whole and it can be partitioned into four and four.

Eight is the whole, four is a part and four is a part.

That's how he created his picture.

Izzy decides to then explore this a little bit further to see what other whole pictures can be partitioned equally, Izzy creates three more castles using her shapes.

I wonder if we can partition these whole pictures into two equal parts.

Let's have a look.

Izzy's going to explore the castle on the left and we're going to join her in exploring the castle on the right.

So let's see what Izzy does first.

Izzy says that her castle has been made from six shapes.

How many shapes have been used to create our castle? Pause this video and have a look at the castle.

How many shapes have been used? Come on back once you've got an answer.

Welcome back, so this castle has been made from 10 shapes.

One, two, three, four, five, six, seven, eight, nine 10, 10 shapes.

Well done if you've got that one.

Let's see what Izzy's gonna do next.

Izzy says that she can partition this castle so that it will have the same number of shapes on both sides.

Let's have a look then Izzy, she can partition six into three and three.

Wow, she shows this using a bar model, six is the whole and she's partitioned it into three and three.

Let's have a look at our shape.

Can we partition this castle so that it has the same number of shapes on both sides? Pause this video and have a think.

Is there somewhere that we could partition this shape so that we have the same number of shapes on both sides? Welcome back, did you manage to find a way to partition this picture equally? Let's have a look.

We can partition it, write there look and both sides of my picture look the same.

What have we done there? How have we partitioned it? Izzy partitioned six into three and three.

We had 10 shapes, what have we now partitioned it into? So 10 is my whole and we have partitioned it into, let's have a look.

One, two, three, four, five on the left.

One, two, three, four, five, because it's the same, five on the right.

So we have partitioned 10 into five and five.

What would this look like as a bar model? Pause this video and see if you can recreate a bar model to represent our partitioning.

Welcome back.

Hopefully you have got me a nice beautiful bar model.

Let's see if yours looks like mine.

We can see that 10 is the whole and five and five are our parts.

We have split the bar at the bottom into five and five.

We have partitioned it.

Well done, and thank you so much to Izzy for helping us and talking us through this step by step.

Now let's have a look at this final castle together.

So we found two so far that we can partition into two equal parts.

First, Izzy partitions it here.

Does that have an equal number of shapes on both sides? No, does that have an equal whole number of shapes on both sides? No, let's try again Izzy, does that have an equal number of shapes on both sides? No, it doesn't.

Izzy has noticed that no matter how she partitions this shape, she cannot find an equal number of shapes on each side.

She explores this a little bit further.

She notices that this castle has been made from seven shapes and she knows that seven is an odd number and we know that an odd number cannot be split into two equal parts.

So Izzy has noticed that if we are given an even number of shapes, we can create a picture that has the same number of shapes on either side.

Even numbers can be partitioned into two of the same, whereas odd numbers cannot.

There is always an odd shape without a pair.

Some great exploring there Izzy, I love how you persevered and explored each and every one of those castles.

Lucas and Izzy now return to the picture that they started with at the beginning of this lesson.

Izzy is asking if she can partition this in any other way.

Lucas is suggesting that they could partition it into the different shapes.

Yes, Izzy notices that this picture is made up of two triangles, four smaller rectangles and two larger rectangles.

But Lucas is reminding her that it does not matter the size of the rectangles.

We can still class them as rectangles.

So Izzy rethinks her idea.

She can now see two triangles and six rectangles.

They now represent this as a bar model.

Izzy knows that the hole will still be eight, but this time they have partitioned it differently to before.

Lucas suggests that they should represent this on a bar model.

So let's have a look.

We know that eight is our whole because eight is the number of shapes in the picture.

That hasn't changed, but the way that we've partitioned it has, we've partitioned it into two and six.

The two represents the number of triangles and the six represents the number of rectangles.

So we can describe this picture and this partitioning as eight is the whole, two is a part and six is a part.

Well done guys.

Okay then, now time for you to have a go at this.

Izzy now creates her own castle using nine shape tiles.

She partitions the picture and represents it as a bar model.

Izzy knows that we can partition nine in many different ways, but for this partition, she wants to partition it into triangles and rectangles just like her and Lucas have just done.

Can you create Izzy's bar model? What is it going to look like? Pause this video and come on back once your bar model has been created to see if yours is the same as Izzy's.

Welcome back.

I hope you had fun exploring Izzy's picture.

Let's have a look at how Izzy created her bar model and then we can see if yours is the same.

Izzy knows that nine is the whole, because nine is the amount of shapes that make her picture.

She can see that she's used four triangles and five rectangles.

So we can partition nine into four and five.

Nine is the whole, let's pop that on our bar model, four is a part, the triangles and five is a part, the rectangles.

So her bar model would look like this.

Does yours look like that? Well done if yours is the same as Izzy's because she is correct, nine is the whole, four is a part and five is a part.

Well done Izzy, and well done to you if your bar model looks like Izzy's, Jun and Alex now explore the shape tiles.

Those shape tiles are getting a lot of excitement today, aren't they? Jun has created a picture and he's describing it to Alex.

I have used nine shapes altogether, seven are rectangles.

How many triangles have I used? Do you think we can help Alex out here? Alex is going to use a bar model to visualise this problem.

He knows that nine is the whole, because Jun said he has used nine shapes altogether, so he pops that onto his bar model.

Jun has used seven rectangles.

So seven is our known part.

We know that seven is a part, let's record it.

The number of triangles is our unknown part, so let's record this with a question mark because we are not sure what this is yet.

So then Alex, how are we going to work this out? Alex knows that if we subtract seven from nine, we can find the difference.

So we can see this as nine subtract seven is equal to something and that should give us our unknown part.

So how are you gonna work this out then Alex? Nine and seven are consecutive odd numbers and we know that odd numbers have a difference of two.

So that missing part must be two because nine, subtract seven is equal to two.

Jun, we think you have used two triangles in your picture.

Are we correct? Wow, look at that picture.

Yes, well done, Alex, Jun did use two triangles.

Look, it's for the elephant's ears.

Look at that picture and well done, Alex, for working out the missing part.

Jun and Alex now play their guessing game again.

Jun has hidden the picture from Alex and describes it.

This time, Jun has used seven shapes.

Two of them are rectangles.

So how many triangles has he used? Off you go then Alex, let's see if we can work this one out again.

Again, Alex uses a bar model because it helps him to visualise the problem.

We know that seven is the whole this time and we know that Jun has used two rectangles.

So two is our known part.

So again, our unknown part will be the number of triangles.

So let's record this with a question mark, there we go.

Now Alex, how are we going to work out what that missing part is? We know that if we subtract the known part from the whole, we will find the unknown part just like we did before.

So if we subtract two from seven, we will find the unknown part.

We can see this as seven.

Subtract two is equal to something.

So how are you gonna work that out then Alex? Alex knows that two less than an odd number is the odd number before.

So two less than seven is five.

Jun must have used five triangles in his picture.

I'm looking forward to seeing what this picture is.

Are we ready everybody? Let's see.

Did you use five triangles in your picture, Jun? Yes, well done, Alex, he did use five triangles.

They were for his flowers, petals and leaf.

Look at that.

I think that picture's wonderful.

Well done Jun and Alex.

Now over to you, Alex has created a picture and he's going to describe it to you.

How many rectangles has Alex used? He says that he's used six shapes altogether and one of them is a triangle.

So how many rectangles has he used? Pause this video and explore this problem.

Can you work out how many rectangles Alex has used? Remember Alex's steps from the previous problems because they will really help you to find this missing part.

Once you found the unknown part, come on back because then we get to look at Alex's picture.

I'm very excited to see this.

Welcome back, I'm hoping you were able to follow those steps that Alex has set out for us to find that number, to find that unknown part and tell us how many rectangles he has used.

Let's see if we did the same steps that Alex would.

Alex sets up his bar model, six is the whole and one is our known part, so the missing part is our unknown part.

He subtracts the known part from the whole to find the unknown part.

So six, subtract one is equal to our unknown part, six, subtract one.

How did you work that one out then Alex? We know that subtracting one is the same as finding one less, so one less than six is five.

Alex must have used five rectangles.

There are six shapes altogether, one triangle and five rectangles.

So six is the whole, one is a part and five is a part.

Shall we see if we are correct? Wow, a wonderful rhino there.

I can see one triangle and one, two, three, four, five rectangles.

So we were correct.

Well done if you worked out that five was our missing part.

Okay then, over to you for task B, we now get to get creative again with our shape tiles just like the children in today's lesson, you're going to choose a number of shapes as your whole and create your own picture.

Then you're going to create a bar model to represent the parts of your picture.

So how many different ways could you partition the whole of your picture? Could you partition it into its shapes? Might you be able to partition it into those equal number of shapes? Remember those even numbers? I would really like you to explore this and to talk about this with your friends around you, just like the children in today's lesson, we learn so much from sharing with our friends.

Pause this video and enjoy creating and partitioning your pictures.

Come on back once you're ready to continue with the lesson.

Welcome back, again, I'm really sad that I can't see some of the amazing creations that you have probably created, so let's have a look at what the Oak children have done.

That will make me feel a little bit better.

Lucas and Izzy chose five as their whole, and I can see straight away that they've both decided to create rockets.

Wow, look at those, but let's see how they partitioned it.

Lucas used two rectangles and three triangles.

Lucas partitioned five into two and three.

Five is the whole two is a part.

Three is a part, well done Lucas, that looks good to me.

Izzy used the same whole, five, but she partitioned it differently.

She used four rectangles and one triangle.

She partitioned five into four and one.

So Izzy's explanation is five is a whole, four is a part and one is a part.

Well done guys.

Lucas notices that although they've used the same whole, they've used a different number of triangles and rectangles, so they've partitioned five differently.

Izzy just reminds him that remember, we can partition a whole in many different ways.

I wonder if any of your wholes were five.

Did you partition it the same as these children or differently? I've really enjoyed our learning today.

Thanks for joining me.

I hope you've enjoyed getting creative with your math today.

Let's have a look at what we've learned.

We can combine two parts to make a whole.

A part plus a part is equal to the whole.

We can partition a whole into two parts.

Our example there is eight is the whole, four is a part and four is a part.

We can also partition a part from a whole, the whole subtract a part equals a part.

Thank you for joining me with your learning today.

I hope to see you all again soon, goodbye.