Lesson video

Hello, I'm Mrs. Cayley and I'm going to help you with your learning today.

So in today's lesson we're going to solve problems using a bar model to represent a whole partitioned into two parts.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson.

So by the end of today, you'll be able to do this.

I can solve problems using a bar model to partition a number into two parts.

Here are keywords for today's lesson.

Can you repeat them after me? My turn, partition.

Your turn My turn combine.

Your turn.

My turn bar model.

Your turn.

Well done.

Do you know what these words mean? So partition means we're going to split a hole into parts.

And combine means we're going to put the parts back together to make the whole.

A bar model is a representation showing the parts and the whole on bars or rectangles.

So let's have a look at today's lesson outline.

Here's the outline of today's lesson.

We will solve problems using a bar model to represent a whole partitioned into two parts.

First of all we will represent problems using the bar model.

And then we'll use the bar model to think systematically.

And that means that we're going to think in a good order, in a sensible order.

Going up by one each time or down by one each time.

To check that we've got all the possibilities.

Let's start on the learning.

Here are some children that are going to help us in today's lesson.

We've got Sophia and Jun.

Jun and Sophia are playing a game called "Bunny Ears." You might have played this game before.

Jun says a number and Sophia shows it on her fingers.

She hides her fingers behind her head.

You could have a go at playing along with Jun and Sophia.

Jun said, "Show me five." Sophia is showing five fingers.

Can you do it as well? She's showing three and two.

And she said, "I have three and two fingers." Does that make five? Jun said, "Show it on a bar model." Here's the bar model, showing five is the whole, three as a part and two as a part.

Jun and Sophia are playing the "Bunny Ears" game.

This time.

Jun said, "Show me four." Sophia has shown four.

Can you do it? Sophia has shown three and one.

I have three fingers and one finger.

Jun said, "Show it on a bar model." There's the bar model.

You can see four is the whole and three as a part, and one as a part.

Jun and Sophia are playing the "Bunny Ears" game again.

This time Jun said, "Show me four." Sophia's going to think of a different way of showing four.

There we go.

Can you try it? She said, "I have two fingers and two fingers." Show it on a bar model.

There's the bar model showing four is the whole, and two as a part, and two as a part.

Jun and Sophia are playing the "Bunny Ears" game again.

This time Jun said, "Show me three." I wonder how Sophia might do it.

She's showing two and one.

I have two fingers and one finger.

Jun said, "Show it on a bar model." There's the bar model showing three is the whole, and two as a part, and one as a part.

Jun and Sophia are playing the Bunny Ears game again.

This time he said, "Show me five." I wonder how Sophia might show five fingers.

She's showing zero and five.

I have zero fingers and five fingers.

Jun said, "Show it on a bar model." Sophia said, "It is tricky to show this as a bar model." We could.

There we are.

We can't really see the zero on the bar model, but we can see the five.

Five is the whole and five is one of the parts.

Jun and Sophia are playing the "Bunny Ears" game again.

This time jun said, "Show me four." Sophia is showing four.

I have zero and four fingers.

Jun said, "Show it on a bar model." There's the bar model again.

Four is a part and zero is a part.

One part is the same as the whole.

Let's check your understanding.

How many more fingers is Sophia holding up? Jun said, "Show me three." Sophia has shown one finger and what do you think the other hand's going to show? Pause the video and have a go.

That's right, it's one finger and two fingers.

That makes three in the whole.

There's the bar model to show three is the whole, one as a part, and two as a part.

Let's check your understanding again.

How many more fingers is Sophia holding up? Jun said, "Show me three." Sophia is showing zero fingers and what do you think she's going to show on the other hand? Pause the video and show me.

That's right.

It's zero and three fingers.

There's the bar model showing three as the whole and three as one of the parts.

Let's check your understanding again.

How many more fingers is Sophia holding up? Jun said, "Show me four." Sophia is showing two fingers and can you show it on your hand? That's right, two more.

Two fingers and two fingers.

That makes four fingers.

And there's the bar model showing four has been partitioned into two and two.

Let's check your understanding again.

How many more fingers is Sophia holding up? Jun said, "Show me four." Sophia is showing three fingers and pause the video and show me your fingers.

That's right.

It was three fingers and one finger and there's the bar model showing four has been partitioned into three and one.

Let's check your understanding again.

How many more fingers is Sophia holding up? Jun said, "Show me five." Sophia is showing two fingers and what's the other hand going to show? That's right, it's two fingers and three fingers.

There's the bar model showing five has been partitioned into two and three.

Did you enjoy playing the "Bunny Ears" game? Do you know any other partitioning games you could play with a friend.

Jun said we could use dice or dominoes.

Sophia said we could hide counters under a cup.

Perhaps you could make up a game to play with your friends.

Here's a task for you to have a go at.

Can you play "Bunny Ears" with a partner? One player says a number up to five.

The other player shows it on their fingers in different ways.

So the first person says, "Show me mmh" and the other person shows it on their fingers behind their head.

I have mmh fingers and mmh fingers.

And the first player can check that they've got it right.

Can you represent your ways as a bar model? You could draw bar models to show the different ways that you've made the number.

Here's the second part of your task.

This is a "Dominoes" game.

I've got some dominoes here and you might have some dominoes that you can try this with.

Can you pick a domino and if the parts combined to make five, shout five and win the domino.

Can you see any there that might make five.

Here are some more dominoes that you could use as well.

Draw bar models to go with the ones that total five.

So pause the video and have a go at your tasks.

How did you find the "Bunny Ears" game? You might have tried something like Jun and Sophia.

Jun said, "Show me five" and Sophia has shown one and four.

And she's drawn it on the bar model.

Here's a different way that they've tried.

Jun said, "Show me four." Sophia has shown two fingers and two fingers.

And there's the bar model to represent the way that she's done it.

Four has been partitioned into two and two.

This is a different one that Jun and Sophia tried.

Jun said, "Show me three" and Sophia has shown one finger and two fingers.

And she's represented it as a bar model.

Three is being partitioned into one and two.

How did you get on with the "Dominoes" game? Did you find some dominoes with five dots? I can see some here that have got five dots in total.

We've got zero and five, one and four, two and three, three and two, four and one and five and zero.

Did you draw bar models to show the ones that total five? I've drawn some bar models here.

Can you see that the whole is always five.

And then we've got the parts.

The first one I've got a part is five.

The second one I've got one and four.

The next one I've got two and three.

Then I've got three and two.

Then I've got four and one.

Finally I've got five and zero.

Can you see that some of them look very similar but the parts have been swapped round.

Let's move on to the second part of the lesson.

We will use the bar model to think systematically, and this means that we're going to think in a sensible order.

We're going to try to get all the combinations by doing them in a good order.

Sophia and Jun are playing a game.

They have five double-sided counters and are throwing them into a tray.

Can you see that they've thrown them into the tray? You could try this with counters if you've got some or you could use a coin to see which way it lands, heads or tails.

Jun said three counters are yellow.

Sophia said two counters are red.

We can represent the counters in different ways.

Can you see the bar model and the part part whole model? They're both showing that five is the whole and three as a part, and two as a part.

Jun said, "I have three counters." Sophia said, "I have two counters." Sophia and Jun are playing the game still.

They have five double-sided counters and are throwing them into a tray.

They've thrown them in a different way this time.

Jun said one counter is yellow.

Sophia said four counters are red.

We can represent the counters in different ways.

Can you see the bar model and the part part whole model? They're both showing that five is the whole and one as a part, and four as a part.

Jun said, "I have one counter." Sophia said, "I have four counters." How many ways might the counters have landed? Can you think of any other ways that they might have landed? So we might have had five red counters.

We might have had one yellow counter and four red counters.

We might have had two yellow counters and three red counters.

We might have had two yellow counters and three red counters.

We might have had three yellow counters and two red counters.

We might have had four yellow counters and one red counter, or we might have had five yellow counters and zero red counters.

Here's the ways that we found.

I've put them into a table.

Can you see that the yellow counters are going up by one each time.

So it goes zero, one, two, three, four, five.

And the red counts are going down by one each time.

So they go, five, four, three, two, one, zero.

Altogether we've got five counts each time.

We've used all the numbers from zero up to five and we've used them in the correct order, so that's how we can check that we've got all the combinations, and that's called working systematically.

We can partition the five counters in six different ways.

Can you see that I've represented the different ways on a bar model.

You can see that we've got five in the whole each time and it's been partitioned into five and zero, one and four, two and three, three and two, four and one and five and zero.

A bar model can represent the whole in its parts.

Can you see the bar models that I've drawn here to represent the different combinations? You could try drawings in bar models and if you've got squared paper that can help.

Can you see on the first bar model we've got five is the whole.

And five is one of the parts.

In the second one we've got five is the whole, one as a part and four as a part.

Then we've got five is the whole, and two as a part, and three as a part.

Then we've got five as the the whole, and three as a part, and two as a part.

Then we've got five as the whole and four as a part and one as a part.

And finally we've got five as the whole and five is one of the parts.

Sophia and Jun are playing the game with four counters this time.

I wonder how the four counters might have landed.

Can you think of any ways? So we could have four red counters or we could have one yellow counter and three red counters, or we could have two yellow counters and two red counters.

Or we could have three yellow counters and one red counter.

Can you think of another way it might have been done? Yes, we could have four yellow counters and zero red counters.

We can show this on a table.

Can you see the yellow counters are going up by one each time and we've used all the numbers from zero up to four.

The red counters are going down by one each time, and again, we've used all the numbers from zero to four, so we can check that we've got all the combinations and we haven't missed any out.

Because we've done the numbers in the right order.

We can partition the four counters in five different ways.

Can you see on the bar models you can see the different parts.

We could have four and zero, one and three, two and two, three and one or four and zero.

A bar model can represent the whole in its parts.

Can you see the bar models to go with each of the combinations here? The first one is showing four is the whole and four as a part.

The second one is showing four is the whole, one as a part and three as a part.

Then we've got four as the whole and two as a part and two as a part.

Then we've got four as the whole three as a part and one as a part.

And finally we've got four as the whole and four as a part.

Sophia and Jun are playing the game with three counters.

I wonder how they might have landed this time.

Can you think of any ways? So we might have had three red counters or we might have had one yellow counter and two red counters, or we might have had two yellow counters and one red counter.

Are there any more ways? Yes, we could have had three yellow counters and zero red counters.

Can you see they've been done in a systematic order.

Here's a table showing the results.

The yellow counters are going up by one each time and we've used all the numbers from zero to three.

The red counters are going down by one each time, and again, we've used all the numbers from zero to three.

So we've got all the possible combinations.

We can partition the three counters in four different ways and they've been represented here on the bar model.

Can you see they can be partitioned into zero and three, one and two, two and one or three and zero.

A bar model can represent the whole and its parts.

Can you see the different bar models here showing the possible combinations for partitioning three counters, so three can be partitioned into zero and three, one and two, two and one or three and zero.

Jun is wondering how many ways can two counters be partitioned? I wonder if you can think about this one.

Sophia thinks there are only three ways of doing it.

I wonder what they might be.

Let's check your understanding.

Which bar model represents these counters? Can you see the yellow and the red counters here and I can see a part, part whole model to go with them.

Which bar model represents these counters? Pause the video and think about it.

That's right, it's four has been partitioned into two and two, so it's the last bar model.

Let's check your understanding again.

Which bar model represents these counters? Can you see we've got three yellow counters and two red counters? Which bar model represents these counters? That's right, it's the middle bar model.

We've got five has been partitioned into three and two.

Let's check your understanding again.

Which bar model represents these counters? Can you see we've got three yellow counters and one red counter? Which bar model represents these counters? That's right, it was the first bar model.

Four has been partitioned into three and one.

Here's a task for you to have a go at.

Can you take five double-sided counters or if you haven't got double-sided counters? You can use coins and see if it lands on a head or a tail.

Throw them into a tray and then look at how many are of each colour.

Represent your results as bar models.

I've given you some bar models here that you could use or you could draw your own.

Think about how do you know which bar model to use for each combination.

So look carefully at the bar models and see if you can choose which one can go with each combination.

So pause the video and have a go at your task.

How did you get on with your task? How many of each colour did you get? Did you represent your results as bar models? Here are some examples of how you might have recorded your results.

You might have partitioned five into five and zero, or one and four or two and three or three and two or four and one or one, one, one, one, one.

How did you know which bar model to use for each combination? We could use the size of the parts to help us choose a bar model for each combination.

If you've drawn your own, you might have made the parts bigger for the bigger numbers and smaller for the smaller numbers.

Well done everyone.

We've got to the end of our lesson.

Today we were solving problems using a bar model, to represent a whole partitioned into two parts.

And this is what we found out.

A bar model can be used to represent different partitioning of numbers up to five.

We can partition and combine numbers and show this on a bar model.

The bar model and part part hole diagram can be used to represent stories and concrete and pictorial representations.

Well done everyone.

See you next time.