Lesson video

Hello, my name is Mr. Tanzimat, and I'm really excited to be working with you on this lesson today.

If you are ready, let's get started.

At the end of today's lesson, I want you to be able to say that you can add two three digit numbers using partitioning.

Here are some of the key words that you are going to be expected to understand and recognise in today's slides.

I'm gonna say them, and then I want you to repeat them back to me.

I'll say my turn and say the word, and then I'll say your turn and you can say it back.

My turn, addend.

Your turn.

My turn, sum.

Your turn.

My turn, unitizing.

Your turn.

Okay, now I'm gonna try to explain some of those keywords, so that we know what they are when we come to do our learning in a moment.

And addend is a number added to another.

The sum means the total when numbers are added together.

Unitizing means treating groups that contain the same number of things as ones or units.

In this lesson on adding two three digit numbers using partitioning, there are gonna be two parts.

In the first part, we are gonna use unitizing to add three digit numbers, and in the second part, we're gonna use partitioning to add three digit numbers.

Let's get started with the first part.

In this lesson, we've got two friends who are gonna help us.

They might help to explain some maths concepts or processes, and they might help with discussions from any maths prompts that you see on the screen.

We've got Izzy and we've got Alex.

Let's start with this.

How many apples can you see? Izzy says, "There are three apples." How many pandas can you see? Alex says, "There are three pandas." How many packs of crayons can you see? Izzy says, "There are three packs of crayons." Now what was the same, and what was different about each of these groups? Hmm.

Well, Izzy says that there are the same number in each group, and I can see that there are three apples, three pandas and three packs of crayons.

Alex says, each group has different objects in it.

This is called unitizing.

Each object within a group is one unit.

Now we're gonna slightly change it, and use place value counters.

How many ones can you see? Alex says there are three ones.

How many tens can you see? Alex says, "I think there are 30 altogether." Izzy says, "30 is the total," 10, 20, 30, "But there are three tens here." Who do you agree with? Well we can see that there are only three counters, and each of them is worth 10.

So the total is 30, but actually there are only three tens here.

How many hundreds can you see? Well Alex says, "So the total is 300, but the number of hundreds is three." Well done Alex, he's understood.

So what's the same and what's different here? "There are the same number of counters in each group," says Izzy, but the counters each have a different value.

Three units of one equals three.

Three units of 10 equals 30.

Three units of 100 equals 300.

This is also unitizing.

We can use this to help us to add larger numbers.

Okay, let's check your understanding.

In pairs, you are gonna look around the classroom, and see how many sets of objects that you can find, that have the same number of units in their group.

Pause the video so that you can go on your mission, and find sets of objects that have the same number of units in their group.

Welcome back.

How did you get on, what did you find? Well, Izzy and Alex have had a go at this, and here's what they found.

It might be similar to yours.

Alex saw four display boards in his classroom.

Izzy found that there were four pencil cases on their table.

So each of those sets had different objects, but the same number of them.

This is unitizing.

Okay, let's move on.

You ready? Izzy has four apples.

Alex has three apples.

How many apples do they have all together? Well, this can be written as an equation.

Four apples plus three apples equals seven apples.

Here are some more equations, this time featuring place value counters.

Three ones plus four ones equals seven ones.

Three tens plus four tens equals seven tens.

What's the same and what's different? Hmm.

Well Izzy says, "Both the equations have the same addends and sum," so she can see that in both of these equations, we have to take three and four, and add them together to make seven.

Alex says the place value of each unit is different.

You can see that the red counters are all worth one, whereas the yellow counters are worth 10.

Here are some more equations again.

31 ones plus 42 ones equals 73 ones.

31 tens plus 42 tens equals 73 tens.

What do you notice this time? Hmm.

Well, Alex says, "Like last time the addends are the same, but the place value of the units are different, ones and tens." Izzy says, "But look, this time the addends are both two digit numbers." So let's write these out as an equation.

31 tens plus 42 tens equals 73 tens.

How might we write 73 tens entirely as a numeral? Well, here's some place value counters to help.

We've got 73 tens.

Alex says, "I know that I can regroup 70 tens into seven hundreds." And then Izzy says, "Seven hundreds and three tens makes 730 in total." So the answer is 730.

What do you notice about these equations? Can you generalise? Have a look, what do you think? Well Izzy says she's noticed that the unitized digits remain the same in the same order.

There's the example below.

You can see that in the expression to begin with, we have 34, and the expression to complete this equation starts with three and four, the same with the second term in each of these expressions.

In the first expression, we have one four making 14 tens, and in the second expression we have a one and four next to each other.

Alex says, "In the second expression, the placeholders are used instead of the word tens." This has been underlined.

You can see that on the expression on the left we have tens underlined, and on the right it's a zero instead.

The same with the second term in those expressions.

We have tens underlined, and then we have a zero in the expression on the right.

Okay, let's check your understanding.

You've got here to fill in the missing digits.

We've got 24 tens plus 11 tens equals something plus something.

And on the second one we have something tens plus something tens equals 420 plus 140.

See how you get on.

Pause the video and then we'll have a little look at the answers in a moment.

Welcome back, let's see how you got on.

So in the first equation, the expression with the missing digits would've been 240 plus 110.

And in the second, it would've been 42 tens plus 14 tens.

How did you get on? I hope you did well.

Okay, let's move on to some problems. Alex and Izzy are working as a pair in a football skills game.

They are kicking a ball at a target wall.

Izzy scores 300 points.

Alex scores 200 points.

How many points do they score as a pair? Izzy says, "What can I use that will help here?" And she starts with a known fact and equation she already understands and knows, which is three plus two equals five.

If we then take three plus two equals five and use our understanding of unitization, we can write this.

Three hundreds plus two hundreds equals five hundreds, which means that 300 points plus 200 points equals 500 points.

Okay, time for you to have a go.

We've got a similar problem here.

Alex and Izzy have another go.

Izzy scores 400 points.

Alex scores 300 points.

How many points do they score as a pair? Pause the video and have a go yourselves.

Good luck.

Welcome back, let's see how you got on.

Alex said, "What can I use that will help here?" And he realised that four plus three equals seven is a known equation, that he can use to help him using unitization.

So we know we've got four hundreds plus three hundreds plus seven hundreds.

That gives 400 points plus 300 points, which equals 700 points.

How did you get on? I hope you got it.

Okay, let's have a look again at another problem based on this football wall.

Alex and Izzy have a third go.

This time, Izzy scores 340 points, Alex scores 120 points.

How many points do they score as a pair? Izzy says, "What can I use that will help here?" And in the past they've used single digit equations that they know.

Might be slightly different this time.

Izzy starts with two digit addends.

34 plus 12 equals 46.

Alex says, "This time it's two digits for each addend." Well done Alex, good spot.

34 tens plus 12 tens equals 46 tens.

So 340 points plus 120 points equals 460 points.

Okay, time to check your understanding.

Alex and Izzy have a final go.

This time, Izzy scores 450 points.

Alex scores 110 points.

How many points in total did they score in their last go? Pause the video and then we'll have a look at the answers in a moment.

Good luck.

Welcome back, let's see how you got on.

So we'll start with 45 plus 11 equals 56.

That's gonna help us to solve the rest of this problem.

45 tens plus 11 tens equals 56 tens, 450 points plus 110 points equals 560 points.

Great.

Let's move on to some practise then.

For your practise, number one, I want you to match the expressions.

You can see there's a column of expressions on the left hand side, and a column of expressions on the right hand side.

And they match, draw a line between the ones that do.

And for number two, we've got a word problem.

Alex and Izzy played a beanbag game as a pair.

They each threw a beanbag at a target, and then added the scores together to make a sum.

What was the sum? Alex says, "I threw a red beanbag and scored 110," and you can see his beanbag on the target there.

Izzy says, "My beanbag was green and I scored 250." Well done Izzy.

So what was the total of their two scores? Pause the video and have a go at these practise questions now.

I'll give you some feedback in a moment.

Good luck.

Welcome back, let's see how you got on.

Here are the matched pairs.

Pause the video here if you need to, to mark your work.

Okay, let's see how you did on the second question, I hope number one went well.

Here's the second question.

11 plus 25 equals 36.

11 tens plus 25 tens equals 36 tens.

So 110 points plus 250 points equals 360 points.

Great.

We are ready to move on to the next part of the lesson, which is using partitioning to add three digit numbers.

Izzy sets a challenge for Alex.

Izzy selects two pairs of digit cards and creates a sum.

You can see there she's got 68 plus 76.

Alex accepts the challenge, and he writes it out 68 plus 76.

Izzy says, "You can use base 10 to represent each addend first." And there it is, represented in base 10.

We've got 68 plus 76.

Alex says, "Then I can partition them by place value." So he's gonna split them up into their place values.

There they go.

And he's also done that in jottings.

You can see that above.

Izzy says, "Now you can group the tens and ones." And she does that.

You can see the tens have swapped to be together, and the ones have swapped to be together.

We write that out in jottings above, 60 plus 70 plus eight plus six.

Alex says, "Next I can combine the tens and ones.

I'll need to use some bridging." So he combines them together, and writes it down as a jotting as well.

We've got 130 plus 14.

Then I will add together the recombined groups to get the sum.

There we go.

He's recombined them, and he's found it's 144.

Time for you to have a go.

You could use base 10 if you want to, or you can have a go with the jottings.

I want you to complete the sum below, 84 plus 58.

Pause the video and have a go.

Good luck.

Welcome back, let's see how you got on.

We had to complete the sum 84 plus 58.

Izzy said, "I'm gonna partition the addends first." And she partitioned them into tens and ones.

She wrote them out into their groups, 80 plus 50 plus four plus eight.

Then she combined the tens and the ones to give her 130 plus 12, which was 142.

How did you get on? I hope you got it.

Okay, let's move on.

This time, Alex selects three digit cards to make a sum.

We've got 290 plus 150.

Alex says, "I'm gonna use partitioning and bridging." 290 plus 150.

Izzy says, "Remember, there aren't any ones, so you only need to partition into hundreds and tens." There we go.

290 has been partitioned into 200, and 90, and 150 has been partitioned into 100, and 50.

Then Alex has written them out, 200 plus 100 plus 90 plus 50.

He groups them together to give him 300 plus 140, and then he finishes off the sum 440.

Okay, now it's your turn.

Let's check if you've understood that process.

I want you to complete the sum below, 340 plus 270.

Pause the video, have a go, and then we'll come back in a moment to see how you've got on.

Welcome back, let's see how you did.

Alex says, "Here's how I would've solved this." 340 plus 270.

He's partitioned them into 300, 40, 200 and 70.

He's written those out, and then he's grouped them together to give him 500 plus 110, which gives him an answer of 610.

Okay, let's carry on.

Izzy is selecting digit cards for both of them to solve.

240 plus 110.

Alex says, "I'm gonna use partitioning," and he partitions 240 and 110, as you can see.

He then writes it out, and groups them to give him 300 plus 50, which gives him 350.

Izzy says, "I think I can use my understanding of unitizing instead." So she writes out the sum, and she changes each of the addends into 24 tens plus 11 tens, giving her 35 tens, which is 350 in total.

Which is the most efficient method? Hmm.

Partitioning or unitizing, what do you think? Well Izzy says she thinks unitizing is the most efficient for this question, because she's comfortable adding 24 and 11.

Well done, Izzy.

Okay, let's check your understanding.

For each of these sums, would you use unitizing or partitioning and bridging, and why? Pause the video here, look at each of the sums. Have a think and justify which you would pick and why.

Good luck.

Okay, welcome back, let's see how we got on.

Remember, some of this is about discussion, so it might be that you don't completely agree with the answers here, but let's have a look and see what Izzy and Alex said anyway.

Izzy said, "I'd use unitizing for the first one because I'm happy adding 14 and 12 together." Alex said, "I'd stick with partitioning and bridging for the second and third one, because the unitizing numbers are tricky to add quickly." How did you get on, did you agree? Okay, let's move on.

Are you ready? Izzy's turn again.

How might she solve this one? 330 plus 204.

330 plus 204? Well, Alex says, "I don't think unitizing is going to help here because there are ones tens and hundreds across both addends." Izzy says, "I'll try some partitioning then." So she partitions the addends, writes them out, and then groups them.

So she gets 500 plus 34, which equals 534.

What's different about the jottings this time? Hmm.

Well, Alex says, "This time Izzy has partitioned the addends and combined the tens and ones together." So you can see in the top row there, she's got 300 plus 200, plus 30 plus four, and in the second row she's taken the 30 and four, and combined them.

She's combined the tens and ones.

Okay, time to check your understanding here.

We've got 540 plus 309.

Pause the video and let's see how you get on.

Welcome back, shall we see how you got on? So you might have partitioned these numbers, as you can see, and then grouped them to give you 800 plus 49, which gives you a final total of 849.

All right, are you ready for some practise? For number one, I want you to fill in the missing numbers.

You can see there are two sets of jottings there, one for A and one for B.

And within those are some underlying sections, which are where there are some missing numbers for you to try to fill in.

For number two, I want you to add these together using unitizing or partitioning, whichever one you feel comfortable with.

And for number three, we've got a word problem.

Izzy and Alex are playing a computer game.

They have to shoot as many targets as they can in two minutes.

They each take two turns.

The table below shows how many they score in each go.

Who has won overall by scoring the most points? Okay, good luck.

Give it your best shot, I know that you will, and I'll be back for some feedback in a little while.

Welcome back, let's give you some feedback to see how you got on.

I'm gonna reveal the answers for number one, and for number two, and I'm gonna give you some time to do some marking.

There are the answers.

Pause the video to see how you got on.

Okay, let's go to the next question.

We had the computer game that Alex and Izzy were playing together.

Well, to solve this, you might have started by combining Izzy's first and second go, which was 304 plus 490.

You could partition that, combine those groups, and get a total of 794.

Let's do the same thing with Alex.

So we are combining 380 and 408.

They are our addends.

We can partition them into their place value groups, combine them, and then we get 788 as our total.

Now the question was who has won overall by scoring the most points? And I think we can safely say now, that Izzy has won.

Okay.

Thanks very much for taking part in this lesson.

I hope you really enjoyed it.

I really did, and I know you worked really hard.

Here's a summary of the lesson.

Unitizing is where we count each object within a group as one unit.

Unitizing can be used to add three digit numbers together.

When adding two three digit numbers, partitioning can be used to separate the addends into place value groups.

The groups can be recombined to find the sum.

Thanks very much and I hope that you had fun.

I did, see you soon.