Lesson video

Hello there.

My name is Mr. Goldie, and welcome to today's maths lesson.

I'm sure you're going to have lots of fun.

And here is the outcome for today's lesson.

So, "I can cross the 100s boundary when adding and subtracting multiples of 10." And here are our keywords.

So our keywords are multiple.

Can you say multiple? And 100s boundary.

Can you say 100s boundary? Let's look at what those words mean.

A multiple is the result of multiplying a number by another whole number.

So 10, 20, and 30 are all multiples of 10.

Two, four, six, and eight are all multiples of two.

The 100s boundary is the point at which the numbers change into 100s numbers or from one set of hundreds to another.

So there's an example of a 100s boundary.

So, 98, 99, 100, 101, 102.

And here's our lesson outline.

So the first part of the lesson, we're going to be adding and subtracting multiples of 10, and in the second part of the lesson, we're going to be adding 10s to and subtracting 10s from any number.

Let's get started.

In this lesson, you will meet Jacob and Aisha, and Jacob and Aisha are going to be asking you lots of different questions.

Aisha and Jacob play a game.

They take it in turns to throw bean bags at a target.

"We each get to throw two bean bags," says Aisha.

"We score points depending on where the beanbags land," says Jacob.

So this is worth 40 points.

So if a beanbag lands on the 40, you get 40 points.

This is worth 90 points.

If a beanbag lands on the 90, it's worth 90 points.

How could they score 100 using two bean bags? So have a look at the target.

Can you see two numbers that add together to make 100? "I know six add four equals 10," says Aisha.

"60 add 40 equals 100." Six 10s add four 10s equals 10 10s equals 100.

"I know seven add three equals 10.

"So 70 add 30 also equals 100.

Seven 10s add three 10s equals 10 10s equals 100," says Jacob.

Which other ways could they score 100? Can you see any other ways they could score 100? So we could have 80 add 20 equals 100.

We could have 50 add 50 equals 100.

There's lots of different ways of scoring 100.

Doubles facts can also be useful for adding multiples of 10.

So, "I know double six equals 12," says Aisha.

So 60 add 60 equals 120.

Six 10s add six 10s equals 12 10s." "I know double 7 equals 14," says Jacob.

"70 add 70 equals 140." If Jacob threw two beanbags and they both landed on 70, he'd score 140 points.

Eight add eight equals 16.

80 add 80 equals 160.

Nine add nine equals 18.

So 90 add 90, 9 10s, add nine 10s equals 18 10s, 180.

So if Jacob had thrown two beanbags and they both landed on 90, he would score 180 points.

So Aisha throws first.

She gets 40 and she gets 70.

"I have to add together 40 and 70", says Aisha.

How could Aisha add 70 and 40 together? "Start on 70 because it's the bigger number," says Jacob.

So normally, when you are adding two numbers together, normally, it's sensible to start on the larger number.

How could Aisha cross the 100s boundary? What adds to 70 to equal 100? So Aisha represents 70 add 40 with base 10 blocks.

Add 70, add 40.

Aisha partitions 40 into 30 and 10.

So 70 add 30 equals 100.

So if Aisha partitions the 40 into 30 and 10, she can add the 30 onto the 70 first of all and add the 10 afterwards.

First, she adds 30 to make 100 so 70 add 30 equals 100.

Then she adds 10 more.

Aisha has scored 110 points altogether.

So 70 add 40 equals 110.

Aisha represents 70 add 40 on a number line.

So Aisha partitions 40 into 30 and 10.

She adds 30 to make it 100.

So 70 at 30 equals 100.

Then she has 10 more.

So 10 more would be 110.

70 add 40 equals 110.

Jacob throws next.

Jacob scores 90.

Good throw, Jacob.

He scores 20.

Not quite so good.

"I have to add together 90 and 20," says Jacob.

How could Jacob add 90 and 20 together? Start on 90 because it's the bigger number.

Good advice, Aisha.

How could he cross the 100s boundary? What adds to 90 to equal 100? What would you have to add to 90 to get to 100? Jacob represents 90 plus 20 with base 10 blocks.

There's nine 10s add two 10s.

He partitions 20 into 10 and 10 'cause 90 add 10 equals 100.

Let's partition the 20 into 10 add 10.

He adds 10 to make 100.

Let's add that 10 across.

So 90 add 10 equals 100.

Then he adds 10 more.

"I scored 110 points altogether." Jacob scored the same total as Aisha, although his bean bags landed on different multiples of 10.

Jacob represents 90 add 20 on a number line.

So Jacob partitions 20 into 10 add 10 and first he adds 10 to make 100.

So 90 add 10 equals 100.

Then he adds 10 more.

So 100 add 10 equals 110.

90 add 20 equals 110.

Aisha throws next.

Aisha scored 60 and 80.

"I have to add together 80 and 60," says Aisha.

How could Aisha find the sum? So she's going to start with 80 'cause 80 is the larger number.

So it's easier to start on 80 and add on 60 than it is to start on 60 and add on 80.

So Aisha's gonna start on 80 and she's gonna have to think carefully about how she's going to add on that 60 to bridge through 100.

So Aisha partitions 60 into 20 and 40.

So she'll start with 80 add 20 because that makes 100.

That equals 100.

80 add 20 equals 100 and then she adds on the 40.

100 add 40 equals 140.

So she's added on 60 altogether.

She starts on 80 and she's added on 60 by partitioning it into 20 and 40.

80 add 60 equals 140.

Jacob throws next.

So he scores a 40 and he scores an 80.

"I have to add together 80 and 40." How could Jacob use a number line to find the sum? Think about which number he would start from and think about how he would partition one of the numbers to help him add on to bridge through the 100.

Pause the video and have a think about it.

And welcome back.

Let's have a look at what you might have done.

So Jacob is going to start from 80.

80 is the larger number.

So he's going to start from 80 and he's going to add on the 40 and he's got to think careful about how to bridge through that 100.

Now he knows eight add two equals 10.

So 80 add 20 equals 100.

So Jacob partitions the 40 into 20 and 20.

He starts with 80 and he adds on a 20.

80 add 20 equals 100.

Then he adds on 20 more.

100 add 20 equals 120.

So 80 add 40 equals 120.

Aisha throws two beanbags.

"I scored a total of 110 points." "One of Aisha's beanbags landed on 30." Where did Aisha's other beanbag land? How could you calculate the answer? So she scored a total of 110 points and we know that one of her beanbags landed on 30.

How could you calculate the answer? What could you do? Or we could use subtraction to work out the answer.

So we could start with her total, 110.

If we subtract 30, we'll get the difference between the two numbers and that will give us the number that the other beanbag landed on.

Aisha calculates 110 subtract 30.

So Aisha is going to represent the problem using base 10 blocks and a number line as well.

First, she subtracts 10 to make 100.

So she's going to bridge through that 100 by subtracting 10, first of all.

So using the base 10 blocks, she subtracts 10 and on the number line, she subtracts 10.

She counts back to 100.

Then she subtracts 20 more.

So she subtracts 10 and then 20 more.

So altogether, she has subtracted 30.

100 subtract 20 equals 80.

10 10s subtract two 10s equals eight 10s.

And on the number line, she subtracts 20 and counts back to 80.

100 subtract 20 equals 80.

So while 110 subtract 30 equals 80, Aisha's other beanbag landed on 80.

Jacob throws two beanbags.

"I scored a total of 120 points," says Jacob.

"One of Jacob's beanbags landed on 50." Now where did Jacob's other beanbag land? How could you calculate the answer? Think about what we just did with Aisha's problem and how we calculated the answer.

What calculation would give you Jacob's other score? Where did his other beanbag land? We could use subtraction to work out the answer.

So we know he's got a total of 120 points.

If we subtract 50 from 120, we'll get the score of his other beanbag.

So Jacob calculates 120 subtract 50.

And again he's going to have to think carefully about how to bridge through that 100.

First, he subtracts 20 to make 100.

Let's subtract 20 using our base 10 blocks and subtract 20 on the number line as well.

So 120 subtract 20 equals 100.

Then he subtracts 30 more.

So 50 is made from 20 and 30.

If Jacob subtracts 20 and then he subtracts another 30, altogether he has subtracted 50.

Using the base 10 blocks, he subtracts three 10s.

So 10 10s subtract three 10s equals seven 10s.

So he's left with the number 70.

And on a number line representation, he subtracts 30 as well.

So 100 subtract 30 equals 70.

"120 subtract 50 equals 70.

My other bean bag landed on 70." And here's one to try on your own.

Aisha throws two beanbags.

"I scored a total of 120 points.

One of my beanbags landed on 30." Where did Aisha's other beanbag land? Now you could use a number line to work out the answer or you could use base 10 blocks if you've got them as well.

So think carefully about the calculation that Aisha would have to do to work out the answer.

Pause the video and have a go.

Can you work out where Aisha's other beanbag landed? And welcome back.

Did you manage to get an answer? Do you think you know where Aisha's other beanbag landed? Let's see if you were right.

So the calculation you should do is 120 subtract 30 and that will give you the answer.

So let's have a think about how to bridge through that 100.

What would you subtract from 120 to get to 100? I would subtract 20.

So 120 subtract 20 equals 100.

What do you then have to subtract? You have to subtract 30 altogether.

So you'd have to subtract another 10.

100 subtract 10 equals 90.

So Aisha's other beanbag landed on 90.

Very well done if you've got the right answer.

And let's look at task A.

This is part one of task A.

Aisha scores 130 points using two beanbags.

"Where could my two beanbags have landed?" says Aisha.

You've got to think of two different multiples of 10 that add up to equal 130.

How many different answers can you find? And use a number line or base 10 blocks to help you represent the problem.

And here's part two of task A.

So work out where both beanbags landed by completing each subtraction calculation.

So the first one, the total is 140 points and you are told that one of the beanbags landed on 50 and you've got to work out where the other beanbag landed.

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

And welcome back.

Let's have a look to see how you got on.

So part one of task A, here are all the possible answers.

These are the different ways that Aisha could have scored 130 points.

And part two of task A, complete each subtraction calculation.

Very well done if you got onto to part two and you managed to work out all those different calculations, excellent work.

And let's move on to part two of the lesson.

So part two of the lesson is adding 10s to and subtracting 10s from any number.

Aisha and Jacob try adding multiples of 10 to other two digit numbers.

So what is 71 add 40? Let's represent the problem using base 10 blocks.

So 71 add 40.

"Let's partition the 40 into 30 and 10 to bridge 100," says Aisha.

Very sensible advice, Aisha.

So seven add three equals 10.

70 add 30 equals 100.

Jacob adds 30 to make 101.

So Jacob takes the 30, adds it to the 71, and that equals 101.

Then he adds 10 more.

71 add 40 equals 111.

Jacob represents 71 add 40 on a number line.

So Jacob adds 30 to make 101, first of all.

So he starts on 71 and he adds 30 to make 101.

So 71 would be there on the number line.

We add on 30 and we get to 101.

Then he adds 10 more.

So 101 add 10 equals 111.

"71 add 40 equals 111." Aisha wants to find the sum of 84 and 40.

"I'll partition 40 into 20 and 20," says Aisha.

So eight add two equals 10.

80 add 20 equals 100.

So Aisha partitions the 40 into 20 and 20.

Then Aisha adds 20 to make 104.

So she adds the 20 to 84 to equal 104.

Then she adds 20 more.

"84 add 40 equals 124." Aisha uses a number line to calculate 84 add 40.

So she starts on 84 and she adds 20 to equal 104.

Then she adds 20 more.

104 add 20 equals 124.

"84 add 40 equals 124." What do you notice? 84 add 40 equals 124.

71 add 40 equals 111.

"The ones number stays the same when you add a multiple of 10." So 84 add 40 equals 124.

71 add 40 equals 111.

That ones number isn't changing and staying the same.

"The 10s number and the 100s numbers change when you cross a 100s boundaries," says Aisha.

So it's the 10s numbers and the 100 numbers that are changing, but the ones number stays the same.

Do these also happen if you subtract multiples of 10? Calculate 86 add 30.

You can use base 10 blocks or a number line to help you.

So pause the video and have a go trying to calculate 86 add 30.

And welcome back.

So here is the calculation represented on a number line.

Let's start with 86.

So 86 and we've got to bridge through that 100.

So if we add on 20 to 86, we get 106.

80 add 20 equals 100.

86 add 20 equals 106 and then we have to add 10 more.

106 add 10 equals 116.

So 86 add 30 equals 116.

Very well done if you've got the right answer.

And it doesn't matter if you're using base 10 blocks or a number line, whatever helps you.

Aisha wants to calculate 117 subtract 30.

There's 117 represented in base 10 blocks.

"I'll subtract ten first to help cross the 100s boundaries," says Aisha.

So Aisha subtracts 10 to make 107.

So then she subtracts 20 more.

So our 100 subtract 20 would equal 80.

"117 subtract 30 equals 87." Aisha uses number line to calculate 117 subtract 30.

So Aisha subtracts 10 to make 107, first of all.

So she starts on 117 and she subtracts 10 to get to 107.

Then she subtracts 20 more.

So while 107 subtract 20 equals 87, "117 subtract 30 equals 87." Jacob calculates 125 subtract 50.

"I'll subtract 20 first to help cross the 100s boundary," says Jacob.

So Jacob subtracts 20 to make 105.

So first of all, he subtracts 20 and that leaves him with a number 105.

What does he need to subtract next? He subtracted 20 and he's got to subtract 50 altogether.

Let's have a look.

Then he subtracts 30 more.

So he's got 105 and he's got to subtract 30.

So we've got the 10 tens subtract three tens or 100 subtract 30.

That would leave him with seven tens or 70.

So 125 subtract 50 equals 75.

Jacob uses the number line to calculate 125 subtract 50.

So he represents that calculation on a number line as well.

So he starts on 125 and he subtracts a 20 to get to 105.

125 subtract 20 equals 105.

Then he subtracts 30 more.

So 105 subtract 30 equals 75.

125 subtract 50 equals 75.

What do you notice? 117 subtract 30 equals 87.

125 subtract 50 equals 75.

"The ones number stays the same when you subtract a multiple of 10." "The 10s and the 100s numbers change when you cross 100s boundary." So the ones numbers don't change when you subtract in a multiple of 10.

It's just the 10s numbers and the 100s numbers that are changing when you cross 100s boundary.

And here's one to try on your own.

So calculate 128 subtract 30, and again, you can use base 10 blocks or a number line to help you.

So pause the video and have a go.

Can you find the answer to that calculation? And welcome back.

Let's see how you got on.

So here is the calculation represented on a number line.

So we start with 128 and we're gonna subtract 20 first of all to cross over that 100s boundary.

So 128 subtract 20 equals 108.

And then subtract 10 more.

So 108 subtract 10 equals 98.

"128 subtract 30 equals 98." And very well done if you've got the answer 98, excellent work.

Now you can use number facts to help you with your calculating.

So Jacob knows that 90 add 70 equals 160.

So what would 93 add 70 be? 93 add 70 would be 163.

What would 97 add 70 be? To use Jacob's number fact to help you, the answer would be 167.

That ones number does not change if we're adding a multiple of 10.

92 add 70 would be 162 and 95 add 70 would be 165.

Now use this number fact to help you with the other calculations.

"140 subtract 60 equals 80." Could you use Jacob's number fact to help you answer those calculations? Pause the video and have a go at those four calculations.

And welcome back.

Let's see how you got on.

So our first one is 144 subtract 60.

So the answer should be 84.

141 subtract 60 equals 81.

149 subtract 60 equals 89.

And 146 subtract 60 would equal 86.

Well done if you managed to answer all those correctly.

And next we're going to look at some problems adding tens numbers and subtracting tens numbers.

So Pedro is 84 centimetres tall.

Here's Pedro.

Yes, Pedro is a panda.

Pedro puts on a blue hat.

So he puts on a blue hat.

Pandas do love their party hats.

So Pedro puts on his hat.

The blue hat is 40 centimetres tall.

What is the total height of Pedro and his hat? So the question is what is 84 add 40? 84 centimetres is Pedro's height and 40 centimetres is the height of the hat.

So if we wanted to find out the total height of Pedro in his hat, we'd have to add those two numbers together.

So what is 84 centimetres add 40 centimetres? Let's use number line to help us work out the answer.

So first, add 20 to help bridge through 100.

So we're going to start with 84 and we're going to partition 40 into 20 and 20 to help us bridge through that 100.

Let's start on 84.

If we add on the 20, that gets us to the answer 104.

Then add 20 more.

Remember we've got to add 40 altogether.

So 104 add 20 equals 124.

So altogether, Pedro and his hat are 124 centimetres tall.

And here's one to try on your own.

Priya is 76 centimetres tall.

A blue hat is 40 centimetres tall.

Just like Pedro, Priya likes wearing a blue hat best.

What is the total height of Priya and her hat? You could use a number line to help you find the answer or you may want to use base 10 blocks instead.

Pause the video and have a go at calculating the answer.

Let's have a look how you've got on.

So Priya is 76 centimetres tall.

So let's start with Priya's height, first of all.

And we've got to add on the height of the blue hat.

So 76 add 40.

How would you partition the 40 to add through that 100? So 76 add 30 equals 106.

And then what do you still have to add? You'd have to add another 10.

So 106 add 10 equals 116.

76 add 40 equals 116.

Altogether Priya and her hat are 116 centimetres tall.

Very well done if you've got that as the answer.

Excellent work.

Pia is wearing a green hat.

There's Pia and she's wearing her green hat.

The total height of Pia and the green hat is 115 centimetres.

The green hat is 30 centimetres tall.

How tall is Pia? Now that's a different type of calculation to the last one.

How you going to work out how tall Pia is? So this time, it's going to be a subtraction calculation.

We're starting off with 115.

That's the total height of Pia and the green hat.

And if we subtract the 30, subtract the height of the green hat, we'll work out the height of Pia.

So what is 115 centimetres subtract 30 centimetres? Let's use a number line representation to help work out the answer.

So first, subtract 10 to bridge 100.

So let's start with 115.

If we subtract back 10, we get to 105.

Then subtract 20 more.

So 105 subtract 20 equals 85.

So 115 subtract 30 equals 85.

Pia is 85 centimetres tall.

And here's one to try on your own.

So Polly is wearing a yellow hat.

Polly likes the yellow hats best.

The total height of Polly and the yellow hat is 143 centimetres.

The yellow hat is 50 centimetres tall.

How tall is Polly? How would you calculate Polly's height? So pause the video and have a go at the calculation.

And welcome back.

Now hopefully you did a subtraction calculation because altogether Polly and the yellow hat are 143 centimetres tall.

If you subtract 50 from 143, you'll get Polly's height.

So start with 143.

What would you subtract back to help you bridge through that 100s number? We'd have to subtract back 40.

So 143 subtract 40 equals 103.

Then what do you still have to subtract? 103 subtract 10 equals 93.

Well, 143 subtract 50 equals 93.

Polly is 93 centimetres tall.

Quite a tricky calculation that one.

So very, very well done if you've got the right answer, excellent work.

And let's move on to task B.

So in task B, the first part of task B, you have to work out how tall each panda is.

You've got there the height of the different hats.

So a green hat is 30 centimetres tall, a blue hat is 40 centimetres tall, and a yellow hat is 50 centimetres tall.

And let's look at A together.

So A says the total height of Perry and the green hat is 119 centimetres.

How tall is Perry? What calculation would you do to work out the answer? And again, you can use base 10 blocks or number lines to help you.

Then part two of task B work out the total height of each panda and their hat.

So A says Poppy is 76 centimetres tall, She's wearing a blue hat.

So what's the total height of Poppy and the blue hat? And then part three of task B, you've got to work out the different possible answers.

So Pat is wearing one of the hats.

The total height of Pat and his hat is 129 centimetres.

How tall could Pat be? So pause the video and have a go at task B.

And welcome back.

Let's have a look at the answers.

So here are the answers for part one.

So Perry is 89 centimetres tall, Peppa is 82 centimetres tall, and Peter is 83 centimetres tall.

Let's look at part two.

So the answer to A was 116.

Poppy and the hat have a total height of 116 centimetres.

B, the answer was 114 or 114 centimetres.

And C, the answer was 115 or 115 centimetres.

And here the answers to part three.

So Pat could have been wearing a green hat, a blue hat, or a yellow hat.

If he was wearing a green hat, Pat would be 99 centimetres tall.

Absolutely brilliant work today.

Very, very well done on adding tens to and subtracting tens from any number up to 200.

Excellent work.

And here is our lesson summary.

When you are adding or subtracting multiples of 10, partition one of the numbers to help you cross the 100s boundary.

The ones number stays the same when you add or subtract a multiple of 10 and the 10s and the 100s numbers change when you cross a 100s boundary.