Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in today's maths lesson.

It's from our unit adding and subtracting ones and tens to and from two digit numbers.

So we're going to be looking at two digit numbers, and we're going to be thinking about adding and subtracting and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be bridging 10 to subtract single digit numbers from two-digit numbers.

You might have thought about bridging through 10 recently.

This time we're going to think about it with subtraction.

So we've got two keywords in our lesson today.

We've got bridge and partition.

So I'll take my turn and then it'll be your turn.

My turn, bridge.

Your turn.

My turn, partition.

Your turn.

Well done.

I hope they're words that you know quite well, but they're going to be really useful so listen out for them in our lesson today to help with our learning.

There are two parts to our lesson today.

In the first part, we're going to be subtracting by bridging 10 with resources.

And in the second part, we're going to be subtracting by bridging 10 on a number line.

So if you're ready, let's make a start.

And we've got Alex and Sam helping us in our lesson today.

So the children wonder how they could solve this equation efficiently.

They've got 14 - 8.

Alex says, "I wonder what we should do.

There are 4 ones in 14, so I can't subtract 8 ones.

"Sam says we could use the bridge 10 strategy to help us." We know there aren't enough just ones, but we know that one 10 is 10 ones, don't we? So we know we've got some more ones we can use.

She says, "14 is greater than 8, so we don't have enough to subtract 8 ones." But Alex says, "If we bridge 10, we can use our number pairs to 10 to help us." So we're going to use 10 frames to show this.

So we can see 14 there, one whole 10 and four ones.

First, we partition the eight into four and four.

So there we can see our 8 partitioned into 4 and 4 because we know that 14 subtract 4 is going to get us to 10.

So there we go.

We can see 8 partitioned into 4 and 4.

There's the four extra ones that will take us back to 10, and then four more.

So we can rewrite our equation slightly.

14 subtract 4, subtract another 4, and we'll still have subtracted 8 in total.

So then 14 subtract 4 is equal to 10.

We're taking away all the ones, we're just left with one 10.

There they go.

So we subtracted 4 but now we've got to subtract another 4 because we've got to subtract 8 in total, and we know 4 + 4 is equal to 8.

So 10 subtract 4 is equal to 6, and we can use our number facts for this.

If 10 is a whole and 4 is a part, then 6 is the other part.

10 subtract 4 is equal to 6.

So 14 subtract 8 is equal to 6.

Let's think about it on a number line.

So Sam says, "I need to subtract 4 from 14 to reach 10 so 8 must be partitioned into 4 and 4.

So 4 and 4.

14 subtract 4 is equal to 10.

So we've taken away the first 4.

We've got another 4 to subtract.

10 subtract 4 is equal to 6.

And we can use our number facts to 10 to know that if 10 is a part and 4 is a part, 6 is the other part.

And Sam says, "I can check that I subtracted 8 altogether." She subtracted 4 and then another 4 so she subtracted 8 altogether.

Let's look at this with base 10 blocks as well.

"14 has 4 ones, so I will partition the 8 into 4 and 4 to bridge 10." Four and four.

14 subtract 8 is equal to 14, subtract 4, subtract another 4.

14 subtract 4 is equal to 10.

Oh, there go our 4.

What about the 10 subtract 4? We need to regroup the one 10 into 10 ones so we can subtract another 4.

10 subtract 4 is equal to 6.

So 14 subtract 8 is equal to 6.

Let's use the same strategy to solve 24 subtract 8.

And we've got it there in base 10 blocks.

This time we're going to bridge 20 and not 10, aren't we, 'cause we've got 24 as our starting number as our minuend.

"24, our whole, has 4 ones." So Sam says, "I will partition 8 into 4 and 4." And there it is.

24 subtract 8 is the same as 24 subtract 4, subtract 4.

So let's do that first.

24 subtract 4 and that's equal to 20.

Now we've got to do 20 subtract 4.

Sam says, "We need to regroup one 10 into 10 ones so we can subtract 4." And there go the 4 and we're left with one 10, and 6 ones which is equal to 16.

So 24 subtract 8 is equal to 16.

So let's look at both of those equations.

What's the same and what's different? With 14 subtract 8, we bridged 10, and with 24 subtract 8 we bridged 20.

You might want to have a think.

What's the same and what's different? Sam says, "In both equations we must regroup one 10 into 10 ones so that we can subtract 8." We subtracted 4 and then another 4, but we had to regroup one of those tens.

When the ones are subtracted, we must use the bridge ten strategy to cross the tens boundary.

In the first equation we crossed 10, and in the second we crossed 20.

Let's look at those on the number line.

14 subtract 4 is equal to 10, subtract another 4 is equal to 6, and we've subtracted 8 altogether, and we bridged through 10.

24 subtract 4 is equal to 20, subtract another 4 is equal to 16.

We subtracted 8 in total, 4 + 4.

And this time we bridged through 20.

Okay, one for us to do together, and then one for you to have a go at.

Let's use the bridge 10 strategy to solve the first equation.

34 subtract 8.

So 34 subtract 8.

Well what's that the same as? We can see those four that are easy to take away.

So we're going to partition our 8 into 4 and 4.

So we can do 34, subtract 4, subtract 4.

34 subtract 4 is equal to 30 and 30 subtract 4, we can regroup one of those tens and subtract 4 is equal to 26.

We can see the two tens and six ones remaining.

Okay, over to you to have a go to solve the second equation.

Can you use the first example to help you to solve the second example? Pause the video, have a go, and when you're ready we'll get together for some feedback.

How did you get on? So did you see some similarities here? We've still got a something 4 subtract an 8, haven't we? This time it's 44 subtract 8.

So we're going to partition the 8 into 4 and 4.

So we can do 44 subtract 4 and then subtract another 4.

So that first one, 44 subtract 4 is equal to 40, and the 4 have disappeared so we've got 40 left.

we've still got to subtract another 4.

So we're going to regroup one of our tens into 10 ones so we can subtract 4, and we know that we've got three tens and six ones left, we've got 36 left.

So 48 subtract 8 is equal to 36.

Sam says she has partitioned the subtrahend, the number she's subtracting, so that she can use the bridge 10 strategy to solve this equation.

62 subtract 6, and she's partitioned the 6 into 3 and 3.

Hmm, is she right? Is that the best way to partition the 6? Alex says, "62 has two ones so to bridge the next multiple of 10, you must subtract 2." "Oh," says Sam, "I should have partitioned 6 into 2 and 4." She could use 6 partitioned into 3 and 3 but she wouldn't bridge through a multiple of 10, so it might not be the most deficient strategy.

Her number ones might not be the right ones to use that strategy.

Ah, she's changed her partitioning now.

So now she says, "She can do 62, subtract 2 and then subtract 4." 62 subtract 2 is equal to 60 and 60 subtract 4, we can imagine regrouping one of those tens taking away 4 would be equal to 56.

Over to you to check your understanding.

Can you bridge a multiple of 10 to solve this equation? We've got 53 subtract 5.

Remember you can use base 10 blocks to help you.

Think about how you will partition the 5 so that you can bridge the next multiple of 10.

Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Did you use some base 10 blocks to help you? We've put some on the screen here.

So 53 subtract 5.

Well we can see that we've got a 3 there to subtract to get to our next multiple of 10.

So it makes sense to partition our 5 into 3 and 2.

So 53 subtract 3 and then subtract 2.

So 53 subtract 3 is equal to 50, but now we've still got to subtract 2.

So what are we going to do? Well, we can regroup our 10 into 10 ones.

So now we've got 5 tens, but one of them has been regrouped into 10 ones, and we can subtract our 2 from our 10 ones.

10 subtract 2 is equal to 8.

So now we've got 4 tens and 8 ones so we've got 48.

So 53 subtract 5 is equal to 48.

Well done if you got that right.

Time for you to do some practise.

You're going to use base 10 blocks to solve the following equations, and then fill in the missing numbers to show what you did and what do you notice in each example.

So pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Let's have a look.

So 33 subtract 5.

So we've got a 3 in the ones of our whole there, our minuend, so it makes sense to partition our 5 into 3 and 2.

So we're going to do 32 subtract 3 and then subtract 2.

So 33 subtract 3 is equal to 30, and then we've still got to subtract to 2.

So we can regroup one of those tens into 10 ones so we'll end up with 20, and then our 10 subtract 2 is 8 so we'll end up with 28.

What about 33 subtract 6? Oh, can you see what's happening? We're subtracting one more this time, aren't we? But we're still subtracting from 33, so it makes sense to partition our 6 into 3 and 3.

So then we can say 33 subtract 3 is equal to 30, and 30 subtract 3 is equal to 27.

Ah, we had one more that we were subtracting, so our answer is one less.

What about C? Can we follow the pattern? Again, we are subtracting from 33, so it makes sense to partition 7 into 3 and 4.

33 subtract 3 is still 30, but this time we're subtracting 4, so our difference is now 26.

And what about the last one? Again, we're subtracting one more again.

So we're going to partition our 8 into 3 and 5.

30 subtract 5 is equal to 25.

And you might have noticed in each example the minuend was the same, our whole, the number we started with, so the subtrahend had to be partitioned into 3, and another number so that we could bridge through 10.

The number we were subtracting, the subtrahend, changed each time, but it always made sense to partition it into 3 and something, so we could remove the 3 from the 33 that we were starting with.

And you also might have seen that the subtrahend, the number we were subtracting increased by one each time.

So the difference, the number we were left with, decreased by one in each example, and you can see that in our answers 28, 27, 26, and 25.

And on into the second part of our lesson.

We're going to be subtracting by bridging 10 on a number line.

So we can draw a number line to help us imagine the tens boundary when we bridge a multiple of 10.

So we've got 52 subtract 4.

So we've put 52 on our number line.

"The number line can help me to understand how to partition the numbers in the most efficient way," says Alex.

Let's practise.

He says, "52 has two ones, so I must subtract 2 to reach the previous multiple of 10." He says, "I will partition 4 into 2 and 2." There we go.

"So 52 subtract 2 is equal to 50.

Now I need to subtract another 2," he says.

50 subtract 2 is equal to 48.

This time the equation is slightly different.

Alex is subtracting 5.

He says, "52 has two ones, so I will still subtract 2 to reach 50.

5 = 2+ 3, so I have 3 to subtract from 50." So this time, he's partitioned 5 into 2 and 3.

He subtracted the 2 to get to 50, and now he still has to subtract the 3 and 50 subtract 3 is equal to 47.

He says, "When I know how many to subtract to reach the previous multiple of 10, I can decide how to partition the subtrahend," how to partition that number that he's taking away.

Sam wonders how she can find the missing numbers on the number line.

Hmm, I wonder if she can use some of that thinking Alex has done.

So she can see 73 bridged through 70 to get to 66 and we've subtracted 7.

She says, "You need to find out how many ones to subtract so that you reach the previous multiple of 10." In this case, 70 from 73.

Then you can use that to partition the subtrahend, the number you're taking away.

"73 has three ones, so partition 7 into 3 and 4," she says.

We know we've taken away 7 altogether, so we've taken away 3 to get to 70, and then we've taken away another 4 to get to 66.

Over to you to check your understanding.

Which number will correctly complete the number line? We've got 54 subtract 7 is equal to 47, and we've got a missing number.

So pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? What was the missing number? Did you spot that it was four? There are 4 ones in 54 and 50 subtract 4 is equal to 50.

So we must partition 7 into 4 and 3.

Well done if you spotted that.

This time, Alex subtracts the same single digit, but the whole is different in each case.

So he's got 42 subtract 7 and 43 subtract 7.

I wonder if he will still partition the subtrahend in the same way.

The subtrahend is 7, the number we're taking away in both.

Alex says, "42 has two ones.

So I must subtract 2 to reach the previous multiple of 10.

I'll partition 7 into 2 and 5." Now, will that work for the next one? "Oh," he says, "43 has three ones so I must subtract 3 this time to reach the previous multiple of 10." So this time he's partitioned his 7 into 3 and 4, and he can see 42 subtract 2 will take him back to 40, the previous multiple of 10.

And in the second example, 43 subtract 3 will get him to the previous multiple of 10, which again is 40.

And in the first one he says, "I have 5 left to subtract." 40 subtract 5 is equal to 35.

And in the second one he has 4 left to subtract and 40 subtract four is equal to 36.

Sam uses the bridge 10 strategy to solve this equation.

Well, what is her mistake? She's got 36 subtract 8.

Hmm.

"Oh," she said, "I've spotted my mistake.

I didn't use the multiple of 10 to bridge, so my strategy wasn't as efficient." She got the answer right, but she didn't use perhaps the most efficient strategy that allowed her to use the number facts that she knows really well.

"36 subtract 6 is equal to 30, so I must partition 8 into 6 and 2." Ah, 36 subtract 6 is equal to 30 and then 30 subtract 2 is equal to 28.

So she did get the right answer before, but she didn't perhaps use the most efficient strategy, bridging through 10.

Ah, so there we go.

So she's adjusted her partitioning, and she's adjusted her number line.

So now she has bridged through 10 to solve the problem.

"I will check, I subtracted 8," she says.

Yes, she subtracted 6 and then 2.

So she has subtracted 8 in total.

Time to check your understanding.

Can you draw the number line to solve this equation by bridging a multiple of 10? We've got 34 subtract five.

Remember to think about how to partition 5 so that you can bridge through a multiple of 10.

Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Alex is going to help us with this feedback.

He says, "34 has 4 ones, so I must subtract 4 to reach the previous multiple of 10.

I will partition 5 into 4 and 1." So 34 subtract 4 is equal to 30.

And now I need to subtract another one.

Well, he probably knows 30 subtract 1 is one less than 30, which is 29.

So 34 subtract 5 is equal to 29.

Let's look at this pattern on the number line.

Can it help us to predict the equation represented by the next number line in the pattern? Let's look at the ones we've got, and see if we can predict the next one.

So let's explore the patterns made when we bridge a multiple of 10 on the number line.

We've got 62 subtract 2 is equal to 60, subtract another 2 is equal to 58.

So we've subtracted 4 in total.

62 subtract 4 is equal to 58.

What about the next one? Well, we've got 72 subtract 2 is equal to 70, subtract another 2 is equal to 68, so again, we've subtracted 4 in total.

Then we've got 82 subtract 2 is equal to 80, and 80 subtract 2 is equal to 78.

So again, 82 subtract 4 is equal to 78 this time.

What do you notice that is the same and what's different? Alex says, "The ones digits are the same on each number line and the tens digits are different on each number line." And Alex has spotted that the tens digits in the difference become one less on the number line when the ones are subtracted.

So what equation would the next number line in the pattern represent? We've had 62 subtract 4 is equal to 58, 72 subtract 4 is equal to 68, 82 subtract 4 is equal to 78.

The next number line will represent the equation 92 subtract 4 is equal to 88.

Time to check your understanding.

Which number line follows the same pattern as the one shown on the left? So we've shown 15 subtract 5 is equal to 10 subtract 3 is equal to 7.

So which number line A, B, or C follows the same pattern as the one shown? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

What did you think? It was C, wasn't it? We subtracted 5 to get to a multiple of 10 and then another 3.

So that was the number line that followed the same pattern.

And in both of those, we subtracted 8, each time we subtracted 5 and then another 3, so we subtracted 8.

Time for you to do some practise.

So for question one, can you find the missing numbers on the number lines and write the equations that they represent? And can you explain the pattern you notice in each set of number lines? So there's a setting A and a setting B, and there's a pattern to spot.

And in question two, you're going to bridge 10 to solve the following equations.

Remember, you can draw a number line to help you.

And again, can you find any patterns that help you? Pause the video, have a go at your tasks, and when you're ready, we'll get together for some feedback.

How did you get on? So these were the three number lines in A.

What did you spot? Well, the first one represented 12 subtract 7 is equal to 5.

The second one represented 22 subtract 7 is equal to 15, and the third one represented 32 subtract 7 is equal to 25.

So did you notice that in set A, the ones digit of the missing number was always a 5 because 7 ones were subtracted from a number with a ones digit of two each time.

And also, that 7 was partitioned into 2 and 5 each time to bridge the previous multiple of 10.

And what about in set B? This time, the ones digit left after 8 was subtracted was always a 7 because 8 ones were subtracted from a number with 5 in the ones each time, and also, 8 was partitioned into 5 and 3 each time to bridge the next multiple of 10.

So we partitioned into 5 and 3, we bridged through 20 in the second one, and we'd subtracted 8 in total in the third one, and we've recorded our equations underneath.

Well done if you spotted all those patterns and spotted the similarities between those number lines.

So in question two, you were filling in the missing numbers.

So in set A, 6 was subtracted from a number with a ones digit of 3.

The 6 was partitioned into 3 and 3 to bridge through the previous multiple of 10 in each equation, and this means that the difference will have a 7 in the ones each time.

So our missing numbers 33 subtract 3 is equal to 27, and 63 subtract something is equal to 57.

Well, we must have subtracted 6.

In set B, 8 was subtracted from a number with a ones digit of 5.

8 was partitioned into 5 and 3 to bridge through the previous multiple of 10 in each equation.

And this means the difference will have a 7 in the ones.

So 15 subtract 8 is equal to 7, 35 subtract 8 is equal to 27, 55 subtract something is equal to 47.

Well, it must be 8.

And something subtract 8 is equal to 57.

Well it must have been 65.

And in set C, different numbers were subtracted from a number with a ones digit of 2.

So each number was partitioned into 2, and another number to reach the previous multiple of 10 to bridge through it.

So each answer has a different ones digit.

So we were always starting with 42.

We subtracted 3, which gave us an answer of 39.

We subtracted 4, which gave us an answer of 38, and we subtracted 5, which gave us an answer of 37.

And to get an answer of 36, we must have subtracted 6, so each time we were subtracting one more.

So our difference was one less each time.

I hope you spotted all those patterns.

And we've come to the end of our lesson.

We've been subtracting by bridging through a multiple of 10.

So what have we learned about? We've learned that when we subtract a one digit from a two-digit number, we can solve the equation more efficiently by using the bridge 10 strategy.

When we bridge a multiple of 10, we partition the number we are subtracting to reach the previous multiple of 10.

Bridging 10 is an efficient strategy because we can use our number pairs to 10 to calculate more easily.

And we've got an example here.

52 subtract 5 is equal to 47.

We can partition our 5 into 2 and 3 so that we bridge through the multiple of 10, which is 50.

Thank you for all your hard work today.

I hope you've enjoyed the lesson too, and I look forward to working with you again sometime.

Bye-bye.