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 are going to be bridging 10 to add single-digit numbers to two-digit numbers.

So we're going to be using our number facts and we're going to be using our number facts to 10, but we're going to be bridging through tens this time.

So are you ready? Let's make a start.

We've got two keywords in our lesson today, bridge and partition.

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

So my turn, bridge, your turn.

My turn, partition your turn.

Well done.

They're words you may well know already, but they're going to be really useful to us, so look out for them as we go through our lesson today.

There are two parts to our lesson.

In the first part, we're going to add by bridging 10 and we're going to use resources to help us.

And then in the second part of our lesson, we're going to be adding by bridging 10 and we're going to use number lines to support our thinking.

So let's make a start on Part 1, and we've got Alex and Sam helping us in our lesson today.

So the children want to use their known facts to solve this equation.

18 plus 4 is equal to something.

Sam says, "We need to use the single digit fact 8 + 4." She's looking at the ones there, isn't she? She can see there's a 10 in 18, but she can see that 8 plus 4.

Alex says, "I wonder what we should do.

8 plus 4 is equal to 12, but I can't put 12 in the ones." Hmm, he's right, isn't he? "I know," so Sam, "let's use the 'bridge tens' strategy to cross the tens boundary." So she spotted that we're gonna have to cross a tens boundary when we add 4 to 18.

Alex says, "Let's use a single digit equation to remind ourselves of how this works." Good idea Alex, always good to start with what we know.

So here's 8 plus 4, and we've used a 10 frame to represent that.

We've got 8 blue counters and we're going to add 4 red counters.

First, we can partition the 4 counters into 2 plus 2.

So there's our 4 partitioned into 2 and 2.

So now we can think about 8 plus 4 as being equal to 8 plus 2 plus 2.

And there we are, we've rearranged our counters in the 10 frame.

Can you see something that's really helping us here? Ah, we can use 8 plus 2 is equal to 10.

So there it is.

2 that we've partitioned from our 4, we can add to our 8, and that equals 10.

So we've made a complete 10, we've bridged through 10.

Now we've got to add the other two.

10 plus 2 is equal to 12.

So we know that our whole answer now, our sum is 12, and we can show this on a number line, let's have a look.

So Sam says, 'I need to add 2 to 8 to reach 10, So the 4 must be partitioned into 2 and 2." So again, there's one of the twos we've added to the 8 to make 10, and we've got the other two to add on, and 10 plus 2 is equal to 12.

So 8 plus 4 is equal to 12, and she says she can check that she added 4 altogether 2 and 2 is equal to 4.

Sam says, "I wonder if I can partition either addend." Can you see what she's done here? We've got 8 plus 4 as our equation, but with the 10 frame we've represented the 4 first and then the 8.

She says, "I know addition is commutative, so we can combine the addends in any order.

The sum will stay the same." So 8 plus 4 is equal to 4 plus 8.

And Alex says, "Let's use 'make 10' to show that." So first we can partition the 8 into 6 plus 2.

Why has she done that do you think? So 8 plus 4 is equal to 8 plus 6 plus 2.

Ah, that's why she's done it because 4 plus 6 is equal to 10.

And there it is, and we can see it in the 10 frame as well.

And then we're going to add the extra two, 10 plus 2 is equal to 12.

So we can see that 4 plus 8 or 8 plus 4 is equal to 12.

And we can show this other way of working with these numbers, the addend in a different order on the number line as well, so we're going to start with 4.

We're going to partition our 8 into 6 and 2, so that we know 4 plus 6 is equal to 10, and then we add on our extra 2, which will get us to 12.

So 4 plus 8 is equal to 4 plus 6 plus 2, and then the 10 plus 2 is equal to 12.

And we can see that we've still added on 8, 6 plus 2 is equal to 8.

So let's return to the original equation that we started the lesson with of 18 plus 4, and we can use the "bridge ten' strategy to solve this.

So 8 plus 4, we partition the 4 into 2 plus 2.

8 plus 2 is equal to 10, and 10 plus 2 is equal to 12, but we wanted 18 plus 4, didn't we? So we need another 10 with our 8 ones.

18 plus 4 is equal to 18 plus 2 plus 2, this time, we're going to bridge 20.

So our 8 plus 2 is equal to 10, which gives us our extra 10.

So 18 plus 2 is equal to 20.

And now we need to add on the extra 2, and we get our sum of 22.

So what's the same and what's different with our 8 plus 4 and our 18 plus 4? What do you think? Well, Sam says, "In both equations, 4 ones are added to 8 ones.

When the ones are added, we must use the 'bridge ten' strategy to bridge the tens boundary.

In the first equation, we cross ten and in the second equation we cross 20." And we can see that on a number line, 8 plus 2 is equal to 10, and 10 plus 2 is equal to 12, and we've added 4 altogether.

And in our other equation, 18 plus 2 is equal to 20 and 20 plus 2 is equal to 22, but we can still see that we've added 4 altogether.

Okay, let's use the 'bridge ten' strategy to solve the first equation together, and then it'll be your turn.

So we've got 28 plus 4, we've represented that with the base 10 blocks.

So how can we partition our second addend to make this easier so that we bridge through a multiple of 10? Ah, well, we can partition 4 into 2 and 2 because we know that 8 plus 2 is equal to 10.

So 28 plus 2 plus 2.

Well, 28 plus 2 is going to be equal to 30, 3 tens, and then we've got to add in our extra 2, and 30 plus 2 is equal to 32.

So 28 plus 4 is equal to 32.

Now it's your turn Can you solve the next equation by bridging 10? You've got 38 plus 4, and we've given you the base 10 blocks to help you out.

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

How did you get on? Did you use the first example to help you? So we can see that 38 plus 4 is equal to 38 plus, ah, and we can partition our 4 into 2 and 2 again, we've still got that 8 plus something to get to our next multiple of 10, so 38 plus 2 plus 2.

So there's our 8 plus 2, 38 plus 2 is equal to 40.

We now have four whole tens, and we've still got to add in our extra 2 and 40 plus 2 is equal to 42.

Well done if you got that right.

Alex says, "He has partitioned the second addend, so that he can use the 'bridge ten' strategy to solve this equation." His equation is 29 plus 6, and he's partitioned 6 into 2 and 4.

What mistake has he made? Sam says, "29 has 9 ones, so to bridge the next multiple of 10, you must add 1, 9 add 1 is equal to 10." He could solve the problem using 6 partitioned into 2 and 4, but would it be the most efficient way? "Oh," he says, "I should have partitioned 6 into 1 and 5," that would allow him to bridge through 10 more easily.

He says, "Now let's solve the equation." 29 plus 1 plus 5 is the same as adding 6, but we've partitioned our 6.

29 plus 1 is equal to 30, and then 30 plus 5 is equal to 35, so he's bridged through 10.

Time to check your understanding.

Can you use the 'bridge ten' strategy to cross the tens boundaries and solve this equation, 37 plus 4? And you can see that we've given you the equations broken down for you to fill in the missing numbers, and you can use base 10 blocks to help you if you like, and think about how you will partition the 4 so that you can bridge 10.

So pause the video, complete the equations, and when you're ready, we'll get together for some feedback.

How did you get on? Did you get some base 10 blocks out to help you? So you can see we've got 37, and then the 4 that we're adding on.

So what do we need to partition our 4 into? Well, 37 has got a 7 in the ones, so it would make sense to partition our 4 into 3 and 1 so that we can use that 3 to make our next multiple of 10.

So 37 plus 3 plus 1 is equal to 37 plus 4.

So now we can combine our 37 and our 3, and you can see that that's made an extra 10 for us.

So 37 plus 3 is equal to 40, so we've got 40, but we still need to add on that extra 1, don't we? And 40 plus 1 is equal to 41.

So you can see that 37 plus 4 is equal to 41.

Time for you to do some practise now.

Can you use base 10 blocks to solve the following equations? And think about partitioning your one digit addend so that you can bridge through the next multiple of 10.

And then can you fill in the missing numbers to show what you did? What do you notice when you partition the second addend in each example? And then for question 2, you've got some more to solve.

Again, fill in the missing numbers to show what you did, and what do you notice when you partition the second addend in each example this time? So 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 let's look at number 1.

So you had four to have a look at here.

So we had 38 plus 4, and then 38 plus 5, 38 plus 6, and 38 plus 7.

Oh, what do you notice? We had a 38 in all of them, didn't we? So let's have a look at how we partitioned.

So 38 add 2 is equal to 40, so it makes sense to partition our 4 into 2 plus 2.

So then we get 38 plus 2, which equals 40 plus the extra 2, which is 42.

What about B? This time we had 38 plus 5.

Well, the 38 still needs a 2 to make the next multiple of 10 to make 40, so it makes sense to partition our 5 into 2 plus 3, then we can add the 38 and the 2 to give us 40, 40 plus 3 is equal to 43.

What about the next one? This time we were adding 6, so it makes sense to partition 6 into 2 and 4.

38 plus 2 is equal to 40 again, and then we've got 4 to add on this time, can you see that the extra ones that we're adding on each time is one more each time? So for D, we've got 38 add 7, again we need a 2 to make that 38 up to the next multiple of 10, which is 40.

So we're going to partition our 7 into 2 and 5, 38 at 2 is equal to 40, and 40 at 5 is equal to 45, what did you notice? Yes, in each example the first addend was the same.

So the second had to be partitioned into 2 and another number, so that we could bridge through 10.

And in each example, the second addend increased by 1, so the sum also increased by 1.

Okay, what about 2? So in 2 we had 45 plus 7, 46 plus 7, 47 plus 7, and 48 plus 7.

Ah, do you notice what's happening this time? This time, our two digit addend is changing, and our one digit is staying the same, we're adding 7 each time.

So 45 add 7, well, 5 add 5 is equal to 10, so we are going to need to add 5 to bridge through the next multiple of 10.

So we need to partition 7 into 5 and 2, 45 add 2 is equal to 50, and we need to add the other 2, 50 add 2 is equal to 52.

What about B? This time we've got 46 add 7.

Ooh, we've changed the ones digit of our two-digit number, 6 add 4 is equal to 10, so we need to partition 7 into 4 and 3, so that we can bridge to our next multiple of 10, which is 50, and then add on our extra 3.

What about the next one? 47 add 7, ooh, that's interesting isn't it? Well, we know that 7 add 3 is equal to 10.

So this time, we want to partition our 7 into, well, it's 4 and 3 again, but we're interested in using the 3 first, so we might record it as 3 add 4.

47 plus 3 is equal to 50, and 50 plus 4 is equal to 54.

And then finally, 48 add 7, so this time we want 8 add 2 is equal to 50.

So again, we need to know that 7 is the whole, 5 is a part and 2 is a part, but this time, we want to use the 2 part first, so 48 plus 2 plus 5 will give us 50 plus 5, which equals 55.

So this time, the first addend increased by one, but the second stayed the same.

The second addend was partitioned differently each time to bridge the 10.

And in each example, the first addend increased by one, but the second addend stayed the same.

So the sum increased by one again each time because one of our addends had increased by one.

And on into the second part of our lesson, this time, we're going to bridge 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.

We've got 48 add 4 here, so we put 48 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.

48 has 8 ones, so I must add 2 to reach the next multiple of 10.

So I will partition 4 into 2 and 2." So he knows that 48 add 2 is equal to 50, and he's shown that on the number line and in the equation, and now he needs to add 2 more, 50 add 2 is equal to 52.

Alex wonders how he can find the missing numbers on the number line here.

So we can see that 67 add something equals 70, add something else equals 72, and in total, we've added 5, so what are those missing numbers? Sam says, "You need to find out how many ones to add so that you reach the next multiple of ten." She's giving Alex a hand here, isn't she? "Then, you can use that to help you partition the second addend.

So 67 has 7 ones, so you'll partition the 5 into 3 and 2, 67 add 3 will equal 70." So our first jump is 3 and our second jump is 2, and 3 dd 2 is equal to 5, so we have added 5.

Over to you to check your understanding, which number will correctly complete the number line? So we've got an equation represented on a number line and we've got three choices.

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

So which number was it? Did you spot that it was C, It was 3, wasn't it? There are 7 ones in 47 and 7 plus 3 is equal to 10, so we must partition the 7 that we are adding into 3 and 4, and that way, we will be able to bridge through a multiple of 10, and we bridge through 50 in this case.

So Sam uses the 'bridge ten' strategy to solve this equation.

What is her mistake? Well, she has got the answer correct, but has she used the most efficient method? Has she bridged 10? "Ah," she says, "I've spotted my mistake! I didn't use the multiple of 10 to bridge so my strategy wasn't as efficient.

When we bridge 10, it's more efficient to partition the second addend, so when added to the first addend, it reaches the next multiple of ten." and she says, "This is more efficient because we can use our number pairs to 10 to help us." She says, "6 + 4 is equal to 10," thinking about the 6 in the 36, "So I must partition 5 into 4 and 1." Ah, so she's changed her partitioning of 5 into 4 and 1, then, "36 plus 4 is equal to 40, and 40 plus 1 is equal to 41," and she's changed her number line to match.

She's going to check, though, that she added 5.

Yes, 4 add 1 is equal to 5, so she has added 5 altogether.

Over to you to check your understanding.

Can you draw a number line to solve this equation by bridging a multiple of ten? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Alex says, "29 has 9 ones, so I must add 1 to reach the next multiple of 10.

So I will partition 5 into 1 and 4.

29 add 1 is equal to 30." We can show that on the number line.

"Now I need to add 4 more.

30 and 4 more is equal to 34." So bridging through a multiple of 10, means that we can use our number bonds to 10, and also it's really easy to add on a one digit number to a multiple of 10 because we only change the ones, and our answer's 34.

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

Can it help us to predict the next equation in the pattern? So we've got 58 add 2 is equal to 60, add another 2 is equal to 62.

So we've added four in total, 58 add 4 is equal to 62.

So how could we continue this pattern? What would we do? 68 add 2 is equal to 70, add 2 is equal to 72.

What about 78 if we follow the same pattern? Add 2 is equal to 80, add another 2 is equal to 82.

Alex says, "What do you notice that's the same and what is different? Well, the ones digit for both the addends and the sum are the same in the equations, we've got 58, 68, 78, so the ones digits are the same.

And each time we're adding 2 plus 2, which is equal to 4.

And our ones digit in our sum is always a 2, 62, 72, and 82.

But the tens digits are different in each calculation.

Each time, we're starting with 10 more, and bridging through that next multiple of 10.

The tens digit and the sum is one more than the tens digit of the larger addend.

So 58 has 5 tens, 62 has 6 tens, 68 has 6 tens, 72 has 7 tens, 78 has 7 tens, and 82 has 8 tens, one more 10 each time.

So the next pattern in the equation would be 88 add 4 is equal to 92." Time to check your understanding.

Which of the following number lines follows the same pattern as the one shown? So we've got 7 plus 8 is equal to 15, and our 7 has been partitioned into 3.

So 7 plus 3 is equal to 10, and then 10 plus 5 is equal to 15.

So which of the other number lines follows the same pattern as that one? Pause the video, have a think, and when you're ready, we'll get back together for some feedback.

How did you get on? Did you spot that it was C that was correct? We had that plus 3 and plus 5 pattern repeated, even though we were starting at 27 this time and ending on 35.

Time to check your understanding again, what number has been added in each example? So what number has been added in C? Pause the video, have a think, and when you are ready, we'll get together for some feedback.

What did you reckon? Well in each example, 3 is added to reach the next multiple of 10, and then 5 more is added, this means the total added is 8, but the 8 has been partitioned so that it can be used to bridge 10.

Well done if you spotted that.

Time for you to do some practise now, can you find the missing numbers on the number lines and write the equations that those are representing? And explain the pattern that you notice in each set of number lines.

So the pattern in the 3 in A, and the pattern in the 3 in B.

And then for part two, bridge 10 to solve the following equations, and remember that you can draw a number line to help you.

So 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 for 1, we asked you to complete the missing numbers on the number lines, and then think about the patterns.

So in A, we were starting on 5, we were adding 5 to get to 10, and adding another 2 to get to 12.

For the second one, we'd started on 15, add 5 to get to 20, add 2 to get to 22.

And for the third one, we had 25 add 5 is equal to 30 add another 2 is equal to 32, and we were adding 7 each time, and 7 had been partitioned into 5 and 2.

So in set A, the ones digit of the sum was always a 2 because 7 ones were added to 5 ones each time.

7 was partitioned into 5 and 2 each time to bridge the next multiple of 10.

What about B? Could you see we were adding 8 each time, but we didn't know how we'd partitioned it.

Well let's look, each time we were starting with a 7, 17, 27, with a 7 in the ones, so we'd need to add a 3 to equal 10.

So 7 add 3 equals 10, and add 5 is equal to 15.

17 add 3 is equal to 20, and 20 add 5 is equal to 25.

And in the last one, we could see the plus 3 plus 5.

The missing number, though, was we were adding 8 each time.

So in set B, the ones digits of the sum was always 5 because 8 ones were added to 7 ones, 8 was partitioned into 3 and 5 each time to bridge the next multiple of 10.

So what about 2? Did you draw a number line to help you to bridge a multiple of 10 to solve these? So in A, we knew that 7 add 6 was equal to 13.

So 17 add 6 was equal to 23.

So if we follow on that pattern, 27 add 6 must be equal to 33.

Ooh, and 67, well, we've got that 7 and then we're going to end up with a number with a 3 in the ones, so we must have added a 6, 67 add 3 is equal to 70, add another 3 is equal to 73.

It followed that same pattern of digits in the ones.

What about B? So 8 add 5, well, 8 add 2 is equal to 10, add another 3 is equal to 13, 8 add 5 is equal to 13.

So 8 add 35 must be equal to 43, and 8 add 65 must be equal to 73.

Oh, now we had a missing addend here, something add 85 is equal to 93, well, that follows the same passion, doesn't it? So it must be 8 is our missing addend.

And what about C? 29 add 5, well, 29 add 1 is equal to 30, and then's another 4 to add, so it'll be 34.

This time, our two-digit add ]end is decreasing by one.

So 28 add 5, well, 8 add 2 is equal to 10, so 28 add 2 is equal to 30, add another 3 is equal to 33.

So our sum is decreasing by one each time.

So 27 add 5 must be equal to 32, and 26 add 5 must be equal to 31.

I hope you were able to use the patterns there to help you, and you may have drawn some number lines as well.

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

We've been adding by bridging a multiple of 10.

What have we learned? We've learned that when we add a single digit to a two-digit number, we can solve the equation more efficiently by using the bridging ten strategy.

When we bridge a multiple of 10, we partition the second addend, so that when the added to the first addend, it reaches the next multiple of 10.

So we partition the single-digit number so that we can add it to the two-digit addend.

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

I hope you've enjoyed exploring bridging through 10 to add single digits to two-digit numbers, and that partitioning that single-digit number is something you'll look for to help you to find that next multiple of 10.

Thank you for all your hard work and your thinking today, and I hope I get to work with you again soon, bye-bye.