Lesson video

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

We're going to be thinking all about place value, numbers up to a hundred, and how we can apply that and other strategies to adding and subtracting.

So, I hope you're ready to work hard and have some fun in our maths lesson today.

So, welcome to this lesson in our unit on securing place value to a hundred and applying to addition and subtraction.

So our outcome for today is that you can use number facts to subtract multiples of 10 and to bridge a hundred.

So let's get on and see what's in our lesson today.

We've got two key words today and they are subtrahend and minuend.

I wonder if you can say those words.

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

Are you ready? So, my turn, subtrahend.

Your turn.

My turn, minuend.

You turn.

Excellent, so listen out for those words as we go through our lesson.

Let's find out what they mean though.

So the minuend is the first number in a subtraction, not always at the beginning, but it's the number that we start with, the number from which another number is to be subtracted.

And that number that we subtract is called the subtrahend.

So the minuend is the number we start with and the subtrahend is the number that we subtract from it.

So the minuend minus the subtrahend gives us our answer and we sometimes refer to that as the difference.

So for example, in eight subtract three equals five, eight is the minuend.

So as we said, the subtrahend is the number that is to be subtracted.

Sometimes it'll be the second number written down in a subtraction.

So the minuend minus the subtrahend gives us our answer, sometimes called the difference.

So in that example again, eight subtract three equals five, eight was our minuend.

Our subtrahend is three.

So look out for those words as we go through our lesson today.

So there are two parts to our lesson today.

In the first part of our lesson, we're going to use number facts to 20 to subtract multiples of 10.

And in the second part, we're going to be crossing the hundreds boundary bridging in tens.

So let's get into the first part of our lesson.

And we've got Izzy, Sofia, Jacob and Alex helping us in our lesson today.

Okay, so what number fact would help you to calculate 120 minus 30? So let's have a think.

Well, 120 minus 30 is the same as 12 tens minus three tens.

So, 12 minus three can help you to calculate 120 minus 30.

So I know that 12 minus three is equal to nine.

So, 12 tens minus three tens is equal to nine tens.

And you can see there we've got 12 tens altogether and three of them in a slightly paler colour there.

There are three tens that we are subtracting and that will leave us with nine tens.

So let's think about that in terms of our 120 subtract 30.

There goes our 30.

So, 120 minus 30 is equal to 90.

12 tens is equal to 120, three tens is equal to 30, nine tens is equal to 90.

So we can use the fact 12 minus three to help us calculate 120 minus 30.

This time we've got 150 minus 70.

So let's have a think about these sentences we're going to use.

Izzy says, "I know that 15 minus seven is equal to eight." So why is that helping us? Well, we know that 150 is the same as 15 tens, don't we? And 70 is the same as seven tens.

So, 15 minus seven and 15 tens minus seven tens are going to be quite closely linked.

So our second sentence says, "So 15 tens minus seven tens is equal to eight tens." So you can see here that we've got our 15 tens, so we're going to subtract seven of them and that leaves us with eight tens.

So 150, 15 tens is the same as 150, minus 70, seven tens is the same as 70, is equal to 80 and eight tens is equal to 80.

And Izzy says, "15 minus seven equals eight can help me to calculate 150 minus 70 equals 80." So, let's have a look here.

We've got a number fact that we know quite well, eight and four is equal to 12 or 12 minus four is equal to eight or 12 minus eight is equal to four.

Because we know that if we've got a part part whole model here represented in a bar model, if we know the whole in one part, we subtract that part to find the other part.

So how many different ways can you complete those stem sentences to help think about these bar models? So let's say the stem sentences together.

So let's look at the first bar model.

I know that 12 minus eight is equal to four.

We could have said 12 minus four is equal to eight, but we've gone with 12 minus eight is equal to four.

So let's think about those number of tens and let's see if we can apply that number fact to the numbers of tens.

So we can also say that 12 tens minus eight tens is equal to four tens.

So can we think about that with our multiples of 10? So, what will we be starting with this time? What will our minuend be? That number we start with.

So we're gonna have 120 minus 80 is equal to 40.

120 is our minuend.

And the number we are subtracting is 80 and that is our subtrahend.

So, 120 minus 80 equals 40.

We also know that 12 minus four is equal to eight.

So we can also say that 12 tens minus four tens is equal to eight tens and 120 minus 40 is equal to 80.

So what we're going to do here is match the number facts to the calculation it will help to solve.

But Izzy says, "How can addition facts help me with subtraction?" Ah.

Jacob says, "You can rearrange an addition fact to make subtraction facts." So let's have a look at that.

So, we've got eight plus five is equal to 13.

So if I know eight plus five is equal to 13, what else do I know? Well, I know that 13 subtract eight is equal to five and 13 subtract five is equal to eight.

We add the parts to find the whole, and then if we know the whole and one part, we can subtract the part we know to find the other part.

So our parts here are eight and five and our whole is 13.

So we can apply that thinking to our other addition facts to create subtraction facts.

So let's have a look at those.

So, there we go, we've created a pair of subtraction facts from each of our addition facts.

And Izzy says the sum in our addition becomes the minuend.

So let's have a think about that.

So the sum, eight plus five equals 13, 13 is the sum.

And then when we turn that into our subtraction facts, that sum of 13 becomes the minuend, the number we're starting with in our subtraction.

So here you can see those minuends are coming up in bold, that number we're starting with.

So 13, 14, 13 again and 14 become the minuends in our subtraction facts.

So Jacob says, "The addends become the subtrahend and the difference." So, eight plus five is equal to 13, eight and five are our addends, the numbers we're adding together, and we can see in our subtraction facts that each time one of those addends becomes the subtrahend, the number we're subtracting, and the other one becomes the answer, the difference.

So let's turn those subtrahends bold so we can see in the other calculations.

So the sum has become the minuend and one of our addends has become the subtrahend.

Izzy says, "Now I can match the number fact to the calculation." So let's have a look at 140 minus 50.

So, 140 minus 50, that's 140 is 14 tens and 50 is five tens.

So I'm looking for a 14 subtract five, there's our related fact.

So have a look at 130 subtract 40.

Can you think of the number of tens and think of the fact that's going to help us to solve that? So we've got 13 tens subtract four tens.

So there's our subtraction fact, 13 subtract four.

140 subtract 80 is 14 tens subtract eight tens, so we're looking for 14 subtract eight, and there it is.

And then 130 subtract 80, 13 tens subtract eight tens.

And there is our related fact.

And Jacob says, "You can think of the number of tens in the calculations," just as we did then.

So Izzy says, "13 tens subtract eight tens is equal to five tens." "14 tens subtract five tens is equal to nine tens," "13 tens subtract four tens is equal to nine tens," as well, and, "14 tens subtract eight tens is equal to six tens." So there we can see our completed calculations linked to the number fact that helped us to solve them.

So let's put this into a context.

A baker has made 160 buns, 70 buns have chocolate icing, the rest have vanilla icing.

How many have vanilla icing? And Izzy says, "Which pair of expressions represent the problem?" Hmm.

So we've got three pairs of expressions down here at the bottom of the screen.

We've got seven subtract 16, 70 subtract 160, we've got 16 subtract seven, and 160 subtract 70, and we've got 16 subtract 10, and 160 subtract a hundred.

So which pair is going to help us? So what do we know about this problem? Well, we know that there are 160 buns in total and 70 have chocolate icing.

So that's part of them, isn't it? So we need to work out the other part.

So we might have seen this before, that if we know the whole and one part, we can subtract the part from the whole and we can find the missing part.

Let's think about the language you've been using today.

So the number we're starting with is 160 buns, so that was our minuend.

And the number of buns we're going to sort of take away, 'cause we know about the 70 buns with chocolate icing is our subtrahend.

So we are going to be doing 160 subtract 70.

And the fact we can use to help us with that is 16 subtract seven, because we know that 160 is 16 tens and 70 is seven tens.

And Izzy says, "We can use those stem sentences," to help us.

Let's have a look.

She says, "I know that 16 minus seven is equal to nine." That's my known fact.

16 tens minus seven tens is equal to nine tens.

So, 160 minus 70 is equal to 90.

So, we've taken a problem now and we've thought about a fact that we can use to help us to solve that problem.

And as she says, "90 buns have vanilla icing." So, one for you to have a go at.

So this time we've got 130 tickets for the school play.

50 have been sold, how many have not been sold? So, which expressions represent the problem? And when you've decided, can you fill in those stem sentences? So pause the video, have a go, and then we'll have a look together.

Okay, so the ones that were gonna help us this time were 13 subtract five and 130 subtract 50 because we know that our whole is 130 tickets, so our minuend is 130.

And the part we know about are the 50 that have been sold.

So we're going to subtract those.

So that's our subtrahend.

And if we subtract the tickets that have been sold, we'll know how many have not been sold.

And 130 subtract 50 is 13 tens subtract five tens.

So the fact that's gonna help us is 13 subtract five.

So let's say those stem sentences together with our correct values in now.

So, I know that 13 minus five is equal to eight, 13 tens minus five tens is equal to eight tens, 130 minus 50 is equal to 80.

So, 80 tickets have not been sold.

Okay, so we've got some number lines here and Izzy's asking us what we notice about the number line.

Jacob says, "The top one counts in steps of one." Doesn't start at zero, does it? It starts at two, but it is counting in steps of one.

We can see two, three, four, five, and so on.

Izzy says, "The bottom line counts in steps of 10." Again, it doesn't start at zero, but we can see it going up 20, 30, 40, and so on, counting in steps of 10.

Jacob's gonna put 12 subtract three equals nine and show it on the number line.

So we're going to start at 12, and we're gonna subtract three ones and we're going to end up on nine.

But we've been looking at how we can use those facts to help us work with bigger numbers with multiples of 10.

So what could we relate that to to show on the other number line? Well, we could look at 120 subtract 30, 12 tens subtract three tens.

So this time our jump is not three ones but three tens.

And Izzy says, "12 tens subtract three tens is equal to nine tens.

120 subtract 30 is equal to 90." So we can see that because the top line is moving in ones, we've jumped three ones.

The bottom line is moving in steps of 10.

We've gone back three tens in our three steps.

So we can see how those facts are related on our number lines in ones and our number line counting in tens.

Ooh, now then, we've got a missing number here.

So we know that our minuend is 140, but we're missing our subtrahend here.

140 subtract something is equal to 90.

And Izzy's saying, "What number fact can I use to calculate that?" So, 140 is the same as 14 tens and 90 is the same as nine tens.

So we can think about using the fact 14 subtract something is equal to nine.

So let's have a look at those numbers.

So we've got 14 and we know we're going back to nine.

So how many steps back are we taking? We're taking a step of five because we might know that nine plus five is equal to 14, and then we can rearrange our addition fact to make that subtraction fact.

14 subtract five is equal to nine.

So can we use that to help us with 140 subtract something is equal to 90? I think we can, can't we? So if we look at those steps of 10 this time, so we've got our 140 and we're jumping back to 90.

So we're still taking five steps, but we're taking five steps of 10 this time.

So we've subtracted five tens and five tens is equal to 50.

So, 140 subtract 50 is equal to 90.

And there are our stem sentences but written as equations.

So let's say those together.

14 subtract five is equal to nine, 14 tens subtract five tens is equal to nine tens and 140 subtract 50 is equal to 90.

And there was our fact that we used.

14 subtract five equals nine helped us to work out what our missing number was.

Time for you to have a go.

So, if you know that 15 subtract six is equal to nine, what is 150 subtract 60? And we've got the number lines there to help you.

So pause the video and work out the answer to 150 subtract 60 and then we'll have a look together.

So, how did you get on? So we know that 15 subtract six is equal to nine, and we're going to think about how we're going to do 150 subtract 60.

So Jacob says, "I know that 15 tens subtract six tens is equal to nine tens, so 150 subtract 60 must be equal to 90." So instead of a jump of six steps of one on our number line, we're making a jump of six steps of 10.

So we're subtracting 60, six tens, and 150 subtract 60 is equal to 90 because we know that 15 tens is equal to 150, six tens is equal to 60, and nine tens is equal to 90.

Okay, time for you to do some practise.

So first task, you're going to use the number lines to create your own subtraction calculations and record them in the table.

So, we've got our known number factor 20, and then our related multiple of 10 fact.

So I've given you an example there, 15 subtract six is equal to nine, 150 subtract 60 is equal to 90.

So, create some subtractions on the number lines and then record them in the table.

And for the second part, you're going to complete some missing numbers.

And we've got some bar models and some part part whole models here.

Thinking about those parts and wholes and thinking about what those missing numbers are and can we use those related facts to help us.

So pause the video, and then we'll have a look at the answers together.

So I wonder which facts you chose for task one.

There's a few in here that I had to go at.

So I looked at 14 subtract five equals nine and related it to 140 subtract 50 is equal to 90.

And then the one at the bottom I chose was 11 minus five is equal to six.

And I know if 11 minus five is equal to six, then 11 tens minus five tens is equal to six tens.

11 tens are 110, five tens are 50, so, 11 tens, 110, minus five tens, 50, must equal six tens, which is 60.

So, 110 subtract 50 is equal to 60.

I wonder which facts you used.

And then we had to complete the missing numbers.

So, A is a bar model.

So our whole is 13 tens, one of our parts is 70.

Ooh, that's interesting, 13 tens.

So I can either decide to say 13 tens is a multiple of 10, or thinking that we're using our number facts, maybe I'll turn the 70 into a number of tens.

Well I know that 70 is the same as seven tens.

So I can say that 13 tens is made up from seven tens and six tens because I know that six plus seven is equal to 13.

So my missing part is six tens or 60.

How did you get on with the others? So B, 20 subtract 60 is equal to.

Well, we might have known that it was, there's something about a half there.

Two lots of 60 are equal to 120, or we might have known that 12 subtract six is equal to six.

So, 12 tens subtract six tens is equal to six tens.

So, our missing number is 60.

So for C, we can use that bar model again, can't we? 'Cause our 13 tens is equal to 130, and if one part is 70, the other part must be 60.

So, 130 subtract 60 is equal to 70.

D has got things the other way round, hasn't it? So this time our minuend, the number we're starting with, is not the first number in the calculation, it's that number after the equal sign.

So, 80 is equal to 140 subtract something.

Ooh, 80 is equal to 140 subtract something.

So, eight tens is equal to 14 tens subtract something.

So, 14 subtract what is equal to eight? Well, it's six, isn't it? So, 14 subtract six is equal to eight.

So, 140 subtract 60 is equal to 80.

And we can write that the other way around, 80 is equal to 140 subtract 60.

For E, we've got a part part whole model.

Our whole is 150, one of the parts is 90.

So I could think of 15 subtract 9, 15 tens subtract nine tens, and I know that my missing part is six tens, which is 60.

And F, there's something a bit similar here, isn't there? 150 is my whole, nine tens is one part.

So let's have a look at that part part whole model.

If nine tens is one part and 150 is the whole, then our other part must be six tens.

Did you notice that all of the calculations had 60 or six tens as the subtrahend or the answer? So we were using 60 quite a lot in there in facts relating to 60.

You've worked really hard in the first part of the lesson.

So now we're going to move on and we're going to think about crossing the hundreds boundary by bridging in tens.

So, can we go two on 100 and then back again? So we're going to be doing some partitioning.

Let's have a look.

So, we can use 12 subtract three equals nine to calculate 120 subtract 30, or we could partition the 30 and bridge through 100.

Hmm, let's have a look at how that would work.

So Jacob says, "Well, where is the subtrahend of 30 in the base 10 blocks?" We've got 120 subtract 30, so our minuend is 120.

Our subtrahend, the number we're subtracting is 30.

Where is that 30 in our base 10 blocks? There it is, isn't it? And we can actually see that that 30 bridges part of the hundred and the 20 there as well, doesn't it? So what we can do is take our subtrahend of 30 and we can partition it to help us to bridge through 100.

So we're gonna partition the subtrahend of 30 into 20 and 10 to bridge through 100.

So there it is.

So there was our 30 and we've partitioned it into 20 and 10.

120 subtract 20 is equal to a hundred.

I can use place value to work that out.

If I take away the value of the tens, I'm left with my hundred.

And there they are, they've gone.

So I'm left with a hundred.

And a hundred subtract 10 is equal to 90.

And there it goes.

So, I can bridge through 100 to work out that 120 subtract 30 is equal to 90.

And we can represent this, bridging a hundred, using a part part whole model.

So there's our 120 subtract 30.

So let's put a part part whole model in and see how that's going to work.

So there it is.

And Jacob says we're partitioning the subtrahend 30, the number we are subtracting, we're partitioning the subtrahend into 20 and 10.

And we're partitioning it into 20 and 10 so that we can easily take away the 20 from the 120 to bridge through 100.

120 subtract 20 is equal to 100.

And then 100 subtract the other 10 is equal to 90.

So we know that 120 subtract 30 is equal to 90.

Okay, so I've still got the subtrahend of 50, I'm doing 140 subtract 50 this time.

So my subtrahend is still 50.

But my question is has it been partitioned in the best way to solve 140 subtract 50? 'Cause we're thinking about the idea of bridging through a hundred, subtracting to get to a hundred and then subtracting the rest.

So, is that the best way to partition 50 for this particular calculation? Jacob says, "To bridge a hundred, it would be better to partition 50 into 40 and 10 because 140 subtract 40 is equal to 100." So we need to think quite carefully about how we partition our subtrahend so that we can bridge through a hundred.

So there we go, we changed our partitioning.

So now we can see that 140 subtract 40 is equal to 100 using our place value knowledge, and we've still got that extra 10 to subtract and 100 subtract 10 is equal to 90.

So, 140 subtract 50 is equal to 90.

Okay, time for you to have a think.

So, which is the best way to partition the subtrahend to solve 140 subtract 60? And we want to bridge through 100.

So you've got three options there.

So which one do you think is the best way to partition 60 so that we can bridge through 100? So pause the video, have a think, and then we'll look at it together.

Did you agree that B was the best way? They are all good ways to partition 60, but for this particular calculation, B is best, as 140 subtract 40 allows you to bridge 100.

Okay, so we can think about this using a number line as well.

So we've got 120 subtract 30.

So we've looked at this already, haven't we? And we know that we can partition the subtrahend into 20 and 10 and that will allow us to bridge through 100.

So, 120 subtract 20 is equal to 100.

And because I've partitioned into 20 and 10, I've got another 10 to subtract.

A hundred subtract 10 is equal to 90.

We know that 120 subtract 30 is equal to 90.

Okay, so we can represent this on the number line again, this time we've got 120 subtract 50.

So what are we going to partition our 50 into so that we can bridge 100? Jacob says, "Partition the subtrahend 50 into 20 and 30." And he's chosen that because then we can subtract the 20 from the 120 and bridge through 100.

So, we're going to do 120 subtract 20 to get us to our 100 and then we still need to subtract another 30 'cause this time we partitioned our 50 into 20 and 30.

So, 100 subtract 30 is equal to 70.

So altogether we've subtracted 50.

120 subtract 50 is equal to 70.

Time for you to have a look.

So which number line shows bridging through a hundred to solve 140 subtract 60? Pause the video and then we'll have a look together.

Did you agree that it was A? A shows that 60 was partitioned into 40 and 20 so that we could subtract the 40 from 140 to bridge through 100.

Okay, time for you to have some practise.

So, we'd like you to record how you would partition the subtrahend in the part part whole model and record the steps of the calculation filling in the blanks underneath.

So you've got two to have a go at.

A is 160 subtract 70, and then fill in the missing parts of the calculations underneath.

And then B is 150 subtract 80.

So think about how you would partition the subtrahend 80 and then fill in the missing gaps in the calculations underneath.

And for the second part of your task, you need to match which partitioned subtrahend would help you to bridge 100 in each equation.

And draw lines to match them.

And then part B of this is to say what's the answer to each equation and what do you notice about the equations? So pause the video, have a go at your tasks, and then we'll have a look at them together.

So, how did you get on? So in the first part in A, we had to work out how to partition the subtrahend of 70 to do 160 subtract 70.

It makes sense to partition our 70 into 60 and 10 so that we can subtract the 60 from the 160 to allow us to bridge through 100.

So those calculations underneath will show 160 subtract 70 is equal to 90 because 160 subtract 60 is equal to a hundred, and 100 subtract 10 is equal to 90.

Part B asked us to solve 150 subtract 80, and we can see that the best way to partition it is to partition the 80 into 50 and 30 so that we can subtract the 50 from the 150 to bridge through 100.

So, 150 subtract 80 is equal to 70, and that's because 150 subtract 50 is equal to a hundred, and 100 subtract 30 is equal to 70.

So in our second question, we asked you which partitioned subtrahend would help you to bridge a hundred in each equation.

So let's have a look at 150 subtract 60, which is equal to 90.

So, which of those ways of partitioning 60 would help here? Well, the top two are 10 plus 50 and 50 plus 10.

We sort of could choose either one, but let's go for the 50 plus 10 because it's that 50 we're interested in first to subtract from the 150 to give us an answer of a hundred so that we can bridge through a hundred.

So, for 140 subtract 60, we're looking to partition our subtrahend so that it gives us a 40 to subtract.

So, 60 can be partitioned into 40 and 20 in order to help us to bridge through 100.

Then we've got 130 subtract 60.

So, how can we partition our 60 this time? So, we need a 30 to subtract.

So I think this time we want to partition our 60, our subtrahend, into 30 plus 30.

The next one is 120 subtract 60.

So, we're looking to get to a hundred.

So, 20 would be useful, wouldn't it? So we can partition the subtrahend 60 into 20 plus 40, which is very similar to 40 plus 20, but we kind of want to use the 20 first, but 40 and 20, 20 and 40 is going to allow us to do that, bridging through a hundred.

And finally, 110 subtract 60.

So again, we want to be able to subtract a 10.

So this time we want our 60 to be partitioned into 10 and 50, very similar to 50 and 10, but we want that 10 available first in a way to subtract from our 110.

So, B asked you what you noticed.

So you might have noticed that one of the parts of the subtrahend when we partition it, one of those parts is always the same as the number of tens in the minuend.

So for example, 150 subtract 60, we partitioned the subtrahend 60 into 50 and 10.

You might also have spotted a pattern somewhere between the minuend and our answers.

So we were always subtracting 60, our subtrahend was always the same as 60, but we started with 150 subtract 60, and that was 90.

Then we decreased our minuend by 10, so, 150 became 140.

And what happened to our answer? And that also decreased by 10.

So you might have noticed that as the minuend decreased by 10, so did the answer.

Or other way up, as the minuend increases by 10, the answer also increases by 10.

So we've come to the end of our lesson today on bridging a hundred by subtracting in multiples of 10.

So what have we learned about? Well, we've learned that place value representations and number lines can help us to represent the subtraction equations.

We've also seen that number facts to 20 can help to subtract multiples of 10 that cross the hundred boundary.

So we took those number facts to 10, turned them into subtraction facts to help us.

And we've also seen that a part part whole model helped us to visualise partitioning the subtrahend to bridge 100.

Thank you for your hard work today and I hope I'll get to work with you again soon.

Bye.