Lesson video

Hello there.

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

I'm sure you're going to enjoy it.

And here is our lesson outcome.

I can subtract through 10 using bridging.

And here are the key words for today's lesson.

So the key words are minuend.

Can you say minuend? Well done.

Subtrahend.

Can you say subtrahend? Excellent.

Bridge.

Can you say the word bridge? And our final word is partition.

Can you say the word partition? Excellent.

And let's take a look at what those words mean.

So the minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

So in our calculation, the minuend is seven and the subtrahend is three.

Seven subtract three equals four.

Bridge means subtracting to make 10, and then subtracting whatever is left.

And partition means splitting a number into smaller parts.

And here's our lesson outline, so two parts to today's lesson.

The first part is subtracting by bridging through 10, and the second part is solving subtraction problems by bridging 10.

Let's get started.

In this lesson, you'll meet Izzy and Alex.

They're going to ask you some questions and help you with the work today.

Let's start with a problem.

There are 12 slices of pizza.

"I'm going to eat four slices," says Alex.

How many slices will be left after Alex eats four of them? How would you work it out? Well, our calculation would be 12 subtract four.

Now, you can partition the four to bridge 10.

You can subtract two to make 10.

So we count back to get to 10.

So 12 subtract two equals 10.

You can then subtract another two.

So another way of working out the answer to the subtraction calculation of 12 subtract four is 12 subtract two, subtract two.

It's an easier way of working out the answer.

You can show this using a 10s frame and a number line.

So 12 subtract four equals 12 subtract two, subtract two.

Let's use a 10s frame to help us work out the answer.

So you can see there the four is a different colour, the four is in red, but we can subtract the two, that gets us back to 10 and then subtract two more, and that would give us our answer, eight.

We could also use a number line to help us work out the answer.

So let's start with 12 subtract two, that gets us to 10, subtract two more, so our answer would be eight.

12 subtract four equals eight, but it's all about bridging through that 10, all about counting back to the 10 and then counting back whatever else is left.

Let's try a different problem.

This time there were 14 slices of pizza.

"I'm going to eat six slices," says Izzy.

She's obviously a bit peckish, Izzy.

So this time the calculation is 14 subtract six.

We're starting with 14 and we're subtracting six.

So how could you partition six to bridge 10? We could work out the answer by doing the calculation like this.

14 subtract four, subtract two.

We're still subtracting six, but we've broken that six up.

We partition the six into four and two.

You can show this using a 10s frame and a number line.

So again, the calculation is 14 subtract six, which is the same as which is equal to 14 subtract four, subtract two.

Let's represent the problem using a 10s frame.

So we've got 14 counters.

Let's subtract four to get us back to 10, so bridging through that 10, and then we have to subtract two more.

So all together we have subtracted six, we partitioned that six into four and two.

We can also represent the problem on a number line.

So again, start from 14, count back four, subtract four gets us to 10, and subtract two more.

That gets our answer, eight.

So 14 subtract six equals eight.

Now it's your turn to have a go at a problem.

There are 16 slices of pizza.

"I'm going to eat seven slices," says Alex.

So what is the best way to partition seven to bridge 10? So in all those calculations, we're subtracting seven, but which is the best way to subtract seven so you're bridging through 10? Pause the video and have a think about it.

Okay, welcome back.

Did you manage to find the answer? What do you think it is? Now remember, it's all about counting back to 10.

So which of those calculations would get us to 10 and help us bridge through 10? Well it would be 16 subtract six, subtract one.

That is the correct answer because 16 subtract six equals 10.

The easiest way to calculate that answer.

So we can represent that problem using a 10s frame and a number line to bridge 10.

So our calculation number is 16 subtract seven, and we thought about already what the most efficient way of bridging through 10 would be.

How are you going to bridge through the 10? How would you use a 10s frame to help you work out the answer? How could you use a number line to help you work out the answer? Could you have a go at using both? So now would be a good time to pause the video and have a go trying to calculate the answer either using a 10s frame or a number line or both.

Okay, welcome back.

Let's see how you got on.

Did you manage to get the right answer? Did you have a go at using both strategies for working out the answer? Let's have a look.

So 16 subtract seven, we've already said is the same as 16 subtract six, subtract one.

So in our 10s frame, we could subtract the six and then subtract one more.

And that leaves us with nine, nine counters, or nine slices of pizza.

Remember, the counters are representing slice of the pizza.

Instead, we could use the number line.

So we could start from 16 and jump back six all the way to 10.

Then we just have to jump back one more to nine.

So 16 subtract seven equals nine.

Well done if you've got the right answer, and well done if you used one of those strategies for working it out.

Let's look at a different problem.

This time there are 13 cherries.

Four cherries get eaten.

How many cherries are left? What calculation would give you the answer? The calculation would be 13 subtract four.

What is 13 subtract four? How will you partition four? How are you going to break up that four to make it easier to bridge through that 10? How will you count back to 10? So Izzy says, "I think we should partition four into three and one." So let's subtract three first of all.

So 13 subtract three gets us to 10, and then we subtract one more.

"There are nine cherries left in the bowl," says Alex.

How would you use partitioning to bridge 10? So the calculation is 13 subtract five.

What would that equal? How would you bridge through the 10? What would you subtract from 13 to get back to 10? Izzy says, "Partition five into three and two, subtract three, then subtract two." Let's use a 10s frame to help us represent that problem.

So first of all, we calculate 13 subtract three.

That gives us our answer, 10.

Then 10 subtract two would equal eight.

So all together, we have subtracted five, so the answer would be eight.

How would you do 11 subtract five? What would you subtract from 11 to get to 10? Alex says, "Partition five into one and four, subtract one, then subtract four." Let's use 10s frames to help us represent the problem.

So first of all, we're going to do 11 subtract one.

That gets us to 10.

Then we just have to subtract four.

10 subtract four equals six.

So all together, five has been subtracted and that gets us our answer, six.

And here's a couple of problems for you to do on your own.

Use partitioning to bridge 10.

So there are two problems on the board and you may want to get some 10s frames and counters to help you work out the answers.

The first calculation is 12 subtract five.

Think very carefully about how you're going to partition that five.

And the second problem is 14 subtract five.

Subtracting five both times, we begin to break apart that five in different ways.

Izzy is saying, "Remember to count back to 10." What do you have to subtract to count back to 10? So pause the video and have a go at those two problems. And welcome back.

Did you manage to solve both of them? Do you think you got the right answer? Let's have a look.

So our first calculation was 12 subtract five.

Hopefully, you did 12 subtract two first of all.

That equals 10.

We take away the two first and then do 10 subtract three.

That equals seven.

So we subtract the three and that gets us our answer, seven.

So all together, we have subtracted five, and the answer is seven.

The other calculation, what would you subtract first of all? Hopefully, you did 14 subtract four.

Gets us back to 10, we subtract the four first of all.

And then how much more do you have to subtract so you subtracted five altogether? Subtracted four already.

Just have to subtract one more.

So 10 subtract one equals nine.

Take away one more, and that gets us our answer, nine.

Very well done if you managed to answer both of those calculations correctly.

And let's move on to our task.

So part one of task A, complete the calculations by partitioning the subtrahend.

The subtrahend, remember, is the number you are subtracting.

You can use a 10s frame to help you.

Or if you'd prefer, you can use a number line instead.

That first one, 12 subtract six, some of the counters are coloured and the six is already broken up into two and four to help you subtract numbers.

And then part two looks like this.

Izzy has these number cards.

She chooses two cards each time.

We got there the number cards from one to nine.

Izzy says, "I'm going to find different ways to make this calculation correct." And the calculation is 13 subtract a number equals another number.

Which ways can you find to make that correct? And again, you can use a 10s frame to help you.

So pause the video and have a go at those two tasks.

And welcome back.

I hope you managed to get on really well.

Let's have a look.

Let's see if you managed to get some of those calculations correct.

So first of all, here are the answers to the first part of task A.

So you can see there the answers.

So 12 subtract six equals six, 11 subtract six equals five, and 15 subtract six equals nine.

But remember, the important bit is how you break apart that six, so how do you count back to get the 10? And here are the answers for part two of task A.

So you may have come up with some of the answers there.

So you could have done 13 subtract four equals nine.

You could have done 13 subtract five equals eight.

You could have done the reverses of those.

You might have done 13 subtract eight equals five, or 13 subtract nine equals four.

So well done if you came up with lots and lots of different answers for part two.

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

So the second part of the lesson is solving subtraction problems by bridging 10.

There are 15 cherries in a bowl.

Izzy eats some.

"There are now seven cherries left in the bowl," says Izzy.

So she's eaten some and there are seven cherries left.

How many cherries did Izzy eat? How could you calculate the answer? 15 subtract what number equals seven? How many cherries did Izzy eat? So we're looking for the missing number, aren't we? What do you subtract from 15 to get to seven? Count back from 15 to seven.

"Use a number line to work out the subtrahend," says Izzy.

So we're gonna start from 15, and we're going to count back to get to seven, and then we're gonna work out what we've counted back.

How would you bridge 10? What would you subtract from 15 to get to 10? 15 subtract five equals 10.

10 subtract three equals seven.

How much have you counted back altogether? What have we subtracted altogether? Subtracted five and we subtracted three.

How much is that altogether? Eight.

Five out of three equals eight.

We subtracted five, then three more.

All together, we have subtracted eight.

"I ate eight cherries," says Izzy.

There are 14 slices of pizza.

Alex eats some.

Now there are only six slices left.

Goodness, Alex was hungry, wasn't he? How many slices did Alex eat? How could you calculate the answer? Well, the calculation would be 14 subtract something equals six, and we're going to be looking for that missing number.

So 14 subtract what number equals six? Use a number line to work out the subtrahend.

Remember, the subtrahend is the number we're subtracting.

So remember, we've got to bridge 10, haven't we? We started on 14 and we're going to bridge through that 10.

What would we have to subtract from 14 to get back to 10? The answer would be four.

We take away four, that gets us to 10, then we've still gotta take away something else to get us to six.

So 10 subtract what number would equal six? It would be another four.

So we subtracted four, and then another four.

How much has been subtracted altogether? How many slices did Alex eat? Alex ate eight slices of pizza.

14 subtract eight equals six.

And here's one for you to try on your own.

So the calculation is 15 subtract a number equals six.

You've got to work out that missing number.

How would you work out the subtrahend? What is the missing subtrahend? Now, you may want to use a number line to help you work out the answer or you can use 10s frames instead.

So pause the video and have a go trying to work out the missing number.

What is the missing subtrahend? Welcome back.

Did you manage to find the answer? Let's have a look and see whether you were right.

So we start with 15.

We've got to subtract to get to 10.

So what number do you subtract from 15 to equal 10? 15 subtract five equals 10.

So we've counted back to 10, then we have to count back to six.

Again, use number pairs that total 10 to help you.

So you probably know that six out four equals 10, so 10 take away four must equal six.

What is the subtrahend? What is the number that has been subtracted? We subtracted five then we subtracted four.

Five out of four equals what number? Nine, so the missing number was nine.

15 subtract nine equals six.

Very well done if you managed to get the right answer.

There are some cherries in a bowl.

Izzy eats seven.

There are now six cherries left in the bowl.

How many cherries were in the bowl before Izzy ate some? How would you calculate the answer? So this time we don't know how many cherries we started with.

We don't know how many cherries were in the bowl before Izzy ate some.

So how would you calculate the answer? This time, it's the minuend that's missing is the number we're starting with.

We've got a missing number at the beginning.

We subtract seven and that equals six.

How would you work out the answer? Izzy says, "If you add the difference and the subtrahend, you get the minuend." So remember, the difference in this calculation is six.

The subtrahend is seven and the missing number is the minuend.

And Izzy's saying, "If you add the difference and the subtrahend together, you get the minuend." If you add six and seven together, you'll get the minuend.

So what we can do is start with six and add seven back on.

So even though it's a subtraction problem, we can use addition to solve it, because addition and subtraction are inverses.

So bridge 10 by adding four, then adding three.

Six add four equals 10, again, we can use number pairs that total 10 to help us work out the answer, and then add three more.

We've added seven all together, but we partition seven into four and three to make it easier to bridge through that 10.

How many cherries were in the bowl to start with? The answer is 13.

There are some slices of pizza.

Alex eats seven slices.

There are nine slices of pizza left.

How many slices of pizza were there to start with? This is a problem for you to solve on your own.

You may want to use a number line to help you work out the answer, but pause the video, and see if you can find the right answer.

Welcome back.

Let's see how you got on.

Let's see if you got the right answer.

So we're looking for the missing minuend.

We take away the subtrahend and we're left with a difference.

Remember what Izzy said, though.

Izzy said, "If you add together the difference in the subtrahend, you get the minuend." So if we add together nine, the difference, and the subtrahend, seven, we'll get the right answer.

So let's start with nine, add on one to get to 10, so it's all about bridging through that 10, remember.

And then we have to add on six more because seven is made out of one and six.

Add on six more, that gets us our answer, 16.

Nine out of seven equals 16.

So that means 16 subtract seven must equal nine, so there must have been 16 slices of pizza to start with.

And let's get started on task B.

This is part one of task B.

You gotta find the missing numbers.

Use a 10s frame or number line to help you.

So with those problems there, you might have a difference missing, or a subtrahend missing, or a minuend missing.

So think carefully about whether you're going to use subtraction to bridge through 10, or whether you can use an addition strategy, whether you need to add the numbers together to get the minuend.

And here is part two.

So Alex chooses two number cards each time.

So we've got the number cards six, seven, eight, nine, 15, 16, and 17.

Alex says, "I'm going to find different ways to make these calculations correct." Which ways can you find? You may use a 10s frame or number line to help you.

So pause the video and have a go at those two tasks, and very best of luck.

And welcome back.

I hope you worked hard.

Did you manage to get onto the second part of task B? Did you? Very well done if you did.

Let's look at the answers.

So here are the answers for part one.

You had to find the missing numbers.

I hope you thought really carefully about how to partition the subtrahend to count back through that 10s number.

And here are the answers for part two, so your answers may have included some of these.

So you may have started with 17.

You could have done 17 subtract nine, that would equal eight.

That was one of the numbers we were targeting.

You could have done 17 subtract eight equals nine.

You could have started with 16 and done 16 subtract nine equals seven.

You could have started with 15 and done 15 subtract nine equals six.

Very well done if you came up with some of those solutions for that problem.

And well done for working so hard in today's lesson, and I hope you're getting really confident at subtracting by bridging through 10.

Very, very well done indeed.

And here is our lesson summary.

So partition the subtrahend to help you bridge through 10.

So subtract back to 10 first and then subtract whatever is left, and use number pairs that total 10 to help you.

Excellent work today.

I look forward to seeing you again soon.