Lesson video

Hello, my name is Mr. Goldie and welcome to today's math lesson.

I'm sure you're going to have lots of fun, and our lesson outcome is, "I can subtract numbers using efficient strategies", and here are our key words, so three keywords today.

The first keyword is minuend.

Can you say that? Minuend? Let's hear you.

Fantastic.

The next keyword is subtrahend.

Can you say that? Subtrahend.

Let's hear you.

Very well done.

And the last word, bit of an easier one this one is difference Can you say the word difference? So the minuend is the number being subtracted from.

Can you see the calculation? It says seven subtract three equals four.

The minuend is seven.

That's the number we're subtracting from.

The subtrahend is a number subtracted from another, so the subtrahend, in that calculation, is three.

Three is being subtracted from seven.

And lastly, the difference is the result after subtracting one number from the other.

Difference is four.

Seven subtract three equals four.

And our lesson outline for today, the first part of today's lesson is all about strategies for subtracting small numbers, and the second part of today's lesson is subtracting numbers that are close together and far apart.

So let's start off with our first part of the lesson.

In this lesson today, you will meet Izzy and Alex and they're going to be helping you today and asking you some questions as well.

So let's start off with a problem.

In our first problem, there are eight cakes.

There's our eight cakes.

Four of the cakes get eaten.

How many cakes are left? And Alex is saying, "I'm going to calculate the answer." So our calculation would be eight subtract four.

What would eight subtract four equal? Alex is saying, "I'm going to represent the problem using a tens frame." So we've got eight cakes altogether in our tens frame, and we're going to take away four.

We're going to subtract four of those cakes.

There we go, so four of the cakes have gone.

So Izzy is telling us, "You can also use doubles.

I know that four add four equals eight." So sometimes you might have some addition number facts you can use to help you with subtraction, because subtraction and addition are inverses of each other.

They're the opposite calculation to each other.

And then we've got a bar model.

So a bar model with a sum being eight at the top and our different addends or subtrahends being four.

Eight is made out of four and four.

Four add four equals eight.

Eight subtract four equals four.

For the answer to our calculation, eight subtract four would be four.

You can use addition facts to help you subtract.

So Izzy's saying, "I know that three add three equals six.

I can use that to work out six subtract three." There we have six cakes.

Izzy's saying three and three equals six, so she could use that to help her work out what six subtract three would be.

Well if six is made out of three and three and we take away one of those threes, we subtract one of those threes, what would we be left with? Three.

Six subtract three equals three.

Alex is saying, "Two add two equals four.

What is four subtract two?" Again, let's use a tens frame with four cakes in it.

Alex is saying, "Two add two equals four, so what is four subtract two?" Well if four is made out of two and two, and we subtract one of those twos, those two cakes get eaten.

How many cakes are left? Just two.

Four subtract two equals two.

So sometimes you can use addition facts to help you subtract.

Use a doubles number fact to solve this.

So the calculation is ten subtract five.

What doubles number fact could you use to help you work out the answer? Pause the video.

Think about the doubles number fact you could use, and see if you can work out the right answer.

Welcome back.

Let's see how you got on.

So the doubles number fact you should have used is five, add five equals ten.

So five add five equals ten.

Ten subtract five must be five.

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

Here's Izzy.

Izzy's saying, "Six add six equals twelve.

What is twelve subtract six?" Can you work out what the answer would be? Well the answer would be six.

Twelve subtract six equals six.

You can also use near doubles to help you work out subtraction calculations too.

So here's Izzy, and Izzy's saying, "I know that three add four equals seven." So Izzy knows three add three equals six, so three add four must equal seven.

"I can use that to work out what seven subtract three is." So three add four equals seven.

What is seven takeaway three.

You can use the bar model to help you work out the answer.

I wonder what the answer would be.

So seven subtract three equals four.

Alex says, "Five add four equals nine." So Alex knows that four add four equals eight, so five add four must equal nine.

"So what is nine subtract five?" And again, here's a bar model to help us work out the answer.

So five add four equals nine, what would nine subtract five be? What's the other part of nine? So nine subtract five equals four.

Use a near doubles number fact to solve this.

So we've got the sum there, eleven.

We've got one of the parts, a six.

Izzy says, "Five add six equals eleven.

What is eleven subtract six?" So again, pause the video, see if you can work out the answer.

Welcome back.

Did you get the answer? Let's have a look to see if you were right.

So the missing part was five.

Eleven subtract six equals five.

Very well done if you got the right answer.

In our next problem there are ten cakes.

Four get eaten.

How many cakes are left? And Izzy's saying, "I'm going to calculate the answer." So calculate ten subtract four.

Izzy says, "I'm going to represent the problem using a tens frame." So here's our tens frame, put 10 cakes in it.

Alex says, "You can use number pairs that total ten." And Alex says, "I know that four add six equals ten." So remember we're trying to calculate ten subtract four Four add six equals ten.

Does that help us work out the answer? And Alex says as well, "I can use a bar model to represent this." There's our bar model with our sum at the top, ten, and one of the parts is four.

What would ten subtract four be? What's the other part? Six add four equals ten.

Ten subtract four must be six, so we take away four cakes, and we're left with six cakes.

The difference between ten and four is six.

Calculate the missing numbers using number pairs to ten.

How do you work out the answer? Alex says, "Seven add three equals ten, so what is ten subtract three?" What would the answer be? Three add seven equals 10, so ten subtract three must be seven.

Let's look at our other bar model.

Izzy's got a helpful bit of information for us as well and she says, "Eight add two equals ten.

What is ten subtract two?" Remember ten is made out of eight and two.

If we subtract the two, what are we going to be left with? Eight and two equals ten.

Ten subtract two must be eight, so our difference between ten and two is eight.

Calculate the missing numbers.

So have a good look at the three bar models and see if you can work out the missing number and think about how you would calculate what that number is.

Don't forget to use subtraction strategies to help you find the answer.

So Alex is saying, "Think about which number facts you would use." And here's Izzy, and Izzy is saying, "You could use doubles, near doubles, or number pairs to ten." So pause the video and have a think about which strategy you would use to work out the missing numbers.

And welcome back and let's see how you got on.

So in our first bar model we've got ten as the minuend.

That's the number we're starting with, and we're going to be subtracting one.

What is ten subtract one? We can use number pairs to ten to work out the answer.

Of course the answer must be nine.

We know that nine add one makes ten.

Ten subtract one must equal nine.

Let's look at our next bar model.

For our next bar model eight is the minuend.

That's the number we're starting with and we're subtracting four.

That's going to be the subtrahend, and looking for the difference, remember, looking for the difference between eight and four.

How do we calculate that though? Eight subtract four.

Well you might remember that four add four equals eight, so actually the difference is quite easy to calculate, the difference must be four.

Eight subtract four must equal four.

And then our last one, the minuend, the number we're starting with, is seven.

Our subtrahend is four, we're subtracting four.

What's the difference going to be? Because a near double you might know that three add three equals six, and you might know that three add four equals seven, so seven subtract four must be three.

The answer is three.

Well done If you managed to find some of those missing numbers, and very well done if you managed to solve all three.

You can also subtract more than one number.

So Alex is looking at this calculation here.

Nine subtract two subtract one equals something.

And Alex is saying, "There are two subtrahends." So we're taking away, we're subtracting a two, and we're also subtracting a one.

Now you could represent this on a number line and a bar model.

Here's Izzy.

Izzy's saying, "Subtract two, then subtract one." Let's start with nine and subtract two.

That gets us to seven.

Then subtract another one, and that would make the answer six.

So in our bar model the missing number is six.

Six add two add one equals nine.

Nine subtract two, subtract one equals six.

It doesn't matter which order you subtract the subtrahends.

So Alex is saying, "I'm going to subtract three first." The calculation actually says seven subtract two, subtract three, but we could subtract the three first, and then subtract the two.

It doesn't actually make any difference.

And again, we can represent this on a number line and a bar model.

So on our number line we're going to start on the seven.

We're going to subtract the three first of all to get to four, and then subtract the two to get to two.

So our missing number on the bar model is two.

Seven subtract two subtract three equals two, and that is the same as seven subtract three subtract two equals two.

Izzy says, "You can add the subtrahends before subtracting them from the minuend." So Izzy's got this calculation here.

Eight subtract three subtract one.

She's trying to work out the answer.

Izzy says, "I'm going to use a bar model." There we've got our minuend at the top.

Our minuend is eight and we're subtracting three, and we're subtracting one.

We could do eight, then subtract three, then subtract one, but instead we could add three and one together.

So, "First I add together three and one." So Izzy's going to work out the total that she's subtracting altogether.

So she's going to add those two together.

Three and one equals four.

And then Izzy says, "I'm going to calculate eight subtract four." Izzy's going to use a number line to help work that out.

Eight count back four, eight takeaway four is four.

You might have remembered doubles there.

Four add four equals eight.

Eight subtract four must be four, so our answer is four.

How could you calculate the answer? So the calculation is seven subtract one subtract four.

Have a think about how you could work out what the answer is.

Can you find more than one way of doing it? Think about what Izzy has just been talking about just a moment ago.

So pause the video, see if you could work out the answer, but more importantly, think about how you found the answer, and can you find more than one strategy? And welcome back.

Let's see how you got on.

So Alex says, "You could subtract four, then subtract one." Remember we can change around those subtrahends.

We can subtract them in any order.

It still gives us the same difference, still gives the same answer.

So we're gonna start from seven.

We're going to subtract four and that gets us to three, and then we're going to subtract one.

Three subtract one equals two.

Izzy says you could instead, "Add four and one together, and then subtract five." Four and one equals five, so we could subtract the five all at once.

So here's a bar model to help us understand what we're doing, and we've got our two subtrahends, four and one, gonna put those together, gonna add those together to get five, and now we're calculating seven subtract five.

Could use a number line to help us work out the answer.

Start on seven, count back five, this time all at once, and that gets us to the answer, two.

Seven subtract five equals two, so the answer is two.

Well done If you manage to solve that problem using one of those methods, and very well done if you came up with both and you remember both ways of doing it.

And here's our task.

You're going to be finding the answers to these calculations.

Now you may use a tens frame or number line to help you work out the answer and think about what to do when you have two subtrahends.

Remember you can take them away in any order, or you can add the numbers together and then subtract them.

And here's part two.

This time you've got bar models.

Can you work out the missing subtrahends? Can you work out the missing numbers from each of those bar models? And again, some of them have three parts at the bottom, so think careful about how you're going to subtract the numbers.

And again, you may use a tens frame or number line to help you.

So pause the video, have a go at those two tasks, and see how you get on.

Welcome back and let's look at our answers.

The first part of task A, there are the answers.

And for the second part, there are the missing numbers from the bar models, and very well done if you managed to get most of those correct.

Some tricky ones there.

Hopefully they weren't too tricky.

And let's move on to our second part of the lesson, which is subtraction and finding the difference.

Now it is usually easy to take away a small subtrahend from the minuend.

So there are nine cakes.

Two cakes are eaten.

How many cakes are left? We could use a number line to help us work out the answer.

Let's start with nine.

Now we can subtract two.

Nine subtract two equals seven.

There's our two cakes that've been eaten.

"Nine subtract two equals seven," says Alex, "There are seven cakes left." Sometimes the subtrahend is almost as big as the minuend.

There are eight cakes.

That's our minuend.

That's the number we're starting with.

There's our eight cakes.

Seven cakes are eaten.

How many cakes are left? Eight subtract seven, so seven is almost as big as eight.

Seven is our subtrahend.

That's the number we're subtracting, and it's almost as big as the minuend.

The minuend is eight, subtrahend is seven, and we're trying to work out the difference, remember, between the two numbers.

What is the difference between eight and seven? "Eight and seven are close together," says Izzy, "I can quickly work out the difference." Here are eight cakes.

That was the minuend.

That was the number we were starting with.

Here are seven cakes.

That's the number being eaten.

And the difference we can see quite clearly between eight and seven.

The difference is one, the difference between eight and seven is one.

Eight subtract seven equals one.

Izzy represents eight subtract seven on a number line.

"I can count back from one number to the other to find the difference," says Izzy.

So let's use a number line to help us work out the answer.

We've got there a couple of number bars to help us work out the answer, so we've got one that goes to eight and one that goes to seven, and then we can look at the difference between the two of them, so the difference is one.

The difference between eight and seven is one, so eight subtract seven equals one.

Alex says, "You can also count on to find the difference between two numbers." And sometimes this is an easier way of doing it than subtracting.

There's our number bars again, so we've got eight and seven, and this time let's start with a seven and count on to get to the eight, so we're adding one on.

The difference between the two numbers is one.

When should you count back? "When the subtrahend is small, count back," says Izzy, so seven subtract two.

I'm trying to find the answer to seven subtract two.

Two is quite a small subtrahend.

We're only taking away a small number, so when we take away a small number, it's easiest to count back.

Start from seven, we count back two, answer would be five.

What about nine takeaway three, nine subtract three? Again, we're only subtracting a small subtrahend.

Again, best to our number line to help us work out the answer.

We're going to start with nine and subtract three.

Count back three.

Nine subtract three equals six.

When you are subtracting a small subtrahend, count back.

What should you do if the minuend and the subtrahend are close together? If there's not a big difference between the two numbers, what should you do then? Alex says, "Work out the difference between them by counting back or counting on." It doesn't matter which one you do, it will give you the same answer.

So seven subtract six.

We can start from seven and see how much we've got to count back to get to six.

So seven subtract one equals six.

Seven subtract six must equal one.

What about nine subtract eight.

Well we could start from the smaller number, eight, and see how much we have to add on to get to nine.

Eight add one equals nine, so if eight add one equals nine, then nine subtract eight must also be one.

So we can count back to find the difference or count on to find the difference, and you do that if the minuend and the subtrahend are close together.

Seven and six are very close together.

Eight and nine are very close together.

Now here's one to try on your own.

Think carefully about how to calculate the difference between the minuend and subtrahend.

Should you subtract the smaller number, or should you start on the smaller number and count on to get to the bigger number? How would you find the difference between the minuend and the subtrahend? Pause the video and see if you can work out the answers.

Okay, welcome back.

Let's see how you got on.

So bit of tricky thinking with these ones.

Let's look at that first one, nine subtract seven.

Well are the numbers far apart or are they quite close together? They're quite close together, aren't they? Nine to seven, there's not a big difference between them, so we could do seven and work out what we have to add to seven to get to nine.

Seven add two equals nine, so nine subtract seven must be two.

Six subtract one, how would you work out the answer? Well we're only subtracting a small subtrahend, so the easiest way to work out the answer there is to start from six and take away one.

Six takeaway one equals five.

Very well done if you've got the right answers, and very, very well done if you thought very carefully about how to solve those calculations.

And here is your second task, so you're going to be calculating the difference.

How would you work out the difference? And Izzy and Alex are there to help you.

Izzy's saying, "When the subtrahend is small, count back," and Alex is saying, "You can also count on to find the difference between two numbers." You may use a tens frame or number line to help you.

And here's our second part of task B.

Use these number cards, so you've got there the number cards from one to nine.

How many ways can you make these correct? So it's lots and lots of different answers there.

See how many you can find.

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

And welcome back.

And let's see once again how you got on, Our first part of task B, there are our differences.

So five subtract four, perhaps you counted on for that one.

Perhaps you started with four and counted on one to get to five.

And here are some solutions for part two of task B.

So had lots and lots of different ways of making two.

You could have done nine subtract seven, that equals two.

There's a difference of two.

You could have had the minuend as being eight and the subtrahend as being six.

So eight takeaway six, eight subtract six equals two.

Difference of six, not as many ways.

So you could have done nine subtract three equals six, or eight subtract two equals six, or seven subtract one equals six.

So very well done.

Well done if you found lots and lots of different answers and excellent work if you managed to find them all.

And here is our summary for today's lesson.

So look for doubles, near doubles, and number pairs totaling ten.

So if you know three at three equals six, six subtract three must equal three.

If you know that six add four equals ten, ten subtract four equals six.

When the subtrahend is small, count back.

So eight subtract one equals seven.

When the minuend and the subtrahend are close together, work out the difference between them.

Remember you can work out the difference by counting up from the smaller one or counting back from the bigger one.

So eight subtract seven, eight and seven are close together, so eight subtract seven equals one.