Lesson video

Hello there, my name is Mr. Goldie.

And welcome to today's math lesson.

I'm sure you're going to have lots and lots of fun.

And here is our lesson outcome.

So our outcome today is I can solve problems using addition and subtraction including bridging through 10.

And here are our keywords today.

So lots of keywords today.

So if I'm gonna say the keyword, could you repeat it back to me please? So the first keyword is minuend.

Can you say that, minuend? The next key word is subtrahend.

Can you say subtrahend? Excellent.

The next key word is difference.

Can you say difference? Brilliant.

Next key word is sum.

And the last key word is partition.

Can you say partition? Excellent stuff.

And let's look at what those words mean.

So the minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

And the difference is the result after subtracting one number from another.

So the calculation 7 subtract 3 equals 4, the minuend is 7, the subtrahend is 3, and the difference is 4.

The sum is the total when numbers are added together.

And partition means splitting a number into smaller parts.

And here is the lesson outline.

So two parts to today's lesson.

The first part is using sum and difference.

The second part is using sum and difference to solve problems. Let's get started.

In this lesson you will meet Izzy and Alex.

And Izzy and Alex have got lots of problems to solve today.

Alex and Izzy are solving problems using number cards.

So these are the number cards, 1 to 9.

I need to find a pair of number cards with a difference of 2 says Izzy.

So Izzy is looking to pick out two number cards and if you subtract one from the other, you get a difference of 2, you get the answer 2.

Can you find two cards with a difference of 2? How can you find the difference? Let's try 9 subtract 7.

Izzy says you can subtract the subtrahend.

So we can start with 9 and subtract 7.

Take 7 away.

9 subtract 7 equals 2.

How else can you find the difference? You can also count on to find the difference between the two numbers, says Alex.

We can count on from 7 to get to 9.

Here's 9 and here is 7.

And we can see there the difference between the two numbers.

How much bigger is 9 than 7? So the difference between 9 and 7 is 2.

We have to add 2 onto 7 to get 9.

So there are two different ways there of working out the difference.

We can subtract the subtrahend to find the difference or you can count on from the smaller number to the bigger number.

Izzy finds other number cards with a difference of 2.

So Izzy says 8 and 6 have a difference of 2.

And Izzy's going to do the calculation 8 subtract 6.

So we can see there the difference between 8 and 6.

So 8 and 6 have a difference of 2.

8 subtract 6 equals 2.

So you can count back to find the difference.

Izzy finds other number cards with a difference of 2.

6 and 4 also have a difference of 2, says Izzy.

So this time the calculation is 6 subtract 4.

And we can see there 6 and 4.

And the difference between them is 2.

This time we can add from the smaller number 4 to get to the bigger one 6.

So you can count on to find the difference.

What other pairs of number cards have a difference of 2? Can you see another pair of number cards where the difference between the two numbers is 2? Remember you can subtract the smaller number from the bigger number, or you can count on from the smaller one to get to the bigger one to find the difference.

So pause the video and have a think.

Can you find other pairs at number cards with a difference of 2? Welcome back.

Let's see how you got on.

Did you manage to find more than one answer? So you may have come up with 7 subtract 5.

7 subtract 5 equals 2.

And because the numbers are close together, it's probably easier to count from 5 to get to 7.

You may have come up with 5 subtract 3.

And again you may have counted up from 3 to get to 5, the difference is 2, or you may have calculated 5 subtract 3 and counted back 3.

4 subtract 2.

4 and 2 also have a difference of 2.

3 and 1 also have a difference of 2.

And there you definitely count back, wouldn't you? You start with 3 and subtract 1 and that'll give the answer 2.

So well done if you came up with some of those different possible answers.

Can you find a pair of number cards with a difference of 4? So we're no longer looking for a difference of 2.

This time we're looking for two number cards with a difference of 4.

Izzy says 9 and 5 have a difference of 4.

The calculation will be 9 subtract 5.

But Izzy says I'm counting on from 5 because the numbers are quite close together.

So Izzy starts on 5 and she adds on 4 to get to 9.

So the difference between 5 and 9 is 4.

Izzy could have started on 9 and subtracted 5.

9 subtract 5 equals 4.

Find a pair of number cards with a difference of 4.

6 and 2 also have a difference of 4, says Alex.

6 subtract 2 is our calculation this time.

Alex is saying, I'm counting back because the subtrahend is small.

So when the numbers are closed together, count up to find the difference.

When the subtrahend is small, when the difference between the numbers is quite large, count back.

So we start from 6, we subtract 2, 6 subtract 2 equals 4.

And this is one for you to try on your own.

So find a pair of number cards with a difference of 3.

There are lots of possible answers for this one, but for some of them you may want to subtract the subtrahend, subtract the smaller number.

You may want to count up from the smaller number to get to the bigger number.

So find a pair of number cards with a difference of 3.

And how many different solutions can you find? Pause the video and have a go at that challenge.

Let's see how you got on.

So here are two possible answers.

There are lots of different answers you may have come up with.

Here are just two possible answers.

So you may have come up with 6 subtract 3.

6 subtract 3 equals 3.

6 and 3 have a difference of 3.

So we could count on from 3 to get to 6.

3 and 3 equals 6.

Or you could have started with 6 and subtracted 3.

4 and 1 also have a difference of 3.

4 subtract 1 equals 3.

And because the subtrahend is small, it's easier to take it away, to count back to subtract it.

That's 4 subtract 1 equals 3.

Now we're moving on to look at sum next.

So Alex wants two number cards with a sum of 12.

Remember what sum means? Sum means when you add the numbers together.

So looking for two number cards that add up to make 12.

He decides to use 9 as one of his numbers.

So Alex thinks one of the numbers could be 9 and he's looking for the other number that adds to it to make 12.

So 9 add what other number equals 12.

What does Alex need to add to 9 to make it 12? Let's start with 9 and let's add on to get to 12.

If we add on 1, we get to 10.

If we add on 2 more, we get to 12.

What does Alex add all together? 9 add 3 equals 12.

So the two number cards could be 9 and 3.

Is there another pair of number cards with a sum of 12? Alex decides to start with 8 this time.

So Alex is gonna start with 8 and he's going to try to work out what the other number card could be.

8 add what number equals 12.

What does Alex need to add to 8 to make 12? Let's use number line again.

Let's start with 8 this time.

8 add 2 equals 10.

So bridging through that 10, how much more do you have to add to get to 12? If you add on 2 more, you get 12.

What's been added altogether? 8 add 4 equals 12.

So the two numbers could be 8 and 4.

8 and 4 are two numbers that have a sum of 12.

There is another pair of cards with a sum of 12.

Can you find it? Pause the video and see if you can work out what the two number cards are.

Welcome back.

Did you manage to solve it? Did you manage to find the answer? Well two number cards are 7 and 5.

7 add 5 equals 12.

Let's just check to make sure that Alex is right.

Start with 7, we add on 3, we get 10.

Don't forget it's all about making that 10, bridging through that 10.

So 7 add 3 equals 10, add on 2 more gets us to 12.

So altogether, we've added 5.

Are there any different answers, says Izzy.

No there are not anymore.

Now you might have thought the 6 add 6 could could be an answer as well.

6 add 6 does equal 12 but there is only one 6 there.

We haven't got a pair of 6s.

Alex wants two number cards with a sum of 15.

He chooses the 7 number card to start.

So Alex thinks one of the numbers could be 7.

7 add what equals 15.

Let's have a go working out the answer.

So we're going to start with 7.

7 add 3 equals 10, and 5 more equals 15.

What has been added altogether? 7 add 8 equals 15.

3 add 5 equals 8.

What other number pair has a sum of 15? Pause the video and see if you can work out what the two numbers are.

Welcome back.

Did you manage to solve it? Did you manage to find the two number cards? Very well done if you did.

Now you should have come up with 9 and 6.

9 add 6 equals 15.

And just to prove that we are right, let's use our number line to check.

We'll start with 9.

9 add 1 equals 10.

And we'd have to add 5 more to get to 15.

And altogether we've added 6.

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

And let's move on to our task.

So you're going to be using the number cards 1 to 9.

So first can you find two cards with a difference of 3? So we've got there the numbers 9 and something, 8 and something, 4 and something.

So if one of the cards is a 9, what other number should you use there is a difference of 3 between the two numbers? Next, can you find two cards with a difference of 4? There we've got 8 and something.

What's the other number card? And see if you can find some answers of your own using two different number cards.

Remember the difference between the two cards got to be 4.

And the last one, find two cards with a difference of 6.

Can you find more than one solution? And part two.

So again we are using the number cards from 1 to 9.

Can you find two cards with a sum of 8? So you've been given one of the number cards, can you find the other number card you'd have to add to it so you have a sum of 8? So 1 and what other number? Next, can you find two cards with a sum of 13? Can you find three different ways of doing it? Can you find two cards with a sum of 14? And can you find two cards with a sum of 16? So pause the video, use your number cards, see if you can work on those difference and sum problems. Welcome back.

I hope you got some really well.

I hope you've managed to find lots and lots of different answers.

Let's have a look to see if you've got them right.

So for the first part of task A, your answers may have included some of these.

So find two cards with a difference of 3.

You should have come up with 9 and 6.

That's the only possible solution for that one, 9 and 6.

You may have come up with 4 and 1.

4 and 1 also have a difference of 3.

You may have come up with a difference solution for that one.

4 and 7 also have a difference of 3.

So for some of these there's more than one answer.

Find two cards with a difference of 4.

Hopefully you came up with 8 and 4, that's the only possible answer.

But then there were lots of different answers.

5 and 1 have a difference of 4.

6 and 2 have a difference of 4.

Then you have to find two cards with a difference of 6.

And they are the only three possible answers.

9 and 3, 8 and 2, 7 and 1.

There are no other possible answers.

And then part two, this is finding two cards with a sum of 8.

We had 1 and 7, 2 and 6, 3 and 5.

They all have a sum of 8.

Find two cards with a sum of 14.

You may have come up with the answer 8 and 6.

You may have come up with the answer 9 and 5.

And then find two cards with a sum of 16, there was only one possible answer and that was 9 and 7.

Although of course again you could have had the numbers the other way around, you may have had 7 and 9.

So very well done if you found lots and lots of different solutions, lots and lots of different answers.

And let's move on to our second part of the lesson, using sum and difference to solve problems. So Izzy puts two of these number cards in an envelope.

So we've got there the numbers, 4, 5, 6, 7, 8, 9, 11, 12, 13.

So Izzy is going to put two of those numbers in an envelope.

She's not going to reveal what the numbers are.

But she tells us that the two numbers have a sum of 13 and a difference of 3.

So the two numbers add up to make 13.

And if you subtract the smaller number from the larger number, you get 3.

The difference between the two numbers is 3.

I'm going to use trial and improvement to work out what the numbers are, says Alex.

So Izzy's creates a little puzzle and Alex is going to try to solve that puzzle.

Trial and improvement means trying something out.

You might not get the answer the first time, but you can use what you have found out.

Each time you try to get the answer, you get a bit closer to the solution.

So trial and improvement is all about trying something out and then thinking about what you've learned and using that to help you solve the problem.

So Alex tries starting on 7 first.

So remember Izzy puzzle was that two numbers have a sum of 13 and a difference of 3.

So Alex is thinking 7 add another number equals 13.

What is that number? So Alex is going to start from 7 and he's going to work out what he has to add on to get to 13? So remember to bridge through 10.

7 add 3 equals 10, add on 3 more equals 13.

What has Alex added altogether? He's added on 6.

7 add 6 equals 13.

Could 7 and 6 be the numbers in the envelope? Has Alex solved Izzy's puzzle? So Alex is going to work out the difference next.

So remember the two numbers have a sum of 13 and a difference of 3.

Alex thinks they could be 7 and 6 because 7 and 6 have a sum of 13.

So to work out the difference, Alex is going to do 6 subtract 6.

He's going to work out the difference between the two numbers.

And because the numbers are close together, Alex is going to add on from 6 to get to 7, and you have to add on 1.

The difference between 7 and 6 is 1.

Alex could have started on 7 and subtracted 6, but it's easier to count on when the numbers are close together.

So the difference between 7 and 6 is 1.

So are 7 and 6 in Izzy's envelope? Remember Izzy said, the two numbers have a sum of 13 and a difference of 3.

No, they are not the answers.

Those aren't the two number cards in Izzy's envelope.

The difference between 7 and 6 is 1.

The difference between Izzy's numbers is 3.

Although they have the correct sum, although they add up to make 13, the difference is not right, the difference is incorrect.

I need to choose two numbers that are further apart.

7 and 6 are too close together.

So Alex tries 8 next.

Alex thinks what are the numbers in the envelope could be 8.

And he's going to use that to help him work out the other number.

So the two numbers have a sum of 13 and a difference of 3.

So 8 add what number equals 13.

Let's start with 8 again.

What do we have to add on to 8 to get to 10? 8 add 2 equals 10, and then add on 3 more gets us to 13.

What has Alex added altogether? He's added 2 and he's added 3.

What is 2 add 3? Altogether Alex has added 5.

8 add 5 equals 13.

Could 8 and 5 be the numbers in the envelope? Alex works out the difference.

Remember, Izzy's puzzle was the two numbers have a sum of 13 and a difference of 3.

Alex thinks he could have found the two numbers.

He thinks they could be 8 and 5.

Let's see if he's right.

What is 8 subtract 5? There's 8 and there is 5.

When looking at the difference between the two numbers.

So the difference between 5 and 8 is 3.

5 and 3 equals 8.

The difference between 8 and 5 is 3.

I think Alex may have found the two numbers in the envelope.

So Izzy reveals the two numbers in the envelope.

The two numbers have a sum of 13 and a difference of 3.

Let's see if Alex is right.

So open the envelope up and inside the envelope there are 8 and 5.

Very well done Alex.

Alex is correct.

8 add 5 equals 13.

8 subtract 5 equals 3.

The two numbers have a sum of 13 and a difference of 3.

Izzy puts two of these number cards in an envelope.

This time the two numbers have a sum of 21 and a difference of 3.

So the difference is still 3, but the sum this time is 21.

So the two numbers add together to make 21.

If you subtract the smaller number from the bigger number, you get the answer of 3.

The difference between the two numbers is 3.

Oh, Alex is feeling confident.

Alex says, I think I know what the numbers are.

And he hasn't even tried anything yet, has he? So Alex chooses two number cards.

He's chosen 12 and 9.

And he's gonna add those two numbers together.

He's going to use a number line to help him work out the answer.

He's gonna start from 12 because it's the bigger number.

What does Alex have to add on to 12 to get to the next tens number? The next tens number is 20.

He'd have to add on 8.

12 add 8 equals 20.

And how much more would he have to add on? He's got to add on 9 altogether.

He's added 8 already.

He have to add on one more.

So Alex has added on 9 altogether.

That gets the answer, 21.

So 12 add 9 equals 21.

So next, Alex is going to work out the difference between the two numbers.

He's got the sum already, he now needs to work out the difference.

So this time he's going to do 12 subtract 9 and work out the answer.

Alex says, I'll count on because the numbers are closed together.

Alex could start from 12 and subtract 9.

But because the numbers are closed together, it's easier to count on from the smaller number to the bigger one to find the difference.

So Alex is gonna start from 9.

He adds on 1 to get to 10, adds on 2 more to get to 12.

What has he added altogether? So 12 subtract 9 equals 3.

Izzy reveals the two numbers in the envelope.

So remember she said the two numbers have a sum of 21 and a difference of 3.

The numbers in the envelope were 12 and 9.

Alex is correct.

12 add 9 equal 21.

12 and 9 have a sum of 21.

12 subtract 9 equals 3.

12 and 9 have a difference of 3.

Very well done, Alex.

Now here's one to try on your own.

Alex puts two of the number cards in an envelope.

There we go.

Those two numbers are disappearing into that envelope.

I wonder what they are.

Alex says the two numbers have a sum of 11 and a difference of 1.

What are the two numbers? Pause the video and see if you can work out what they are.

Don't forget they have a sum of 11, they add together to make 11 and they have a difference of 1.

Good luck.

Welcome back.

Did you manage the solve of Alex's challenge? Have they definitely got a sum of 11 and a difference of 1? Let's have a look to see if you were right.

So the two numbers are, let's open the envelope, look inside.

Two numbers were 6 and 5.

6 and 5 have a difference of 1.

6 subtract 5 equals 1.

6 and 5 also have a sum of 11.

So we start from 6.

If we add on 4 and then add on 1, so bridging through that 10.

So we've added on 5 altogether.

That gets us to the answer 11.

6 and 5 have a sum of 11.

6 and 5 equals 11.

Very well done if you manage to solve Alex's challenge and managed to work out what two numbers were in that envelope.

Excellent work.

Now let's move on to task B.

So in task B, you're going to use these number cards to solve the problems. Izzy and Alex have got four different puzzles for you to solve.

So one of Alex's puzzles is find two numbers with a sum of 9 and a difference of 1.

One of Izzy's puzzles is find two numbers with a sum of 17 and a difference of 5.

So some of those puzzles are tricky than others, but see if you can work out the two number cards that are hidden in each of those envelopes.

And then part two of task B, you are going to create your own problem to challenge a friend.

So choose the same two numbers to complete these calculations.

So add the two numbers together and work out the sum, subtract the smaller number from the larger number and work out the difference.

And then you're going to give one of those speech bubbles to a friend to see if they can work out what the two numbers are.

Your challenge will say find two numbers with a sum of whatever the sum is, and a difference of whatever the difference is.

So pause the video and have a go at those challenges.

Welcome back.

I hope your brain's hurting after all that thinking.

Some really good maths going on there.

And let's have a look to see how you got on.

So for part one, here are the answers.

So find two numbers with a sum of 9 and a difference of 1.

The two numbers were 5 and 4.

Find two numbers with a sum of 17 and a difference of 5.

The two numbers were 11 and 6.

11 add 6 equals 17.

11 subtract 6 equals 5.

So very well done if you manage to solve some of those challenges and excellent work if you manage to do every single one of them.

And let's look at part two.

So part two is creating your own challenges.

So you may have decided to use numbers 11 and 9.

11 add 9 equals 20.

11 subtract 9 equals 2.

And then the challenge you would give to a friend would look like this.

Find two numbers with a sum of 20 and a difference of 2.

Did you manage to make up one of your own challenges? Did you manage to give it to a friend? Did your friend manage to solve it? Excellent work.

Very, very well done.

Lots and lots of really good thinking today.

And I hope you made some use of trial and improvement as well to help you find the answers.

Excellent work today.

So here is our lesson summary.

So difference can be worked out by using the subtrahend to count back or by looking at the difference between the minuend and the subtrahend.

And trial and improvement is useful when solving problems..