Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

I can't wait for us to have lots of fun together and hopefully learn lots of new things.

So let's get started.

This lesson is called "Use knowledge of the five and 10 times tables to solve problems." And it comes from the unit "Doubling, halving, quotative and partitive division." By the end of this lesson, you should be able to use your knowledge of the five and 10 times tables to solve problems. Let's have a look at our keywords for this lesson.

Product, factor, double, and half.

Let's practise them.

My turn: Product.

Your turn.

My turn: Factor.

Your turn.

My turn: Double.

Your turn.

My turn: Half.

Your turn.

Fantastic.

Now that we've said them, let's use them.

Let's have a look at our lesson outline.

In the first part of our learning, we're going to be identifying missing numbers and in the second part of our learning we're going to be solving some problems in context.

So let's get started with our first part of our learning, identifying missing numbers.

Jacob and Sofia are here to help us with our learning again today.

Are you ready, guys? Let's get started.

Jacob and Sofia are testing each other.

"How many fives are equal to four tens?" Jacob knows that four tens are equal to 40.

So how many fives will also be equal to 40? Four times 10 is equal to 40.

Double four is equal to eight.

So Jacob knows that eight fives are equal to 40 or four tens.

So we can say that four times by 10 is equal to eight times by five.

So eight fives are equal to four tens.

Well done Jacob.

I love how you use what you knew to help you to find that missing factor there.

Well done.

Now it's your turn, Jacob.

"How many tens are equal to six fives?" Sofia's not sure what six fives actually are, but she knows that six times five will be equal to half of six times 10.

So half of six is equal to three.

So we know that that is three times 10 because six times five will be equal to three times 10.

Three times by 10 is equal to 30.

So we also know that six times by five will also be equal to 30.

So to answer your question, Jacob, three tens are equal to six fives.

Well done, Sofia.

I love how you didn't know the product there but you were able to use what you knew about the factors and the knowledge of five and 10.

Well done to you.

Over to you then.

It's your turn.

Jacob is giving you three problems that he'd like you to solve.

Match the problems to the correct answers.

You might want to record the equation here just like Jacob and Sofia did to help you to visualise the problem.

So pause this video and come on back when you've matched up the questions with the answers.

Welcome back.

Let's see how Jacob got on with solving his own problems. Oh, he answered those two really quickly.

How did you answer those so quickly, Jacob? Jacob noticed that these two problems involved the same facts.

How many fives are equal to five tens and how many tens are equal to 10 fives? 10 fives are equal to five tens and five tens are equal to 10 fives.

Well done and well done to you if you spotted that.

How many tens are equal to four fives? We know that two tens will be equal to four fives because we need half the amount of tens.

Well done to you if you've got those correct.

Sofia now moves on to solve some missing number problems using what they've learned.

Here, we can see that we are missing the product, but two is the factor in both of the equations so we can use this knowledge to help us.

Five is half of 10, so if two times by 10 is equal to 20, two fives will be half of 20 because five is half of 10.

Half of 20 is equal to 10.

So Sofia knows that the missing product must be 10 and two times five must be equal to 10.

Well done, Sofia.

I love how you remembered that when our factors are the same we can use the knowledge to help us find the missing products.

Over to you then.

Have a look at this one.

What would be the missing product here? Pause this video and come on back when you've managed to find the missing product.

Remember to explain how you worked out the missing product.

Welcome back.

Let's have a look then at what we noticed.

Sofia noticed that four was the factor in both of these equations so we could use our knowledge that 10 is double five to help us define the missing product.

If four times five is equal to 20, then four times by 10 will be double that product because 10 is double five.

Sofia knew that double two was equal to four, so double two tens is equal to four tens and we know that four tens is equal to 40.

So four times by 10 is equal to 40.

Well done if you used that knowledge to help you to find that missing product.

Remember though, Jacob noticed that he didn't actually need to use that relationship between five and 10 because he was confident in his 10 times table.

If you know your 10 times table and you know that four times 10 is 40, then you can complete the product without doing any other thinking at all.

Let's have a look at this one then.

What will be the missing number in this equation? We can see that we are missing a factor, but we know the strategy to work out a missing factor, don't we? We know that five is half of 10.

So 10 times 10 is equal to double 10 times five because we need double the amount of fives to get the same product.

So we know that double 10 is equal to 20.

So 20 times five will be equal to 10 times 10.

10 times 10 is equal to 100 and 20 times five is in fact equal to a hundred.

Well done, Jacob.

I love how you use your knowledge there to find that missing factor.

Well done if you also noticed that 20 would be the missing factor.

Over to you then.

Have a practise to see if you can find the missing factor here.

Look at what information we have.

So we know that 40 times by five is equal to something times by 10.

What are we going to have to do to that factor to find the missing number? Pause this video and come on back when you found a missing factor.

Welcome back.

Let's have a look then, Jacob.

How did you find the missing factor? "10 is double five, so 40 times five will be equal to half of 40, times 10." Because remember, 10 is double five, so we only need half the amount to get that same product.

So half of 40 is equal to 20, so 20 times by 10 will be equal to 40 times by five.

Well done if you managed to find that missing factor.

20 times by 10 is equal to 200 and 40 times by five is equal to 200.

So even when we're using larger numbers, we can still use this strategy to help us.

Well done to you and well done to Jacob for completing that check.

Let's continue then to practise this strategy to make us feel really confident at using this knowledge to help us find missing numbers with task A.

Task A is to find the missing numbers but each time to talk about what you know that's going to help you to find the missing number.

Also double check really carefully, is it a missing product that I'm finding or is it a missing factor? Because that's going to depend on what knowledge you have to use.

So pause this video, have a go at one, A to E and then come on back to see how you've got on.

Welcome back.

Let's have a look then at how Jacob solved the missing numbers.

In A, Jacob noticed that nine is the factor in both of these equations, but we know that five is half of 10.

So nine times by five will be half of nine times by 10.

Half of 90 is equal to 45.

Well done If you've got that one.

B, we can see we are missing four times by 10.

We know four times by five is equal to 20 and we are missing our product.

So because we are now looking at four times by 10 rather than four times by five, we know that the product is going to be double.

So double 20 is equal to 40 or you might have just known that four times by 10 is equal to 40 and you didn't have to think about that relationship at all.

Well done if you got that one.

Let's move on to C, D and E then.

We can see here that we are now looking at the equations that has an expression on either side.

We haven't got our products.

We're looking for those missing factors.

Something times by 10 is equal to 60 times by five.

I know that the factor times by 10 will be half of the factor times by five.

So 60 times by five will be equal to half of 60 times by 10.

Half of six is equal to three.

So half of 60 will be equal to 30.

30 times by 10 is equal to 60 times by five.

Well done if you've got that one.

Let's have a look at D then.

I can see that I've got 20 times by five and it's equal to something times by 10.

The factor times by five will be half the factor times by 10.

So half of 20 is equal to 10.

So 20 times five is equal to 10 times by 10.

Well done if you've got that one and let's have a look at E then.

Something times by five is equal to 40 times by 10.

We know that five is half of 10.

So we are going to need double the amount of fives then tens.

So double 40 times by five will be equal to the same product.

I know that double four is equal to eight.

So double 40 is equal to 80.

So it's 80 times by five is equal to 40 times by 10.

Here you can see that even though those numbers got quite large, we were still able to use that same strategy because we didn't actually need to work out what the product was.

We just used our knowledge of the factors.

Well done if you got those correct and well done for completing task A.

Let's move on to the second part of our learning.

In the second part of our learning we're going to solve problems in context.

So let's get started.

The children take a trip to their local theme park.

They can't wait to go on all the amazing rides.

Jacob's really excited to get on The Swirler.

It costs five pounds for children and 10 pounds for adults to ride the Ferris Wheel.

Yesterday the ride made 80 pounds.

If they were all children or all adults, how many children rode the Ferris Wheel yesterday and how many adults rode the Ferris Wheel yesterday? Hmm, let's have a go at solving this problem then.

Sofia and Jacob show their different strategies to work out how many children or how many adults rode the ride.

We know that 80 is our product because that's our whole and we know that the adults will be something times 10 and the children will be something times by five.

So let's record those equations to help us.

Right.

Now that's helped me to really visualise this problem.

Let's see if we can find those missing factors.

We need to work out the missing factors for how many children and how many adults.

We know that eight tens are equal to 80.

So we know that it could have been eight adults that rode the Ferris wheel yesterday to make 80 pounds.

Let's use this knowledge to now help us work out how many children.

When the product is the same, the factor times by five is double the factor times by 10.

So eight times by 10 is equal to 80.

So to find the same product we're going to have to double that times by five.

So double eight is equal to 16.

So 16 times by five is equal to 80.

So we can say that 80 pound could have been made by eight adults riding the Ferris Wheel or 16 children paying to ride the Ferris Wheel.

Well done Sofia and Jacob.

Over to you then.

Let's see if you can use that same knowledge to solve this problem.

On Saturday, the Ferris Wheel made 100 pounds.

This could have been made from 10 adults riding the Ferris Wheel because 10 times 10 is equal to a hundred.

But how many children would've had to pay to make a hundred pounds? Use what you know to help you.

Welcome back.

Let's see how we got on then.

When the product is the same, the factor times by five is double the factor times by 10.

We know that 10 tens are equal to a hundred, so double 10 times by five will also be equal to a hundred.

Double 10 is equal to 20, so 20 times five will be equal to a hundred.

That means that a hundred pound could have been made from 20 children paying to ride the Ferris Wheel.

Well done if you manage to solve that problem.

They now move on to The Wavy Rapids.

The Wavy Rapids have boats of 10 and boats of five.

On the first turn there were six full boats of five and on the second turn there were six full boats of 10.

How many people were there on the first and second turn? Let's use our knowledge to solve this problem.

Sofia notices that both turns had six boats going out.

So one factor in both equations will be six.

The first turn was boats of five and the second turn was boats of 10.

So the first turn will be six times by five is equal to something and the second turn will be six times by 10 is equal to something.

Now we're going to work out the products to work out how many people were on each turn.

When the factor is the same, the factor times by five will be half of the factor times by 10.

Six tens are equal to 60.

So we know that there were 60 people on the second turn.

We can now use this knowledge to help us solve how many people were on the turn.

Six times by five will be half of six times by 10, so half of 60 is equal to 30.

So we know that there were 30 people on the first turn of the ride and there were 60 people on the second turn of the ride.

Well done Jacob and Sofia again.

Fantastic use of your knowledge there.

Do you think you could have a go now? Over to you then with this check.

On the third turn there were four full boats of 10 and on the fourth turn there was four full boats of five.

How many people were there on the third and the fourth ride on The Wavy Rapids.

Record each of the turns as an equation just like Sofia and Jacob did to find out how many people were on the third turn and the fourth turn of The Wavy Rapids.

Pause this video and come on back when you've got an answer.

Welcome back.

Let's have a look then.

So on the third turn we can see that there were four full boats of 10.

So we can record this as four times by 10 is equal to something and on the fourth turn there were four full boats of five.

So we can see this as four times by five is equal to something.

When one factor is the same, the factor times by five is half of the factor times by 10.

We know that four tens are equal to 40, so four fives will be half of 40 which is 20.

4 times by five is equal to 20.

There were 40 people on the third turn and there were 20 people on the fourth turn of The Wavy Rapids.

Well done to you if you managed to record those equations and get those products.

Jacob finally gets his chance to get on The Swirler.

To queue up for The Swirler, children have to line up in lines of 10.

Each cart holds five children and there are six full lines of children waiting.

So how many carts are needed for the children to get on this ride? Jacob and Sofia now solve this problem.

We can see this as a two-step problem, but Jacob thinks that he can just solve it in one step.

Sofia's going to show us her way first and then we can see Jacob's strategy.

We can see that there are six full lines of 10 children, so we know that this is six times by 10, which is 60.

So we have 60 children waiting to ride The Swirler.

Each of the carts hold five children, so we need to now work out how many carts will be able to hold those 60 children.

We can record this as something times by five is equal to 60.

We know that 12 times by five is equal to 60.

So Sofia works out that they will need 12 carts for all of the 60 children to get a turn on The Swirler.

Hmm, I wonder how Jacob worked this out.

He thinks he could do it in one step.

Should we have a look? Jacob now explains how he solved this.

He didn't need to calculate the product because all he needed to do was work out what the missing factor would be.

He recorded his equation as six times by 10 is equal to something times by five.

I like what you've done there Jacob.

Well done.

You are using the two expressions to just find that missing factor.

We know that five is half of 10, so double six times by five will be equal to six times 10.

Double six is equal to 12.

So we know that 12 times by five is equal to the same amount as six times by 10.

So 12 carts will be needed for all the 60 children to ride The Swirler.

Well done, Jacob.

That was a super efficient strategy.

Sofia is very impressed.

Over to you then.

Let's see if you can use Jacob's strategy to help you find how many Swirlers will be needed this time.

On the next turn, there were 12 lines of 10 people waiting for The Swirler.

How many carts of five would be needed for this turn? 12 times by 10 is equal to something times by five.

Pause this video and use your knowledge of Jacob's strategy to find out how many carts are needed for this turn.

Come on back once you've found an answer.

Welcome back.

Let's have a look then.

We know that five is half of 10 so we are going to need double the amount.

So double 12 times by five will be equal to 12 times 10.

Double 12 is equal to 24.

So we know that 24 carts will be needed for all the people to ride The Swirler.

Well done if you've got 24.

This strategy is really great because it means that we haven't got to worry about finding the products, we just use our knowledge of the factors to find the missing factor.

I don't know about you, but 24 times five would take me a while to work out.

Let's continue using this strategy throughout task B.

Task B, we're going to join Jacob and Sofia as they take a trip to The Prize Pavilion.

Help Jacob and Sofia to solve the problems that they face.

Part one.

Sofia and Jacob have a go on the Crazy Cups.

Each ball in the cup is worth five points, but if you get one in the golden cup, each ball scored is then worth 10 points.

How many points did Jacob score? Sofia got seven balls into the regular cups and she scored 35 points.

Jacob got seven balls in too but his first went into the golden cup.

So each of his balls are now worth 10 points, not five.

Record the equation to represent each of the child's scores and use this to work out what Jacob's score would be.

Part two.

Sofia and Jacob now play Basket Bonanza.

All of their points were scored in the same basket.

How many five-point baskets could each of them have scored and how many 10-point baskets could each of them have scored? Sofia scored 30 points and Jacob scored 20 points.

Record each equation to represent each child's possible score.

And part three.

Finally, after playing on the Wizards Wands, they tried to crack the Wizard's code to win an extra prize.

What is the value of the triangle and the star? So using our knowledge from today's learning, what could those missing parts be? Pause this video, have a go at part one, two and three and then come on back when you are ready to see how you've got on and continue your learning.

Welcome back.

I hope you enjoyed those three problems there using what you've learned.

Let's have a look at how you've got on.

Part one.

Remember we were trying to work out how many points Jacob and Sofia scored.

Sofia scored seven points from the regular cups, so that's seven times by five which is equal to 35, but Jacob got seven balls.

But he managed to get one into the golden cup, so each of his balls were worth 10 points, not five.

If each of his balls were worth 10 points, that means that he scored seven times by 10, which is equal to what? We know that seven times by 10 is equal to 70.

Because Jacob's were worth 10 points instead of five points, his points were double the number that Sofia scored.

Well done if you managed to say that Jacob would score 70 points.

Part two.

This time we were working out how many baskets they could have scored.

Sofia scored 30 points.

She remembered that when the products are the same, the factor times by five is double the factor times by 10.

We know that three times by 10 is equal to 30 and double three is equal to six.

So six times by five would also be equal to 30.

That means that Sofia could have scored three 10-point baskets or she could have scored six five-point baskets.

Let's have a look at Jacob's then.

Jacob decides to use his strategy to find the missing parts.

Something times by 10 is equal to something times by five.

When the products are the same, the factor times by five is double the factor times by 10.

Two times by 10 is equal to 20 and double two is equal to four.

So four times by five would also equal to 20.

This means that Jacob could have scored two 10-point baskets or four five-point baskets.

Well done to you for completing part two.

Let's have a look at part three.

Let's see if Sofia managed to crack the Wizard's code.

Sofia noticed that the triangle times the triangle was equal to a hundred.

These two numbers must be equal.

She knows that 10 times 10 is equal to 100, so she thinks the triangle is worth 10.

If the triangle has a value of 10, then we know that 10 times by five is equal to 50.

So the star must be worth five.

10 times by five is equal to 50.

Let's see, is she correct? Something's happening.

Yay! Well done, Sofia.

Look at that fancy new wizard's hat.

You're right Sofia, you are the wizard now.

Well done to you.

Well done for completing task B.

Let's have a look at what we've covered today.

We know that 10 is double five, so this means that when we multiply the same factor by five and 10, the product of the factor times by 10 is double the product of the factor times by five and because 10 is double five when the products are the same, the factor times by 10 is half of the factor times by five.

We also know that five is half of 10 and because we know this, we know that when we multiply the same factor by five and 10, the product of the factor times by five is half of the product of the factor times by 10.

And when the products are the same because five is half of 10, the factor times by five is double the factor times by 10 because we need double the amount.

Well done for all of your hard work today.

I hope you're feeling so much more confident now at the relationship between the five and 10 times tables and were able to solve all of these problems during our learning today.

Thank you for joining me today and I hope to see you all again soon for some more maths learning.

See you soon.