Lesson video

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

And it comes from the unit all about the seven times table, odd and even patterns, square numbers, and tests of divisibility, lots to be thinking about.

So if you're ready, let's make a start on today's lesson.

So in this lesson we're going to be using the patterns of odd and even numbers in times tables to solve problems. So you're ready to solve some problems? Let's make a start.

We've got two keywords in our lesson today and I'm sure they are words you know very well.

It's odd and even, but let's just rehearse them and remind ourselves about what they mean.

So are you ready? I'll take my turn and then it'll be your turn.

So my turn, odd, your turn.

My turn, even, your turn.

Well done.

As I say, I'm sure you've been using these words for many years to talk about numbers.

Let's just remind ourselves about the definitions.

So an odd number is any whole number that cannot be divided exactly by 2.

And the ones digit in an odd number will be 1, 3, 5, 7 or 9.

And any whole number that can be divided exactly by 2 is an even number.

And the ones digit will be 0, 2, 4, 6 or 8.

And remember, it's only the ones digit we need to look at when we're deciding if a number is odd or even because all multiples of 10, 100, 1000, and anything larger than that will be even.

So it's just the ones digit that allows us to make that decision.

So there are two parts to our lesson.

In the first part we're going to be using patterns and thinking about multiplying a 2-digit by a 1-digit number.

And in the second part, we've got a maze game to solve, thinking about products.

So let's make a start on part one.

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

So here's a quick recap of odd and even products.

You may have done some work thinking about these, but let's just remind ourselves.

Here's Andy to help us out as well.

He says an odd factor multiplied by an odd factor will be equal to an odd product.

And that's the only way we can make an odd product, if both our factors are odd.

And Jacob says an even factor multiplied by an odd factor is equal to an even product.

And Sofia says an odd factor multiplied by an even factor is equal to an even product.

So if one of our factors is even, we're going to have an even product.

And we can only get an odd product if both of our factors are odd.

Those are worth remembering.

And if you're not quite sure why they work, it's worth exploring those, perhaps with some number shapes to help you.

Sofia and Jacob are playing maths wizards.

They need to sort the multiplication expression cards into the correct cauldron.

They've got one cauldron for odd expressions and one cauldron for even expressions.

So they're not going to calculate the value, they're just going to look at the factors and decide where the expressions belong.

So here we've got 23 x 3, 2 x 8, and 29 x 8.

Hmm, where should we start? Ah, Sofia's gonna start with 29 x 8.

What do you notice? Well, Jacob says he's stuck.

He doesn't know his 29 times table.

I don't think I know where 29 times table either, do you? Ah, but he can use the odd and even factor rules to help him.

So the factor 29 is odd and 8 is even.

29 is odd because the ones digit is odd, it's a 9 isn't it? What do we know then about multiplying an odd number by an even number? If one factor is odd and one factor is even, what do we know about the product? Ah Sofia says, remember an odd factor multiplied by an even factor is equal to an even product.

And if you can't picture it with 29 x 8, think about, say, 2 x 3.

So 2 is an even factor, 3 is an odd factor.

If we've got two groups of three, can you picture two groups of three going together? Maybe picture those number shapes.

Can you see that the two ones will link up and we'll have an even number, 6.

So an odd factor multiplied by an even factor will give us an even product.

So 29 x 8 needs to go into the even cauldron.

Shall we see if it's right? Absolutely, puff of purple smoke shows it's correct.

So they're going to move on to another card now.

Which cauldron will this one go into? 23 x 3, what do you think? Jacob and Sofia look carefully at the numbers.

What can you see there? Well 23 and 3 are both odd numbers.

Ah, so both our factors are odd.

What do you know about that? Ah, Sofia says, remember odd factor multiplied by odd factor is equal to an odd product.

It's the only way we can get an odd product, if both of our factors are odd numbers.

So 23 x 3 is an expression that will go in the odd cauldron.

Should we see if we're right? Absolutely, yes, well done.

Another puff of purple smoke to show us we're correct.

Time to check your understanding.

Which of these expressions will result in an even product? So which of these will give us an even product? Remember you don't need to work out the product, just look at the factors.

Pause the video, have a go and when you're ready for some feedback, press play.

What did you think? Ah, did you spot that it was the second two, 8 x 26 and 10 x 25.

Can you spot that each of those has got at least one even factor.

8 x 26 has got two even factors, and 10 x 25 has got one even and one odd factor.

So the factor 25 is odd and 10 is even, but an odd factor multiplied by an even factor is equal to an even product.

For the middle one they were both even so we knew the product was going to be even.

And for the first one, 47 x 5, well they're both odd factors aren't they? And the only way we can get an odd product is with two odd factors.

Now Sofia is given a challenge with six cards.

She can only use the cards once for each equation.

Sofia needs to arrange the cards so that she can make an odd product and an even product.

I wonder what she's going to do, what would you do? What advice would you give to Sofia? What do you know about odd products and even products? Okay, so Sofia says remember odd factor multiplied by odd factor is equal to odd product.

So she's going to start with making that odd product.

That means she says I can arrange my digits like this: 21 x 3, 21 is an odd number, it's ones digit is 1 and 3 is an odd number.

So 21 x 3 will give an odd product.

Can you think another way to do it? Oh yeah, she could have done this: 41 x 3, 41 is odd.

We've got four tens but that's fine.

We've got a 1 in the ones place and 1 means that we have an odd number, and 3 is an odd number again.

She says the ones digit of my 2-digit number must be odd and the factor I am multiplying must also be odd.

And that's got to be true to get an odd product.

Well done Sofia.

What about to get an even product? Well Sofia's remembered that an odd factor multiplied by an even factor is equal to an even product.

So as long as one of her numbers is even then she will get an even product.

So what could she have? She says that means I could arrange my digits like this: She could have 12 x 3.

12 is an even number because it has a 2 in the ones and three is an odd number.

But that's okay because one of our factors is even.

That will give us an even product.

Or she says I could do it like this: 41 x 2, 41 is an odd number because one is odd and two is an even number.

So we have one even factor.

So our product will be even.

She says as long as one of the ones digits is an even number, your product will be even.

Ah yes, so the ones digit of the 2-digit number could be even, or the ones digit that is our single digit factor could be even.

So as long as one of those is even, our product will be even.

Great thinking Sofia, and I like your generalisation there.

Time to check your understanding.

Using only the digits on the cards, create an expression that will have an even product.

Can you make more than one example? So you've got 3, 4, 5, and 6 to use.

Can you make a 2-digit by 1-digit multiplication that will have an even product? Pause the video, have a go and when you're ready for some feedback, press play.

How did you get on? So you may have had 34 x 5 or 64 x 5 perhaps.

Again thinking about Sofia's generalisation, if we're going to have an even product then one of our ones digits must be even.

In those cases our ones digit of our 2-digit number was an even number.

But we could have had 35 x 4 or 65 x 4.

Time for you to do some practise now.

So question one says, without calculating, can you sort the expressions into the correct cauldrons and explain how you know.

Now we've got some 2-digit x 2-digit numbers in there.

But I think with what you know about odd and even factors, you'll be able to work out whether those products are odd or even.

And for question two, can you use the cards below to answer the questions? So you've got 6, 7, 8, and 9 cards.

In a, Sofia says she thinks of a 2-digit number multiplied by a 1-digit number.

Her product is even, what could the expression be? And for b, Jacob thinks of a 2-digit number multiplied by a 1-digit number.

His product is odd, what could the expression be? I wonder how many different ways you can come up with expressions that meet what Sofia is thinking about and what Jacob is thinking about.

Pause the video, have a go at questions one and two, and when you're ready for some feedback, press play.

How did you get on? Did you sort the expressions? So the odd expressions were 27 x 7, and 7 x 33.

Both of the factors were odd, so therefore the product would be odd as well.

And all of these expressions would give us an even product because either one or both of the factors are even.

So 45 x 12, 12 is even.

36 x 11, 36 is even.

52 x eight, both numbers are even.

And 40 x 19, 40 is an even number.

So all of them had at least one even factor and that would mean that they would have an even product.

And did you notice again that an odd product is only possible when both factors are odd? It's the only way we can make an odd product.

So in question two, let's look at a.

Sofia was thinking of a 2-digit number multiplied by a 1-digit number, and her product is even.

So what could the expression be? So the expression would have to have two even factors or one even and one odd factor.

So you could have had 6 x 78, both of them even, 8 x 96, both of those are even as well.

Or you could have had 7 x 68 because 7 is odd but 68 is even.

So it will still result in an even product.

And 6 x 89, 89 is an odd number 'cause 9 is odd but six is even.

So it'll still give us an even product.

And for b, Jacob thought of a 2-digit number multiplied by a 1-digit number and his product was odd.

What could the expression be? So this time the expression had to have two odd factors to have an odd product.

So you could have had 67 x 9 or 69 x 7.

7 and 9 were our only odd numbers in that selection.

So they both had to be the ones digits, the ones digit of the 2-digit number and the single digit factor as well.

Well done if you've got all of that correct.

And onto part two where we've got a product maze game to play.

So Jacob and Sofia enter a maze.

And at various points they've got to make a decision as to whether they go left or right or straight on or turn, haven't they? And at each of those points they pick a card with a multiplication expression.

And they have to decide if the product is going to be odd or even to proceed.

If it's odd they go one way, if it's even they go a different way.

So let's help them play the game.

In they go, here's their first decision point.

So depending on whether they get an odd or an even product, they go in one of two directions.

So this is their expression, 43 x 9.

Is that going to give us an odd or an even product? Let's have a look.

Oh dear Jacob's stuck.

He says he doesn't know his 43 times table.

I don't know my 43 times table, do you? Do we need to know our 43 times table, though? Ah, you can use the odd and even rules to help you.

Remember we've been thinking about odd and even factors and what that does to the product.

So what do you notice about 43 x 9? The factors are 43 and 9 and they're odd.

So the product is odd.

If we have two odd factors, we will have an odd product, as Sofia is reminding us.

So Jacob says if the product is odd, we follow the blue arrow, and if it's even we follow the red arrow.

So this product is going to be odd.

So they're going to follow the blue arrow.

So that's the direction their dot's going to move.

So they move forward and they come across their second problem.

So they've gone round this way, they've got a new problem now, 55 x 6.

What's it going to be, odd or even? That's where they've moved to following their blue arrow.

So is this going to be odd or even, are they going to go back the way they came or are they going to move on? Oh again Jacob, do you need to know your 55 times table? I don't think you do.

No, you can use those odd and even rules thinking about the factors to help.

So the factor 55 is odd and 6 is even.

So this time the product will be even.

And Sofia's reminding us, remember, odd factor multiplied by even factor will give us an even product.

So this time we're going to be following the red arrow, product is even so they follow the red arrow.

There they go, all the way up there, so they've got to the next decision point.

Ah, and you are gonna help them make the decision this time.

It's time to check your understanding.

So we've got 78 x 8, and Jacob makes a prediction.

All products with 78 as one factor will be even because 78 is even, so we can follow the red arrow.

Do you agree with Jacob? Why or why not? Pause the video and have a think and when you're ready for some feedback, press play.

What did you think? Did you agree with Jacob? Yes, Jacob's correct, 78 is an even number.

If 78 is a factor then the product will be even.

So we could multiply 78 by anything and we'd still have an even product.

This time it's 78 x 8, so we've got two even factors.

So we're definitely gonna have an even product so we can follow the red arrow.

So there we go, they've moved on a little bit further.

Can you see? I think that's a sort of golden sun in the middle there.

I wonder if that's their prize.

They pick another card, it's 59 x 3.

Jacob says, I already know the product will be odd because both of the factors are odd.

Do you agree with Jacob? Can you explain your thinking? That's right, Jacob's correct.

When both factors are odd, the product will be odd.

So this time they've got to go in a blue direction, haven't they? Right, okay, so they've got one final bit of the journey to do and they need to follow a blue arrow.

Jacob and Sofia have to select a card to get to the centre.

Which card should they choose? They need an odd product to follow the blue arrow.

So should they pick a or b to get to the centre of the maze? Pause the video, make your decision and when you're ready for some feedback, press play.

What did you think? Should they pick 44 x 9 or 9 x 73? They need an odd product, remember.

Ah, they could only pick b, couldn't they? The product needs to be odd.

So picking option b is correct because odd factor multiplied by odd factor will be equal to an odd product and that's what they needed to get to the centre of the maze.

Well done Jacob and Sofia, you've made it with your help, of course.

Thank you for helping them.

Time for you to have a go.

Here is a product maze game for you to play.

So can you continue playing the game with a partner? Each time you come across a red dot, you and your partner will have to give an example of a multiplication expression which would have an odd or an even product.

Which is the quickest way you can get to the centre? Remember if you get an odd product, you follow a blue arrow.

If you get an even product, you follow a red arrow.

So if you start on the way in, you can see in the middle at the bottom there, you are going to get to a red dot.

Even you can go along the bottom or you can go up into the next part.

So you've got to come up with a multiplication expression that will allow you to follow the arrow you want to go on.

Can you find the quickest way to get to the centre? Pause the video, have a go at playing the game, coming up with those multiplication expressions and when you're ready for some feedback, press play.

How did you get on? Did you have fun playing? So Jacob is here.

Can you see there's a green circle down in that bottom right hand corner? There he is.

He says I want to follow the red arrow.

So he wants to go up.

So what could he give as a multiplication expression that would have an even product? Well he's gone for 53 x 6.

One odd and one even factor will give him an even product.

So well done Jacob, that would work.

The factor 53 is odd and six is even, so the product will be even.

And you can see the shortest route to get to the centre has been marked in green.

I wonder if that was the one you managed to pick.

I wonder if you managed to pick the right expressions to let you move along the arrows that you wanted to move along.

I hope you had fun.

And we've come to the end of our lesson.

We've been using patterns of odd and even numbers in the times tables to solve problems. We can understand that knowing if the product will be odd or even can help us to solve problems. And we also understand that when we're thinking about times tables, if it's an odd times table, the products will alternate between odd and even.

And we know that if a timetable is even, the products will always be even.

We also know that to get an odd product, both factors must be odd.

And to get an even product, one or both of the factors must be even.

I hope you've enjoyed exploring odd and even numbers and their products.

And I hope I get to work with you again in another lesson soon, bye-bye.