Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson on representing the five times table and linking it to the 10 times table.

So are you ready to do some counting in fives and 10s and explore how the five and 10 times table are related to each other? Are you? Excellent, let's make a start.

So in this lesson we're going to be explaining how a factor of zero or one affects the product.

We've got two Keywords, zero and product.

So I'll take my turn and then it'll be your turn.

Are you ready? My turn, zero.

Your turn.

My turn, product.

Your turn.

Well done, I'm sure you've used those words before.

They're gonna be really useful to us today.

So listen out for them as we go through the lesson.

So there are two parts to our lesson today.

In the first part, we're going to be looking at a factor of zero or one.

And in the second part, we're going to be doing some comparing.

So let's make a start on part one.

And we've got Aisha and Laura helping us with our lesson today.

Look at the two equations.

What's the same? Can you see something? Aisha says, "One factor is zero." So there's the digit we use to write the 0 and, "The other factor is 2." So in both of those equations we've got a 0 and a 2 as our factors.

Laura says, "The product is 0 in both equations." 0 x 2 = 0 and 2 x 0 = 0.

What's different about them? Aisha says, "The order of the factors has changed." We've got 0 x 2 in the first one and 2 x 0 in the other one.

But Laura says, "The product is still the same." The product is still 0.

Now Aisha and Laura, look at the Two and Five times tables.

What's the same? Aisha says, "One factor is 0 and the other factor is not zero." But Laura says, "The product is 0." In all of those times table facts, the product is 0.

Time to check your understanding.

Just looking at these equations, what's different about the equations? Is it A the product, B the order of the factors, or C the operation? Pause the video, have a go, and when you're ready for some feedback, press play.

What did you think? What was different about the equations? That's right, it was B, wasn't it? It was the order of the factors that changed.

We had 0 x 2 = 0 and then 2 x 0.

And then 0 x 5 = 0 and then 5 x 0.

All of them equal to 0.

So what is the product of two and zero? Aisha says, "I can use the pattern in the table to help me." Laura says, "Imagine two groups of nothing, or zero." Well, it's going to be zero, isn't it? If I've got nothing and I've got it two times, I've still got nothing, haven't I? So the product of two and zero is zero.

What about the 10 times table? What's the product of 10 and 0? Laura says, "Now imagine 10 groups of zero.

That would still be zero." All zero groups of 10 would still be zero, wouldn't it? So the product of zero and 10 is zero as well.

So this could be the zero times table, couldn't it? We've got 0 x 0, 1 x 0, 2 x 0, 3 x 0.

And then with our factors written the other way round, what do you notice? Laura says she's noticed that, "When zero is a factor, the product is zero." And for all of those, that's true, isn't it? When zero is a factor, the product is also zero.

"When you find groups of zero, or nothing, your product will be zero." Time to check your understanding.

Look at the table and using what you know about zero as a factor, fill in the gaps.

So there are two gaps at the bottom of the table there.

What could you write there to continue the pattern, thinking about what you know as zero as a factor? Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? Did you spot that carrying on the pattern we'd have 4 x 0 = 0 and 0 x 4 = 0.

And Laura says it's still working, "When zero is a factor, the product is zero." It doesn't matter how many groups of zero we've got or if we've got zero groups of something, our product will always be zero.

Aisha continues to explore the zero times table.

She says, "I know that 15 x 0 must be equal to zero." Is Aisha right? Can you explain your thinking? Laura says, "Yes, you're right, because when zero is a factor, the product is zero." It doesn't matter how many of those zeros we've got, the product is always going to be zero.

And Laura says, "Imagine 15 groups of no sweets, or zero sweets.

You'd have lots of nothing." Time to check your understanding.

Is Aisha, right, and can you explain your thinking? Aisha says, "I know that 0 x 50 = 0." Pause the video, have a think, and when you're ready for some feedback, press play.

What did you think? Laura says, "Yes, because when zero is a factor, the product zero." It doesn't matter how big the other factor is, if one of those factors is zero, then the product will be zero.

Aisha and Laura now look at the One times table.

So what's the same here? Aisha says, "One factor is 1 and the other is 2." 1 x 2 and 2 x 1.

And Laura says, "The product is 2 in both equations." 1 x 2 = 2 and 2 x 1 = 2.

What's different about these equations? Ah, Aisha says, "The order of the factors has changed." We've got 1 x 2 and then we've got 2 x 1.

"Cool," says Laura.

"But the product is still the same." One group of 2 is equal to 2 and 2 groups of 1 are equal to 2.

Or 1 group of 2 is equal to 2 and 2 one time, is equal to 2.

Now Aisha and Laura are looking at the 2 and 5 times tables.

Aisha says again, "One factor is 1 and the other factor is not 1." They are both one group of something.

So we've got one group of 2 or 2 one times, and one group of 5 or 5 one times.

Now look at these two equations, and what's different about them? Pause the video, have a think, and when you read for some feedback, press play.

What did you spot that was different? Was it the product, the order of the factors, or the operation? That's right, it was the order of the factors again, wasn't it? We had 1 x 10 = 10 and 10 x 1 = 10.

So what is the product of one and two? Remember, a product is when we multiply two factors together and the factors in this case are one and two.

Aisha says, "I can use the pattern in the table to help me." Laura says, "1 group of 2 is 2.

I'm imagining 1 group of 2 bananas, which is 2 bananas." So the product of 1 and 2 is 2.

And we could have those 2 bananas 1 time for 2 x 1, couldn't we? What is the product of one and 10? Laura says, "If I imagine one group of 10 bananas, that's 10 bananas." So the product of 1 and 10 is 10.

1 x 10 = 10 and 10 one time is equal to 10.

So these facts can be seen as the one times table.

What do you notice? Well, Laura says, "When one is a factor, the product is equal to the other factor." Ooh, let's just think about that.

"When one is a factor, the product is equal to the other factor." Let's look at those times tables.

Well, 1 x 1 = 1, but 2 x 1 = 2, 3 x 1 = 3.

So yes, when one is a factor, the product is equal to the other factor.

And we can see that especially in the 2 x 1 and the 1 x 2 and the 3 x 1 and the 1 x 3.

So Laura says, "Having one group of something will give you the value of that group." So one group of 3 is equal to 3.

3 one time, is equal to 3.

Time to check your understanding.

Look at the table, use what you know about 1 as a factor to fill in the gap.

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

How did you get on? Did you spot that continuing the pattern, we'd get 4 x 1 = 4 or 1 x 4 = 4? And Laura says again, "When one is a factor, the product is equal to the other factor." We've got 1 group of 4, which is equal to 4, and 4 one time, which is equal to 4.

Aisha and Laura move on to solving problems using what they have learned.

So here they've got a sort of game board here, haven't they? And they're multiplying by zero.

So all the numbers outside are being multiplied by zero and the products are in the outside.

Laura says, "Let's look at this section first." They've put a purple box around it.

"0 x 2 is to.

." Ah, we've got to remember, when zero is a factor, the product is equal to zero.

"0 x 2 is equal to 0, so we place a zero here." And she's added a zero into the outside ring.

"Now let's look at this section," here.

We've got 0 x 3 or 3 x 0.

And Laura says, "I know that anything multiplied by zero is zero because there will be zero groups." So we can put a zero here in our outside ring.

Then there's a slightly different problem.

This time we've got a times one problem.

So we've got a times one in the middle and all the numbers in the next ring out, are going to be multiplied by one, and we put the product in the outside.

So let's look at this bit first, 1 x 2.

Remember, when one is a factor, the product is equal to the other factor.

So 1 x 2 must be equal to 2.

So we can place a 2 here.

Laura says, "Now let's look at this section." We've got 1 x 3.

She says, "I know when anything is multiplied by one, the product is equal to the other factor." So 1 x 3 must be equal to 3.

So time to check your understanding.

You've got one of their boards with a times 1 in the middle and one with a times 0 in the middle.

Can you fill in the gap in each one, using your knowledge of 0 and then 1 as a factor? So pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So with the times one, we had 1 x 5, and we know that when one is a factor, the product is equal to the other factor, so 1 x 5 = 5.

And for the other one, we had 0 x 5.

And we know that when zero is a factor, the product is also equal to zero.

So 0 x 5 must be equal to 0.

Well done, if you've got those right.

And it's time for you to do some practise now.

You've got some more of these boards, you've got some times zero boards, and then you've got one with a missing bit.

What are we multiplying by? And Laura says, "Can you fill in the gaps and remember that when zero is a factor, the product is.

." Hmm, you're going to fill in the missing word there in the stem sentence.

And then for question two, you've got some boards with a times 1 in the middle or a missing gap in the middle for E.

And Aisha says can you fill in her stem sentence, "When one is a factor, the product is.

?" Hmm, so pause the video, have a go at your tasks and when you're ready for some feedback, press play.

How did you get on? So in this first one, all of these were about multiplying by zero.

So all of our products around the outside were going to be zero, because our stem sentence is completed.

"When zero is a factor, the product is 0." And there was a gap there in E wasn't there? And Laura says, "This could have been any number, as the product will always be zero." You could have had as big a number as you know to write in that gap, but zero times whatever number it is, will always be equal to zero.

When zero is a factor, the product will always be zero.

How did you come with number two? This was all about multiplying by 1.

And we know that when 1 is a factor, the product is equal to the other factor, isn't it? So we had gaps to fill in here, but they would always be equal to the other factor, the factor that isn't 1.

So well done, if you've got all those correct.

You might want to pause here and just check that your numbers were all correct on your sheet as well.

And on into the second part of our lesson.

We're going to be looking at comparison, comparing things.

So Aisha is comparing the zero times table expressions.

So she's got 0 x 2 and 2 x 0.

"This is the same as saying zero groups of 2 equals 0," Aisha says.

And Laura says, "When zero is a factor, the product is 0." So 0 x 2 must be equal to 2 x 0.

So they can write an equal sign in that circle that has the missing symbol between our two expressions.

0 x 2 is equal to 2 x 0.

So we've now got 2 x 0 and 5 x 0.

And the question is, which is greater? Hmm, what do you think? And Aisha says, "Remember, when zero is a factor, the product is zero." And Laura says, "Well, zero groups of 2 is equal to zero." And, "Five groups of 0 is equal to zero," as well.

So 0 x 2 is equal to 5 x 0.

Because zero is one of those factors, the product will always be zero.

So it doesn't matter how many times we've got zero, we are always going to have a product of zero.

So those expressions will also be equal.

Aisha is comparing the zero times table and the one times table this time.

So she's got 1 x 10 and 0 x 10, and she's got to put a symbol in the circle to say which one is greater or less than or whether they are equal.

So let's look at the 10 times table.

Well, 1 group of 10 is 1 group of 10, isn't it? And there it is with a 10 stick.

And it's got to be greater than 0 groups of 10, because there is one more group of 10.

And we also know that when zero is a factor, the product is zero.

We know also that when 1 is a factor, the product will be equal to the other factor.

So, 1 x 10 = 10 and 0 x 10 = 0.

So 1 x 10 is greater than 0 x 10.

Aisha is comparing the zero times table and the one times table.

So she's got 1 x 10 is greater than, less than or equal to 0 x 10 + 0.

What do you think should go in the circle? Aisha says, "I think the second expression is greater because there are more numbers." She's got 0 x 10 + 0 there, hasn't she? So she's got three numbers in her expression.

Let's represent them with the base 10 blocks.

We've got 1 x 10 on this side.

And Laura says, "Zero groups of 10 add zero is equal to zero." We know that when zero is a factor, the product must be zero.

So 0 x 10 is equal to zero.

And we've added on another zero, so there's no more to add.

So 1 group of 10 is greater than 0.

Any factor multiplied by zero is zero, and 0 x 10 + 0 just adds another zero to the zero.

So 1 x 10 is greater.

Aisha and Laura are playing a card game.

The card with the highest value wins.

Let's have a look at their cards.

They've got 1 x 0 and 1 x 1.

Ah, which is greater? Aisha says, "One of my factors is zero, which means I have 1 group of nothing." "Laura wins because she has 1 group of 1." And she's got 1 group of 1 cupcake on her plate, 7 x 0 and 0 x 5.

Hmm, Aisha says, "One of my factors is zero, which means I have 7 groups of nothing." "Laura also has 5 groups of nothing, which means we both lose." They each had a factor of zero, so the product would be zero.

Time to check your understanding.

Who won and how do you know? Here are the cards.

So who won, Aisha or Laura? Pause the video, have a go, and when you're ready for some feedback, press play.

What did you think? Aisha wins, doesn't she? Because Laura has a card with a factor of zero.

This means her product is 0.

So Aisha wins, she had 12 x 1.

Time for you to do some practise.

So question one, "Using your knowledge of groups and when factors are 0 and 1, can you fill in the gaps?" Can you put in a greater than, less than, or equal sign, in between these expressions? And for question two, you could continue playing Aisha and Laura's game.

You've got some cards, I think.

Whoever has the greater value on the card wins the point.

So in this one, Aisha wins, because she has 1 group of 12, which is greater than 0 groups of 5.

And for question three, Aisha picked the card, 2 x 1.

Laura lost that round.

Can you write down two cards that Laura might have picked that would've been less than 2 x 1? Pause the video, have a go at your tasks, and when you're ready for some feedback, press play.

How did you get on? So in A, we had 0 x 5 and 1 x 5.

And we know that when zero is a factor, the product is zero.

So 0 x 5 is less than 1 x 5.

In B, we had 0 x 5 again and we added 0.

It's still equal to zero, isn't it? So it's less than 1 x 5.

In C, 2 x 1 is equal to 1 x 2.

We know that multiplication is commutative.

So we can change the order of the factors and the product stays the same, so those are equal.

In D, we've got 2 x 1 again, and we've got 1 x 2, but this time, we've added a 2.

So 2 x 1 must be less than 1 x 2 + another 2.

In E, 10 x 0 is less than 10 x 1.

And did you spot in F, we just swapped the expressions around.

10 x 1 is greater than 10 x 0.

In G, 5 x 1 is greater than 7 x 0.

7 may be a larger number than 5, but 7 lots of 0 is going to be equal to 0, because we know that when zero is a factor, the product is zero.

In H, we've got 5 x 1 again, and we've got 7 x 0 again plus 0.

It's still equal to zero, so 5 x 1 is still greater.

In I, 12 x 0 is less than 1 x 12.

And in J, 12 x 0 is less than 1 x 12 plus another 12 as well, isn't it? And for question two, I hope you had fun playing Aisha and Laura's game.

Here's one round that they played.

And Aisha says, "We drew because when zero is a factor, the product is zero." Because 5 x 0 and 0 x 5 both have a product of 5.

And for question three, Aisha picked the card 2 x 1, but Laura lost that round.

Can you write two cards that Laura may have picked? So Laura could have picked 1 x 1, which would be less than 2 x 1.

Or she could have picked 0 x 1, or anything times zero actually, would've been smaller, wouldn't it? So 1 x 1 or anything multiplied by 0.

Well done, if you got those right.

And I hope you enjoyed the activities.

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

We've been explaining how a factor of zero or one affects the product.

What have we learned about? Well, we understand now that when zero is a factor, the product is zero.

And we also understand that when one of two factors is 1, the product is equal to the other factor.

And we can now use this knowledge to solve problems and to make comparisons.

Thank you for all your hard work and your mathematical thinking today.

I hope I get to work with you again soon.

Bye-Bye.