Lesson video

Hello, and welcome to today's math lesson.

My name is Miss Thomas and I'll be going through the lesson with you today.

We're looking at multiplication and division.

So I hope you brought your thinking caps with you, and you've got yourself in a good frame of mind ready to get stuck in with the learning.

Off we go, let's get started.

So in today's lesson first will be representing division and multiplication equations.

Then you'll complete the let's explore task where you can have a practise on your own.

After that, we'll learn how to derive multiplication and division facts.

Finally, you can show your understanding in the end of lesson quiz.

The equipment you will need for the lesson is a pencil, paper and a ruler.

Pause the video now and gather your equipment if you have not done so already.

Let's begin.

Our new star word is my turn, divide your turn, divide means to share an amount equally.

My equation says, 21 divided by three is equal to seven.

I'm going to write a word problem to match the equation.

So I need a whole of 21 and share it equally by three to find my missing part of seven.

My problem says, Tayvon shared 21 of his Pokemon cards equally by three of his friends.

How many Pokemon cards did each friend get? Have a go now at writing your own division word problem to match the equation.

Pause the video to write your word problem.

Great job.

You may have found that you use the term share equally in your word problem, as we know now from our star word divide.

This is what it means to divide.

We've got another star word, my turn commutative, your turn.

Commutative means getting the same product, whatever order the digits are in.

Now we're going to have a look at what happens when we change the order of the digits, or the order of the factors.

Here we have an array.

I'm going to group the counters to show three times seven, or three lots of seven, or three groups of seven.

So I've got one group of seven, two groups of seven, three groups of seven.

This is shown three times seven.

Here is the exact same array.

Can you have a go at grouping the array, so the factors three and seven are in a different order? Pause the video now and have a go.

Great, you may have found that if you change the order of the factors, it would be seven times three or seven groups of three or seven lots of three.

Let's check my grouping.

Compare yours to mine, one group of three, two groups of three, three groups of three, four groups of three, five groups of three, six groups of three, seven groups of three.

What do you know about the order of the factors in multiplication? Call out your answer now.

That's fine, you can change the order of the factors and the answer will be the same.

Here both arrays have 21 counters.

So three times seven is 21.

And seven times three is 21.

Can you now have a go at saying a sentence out loud with the word multiplication and commutative in the same sentence? Have a go.

You could have said multiplication is commutative.

The array shows commutativity on its own, depending on which way we group the counters.

Our Pokemon word is my turn, inverse, your turn.

This means opposite.

Multiplication and division are the inverse operations to each other.

Here we have the equation three multiplied by seven is equal to 21 and 21 divided by three is equal to seven.

The arrays represent the equations.

Have a look at the arrays carefully.

What do you notice about the arrays? Pause the video and decide.

Welcome back, you may have noticed that the arrays are in fact the same, you might have realised that this is because division is the inverse to mode of multiplication.

Three times seven is the same as saying three groups of seven.

One group, two group, three groups of 7.

21 divided by three is the same as saying, sharing 21 equally by three.

So we've got 21 counters in our array, and we're going to put them in groups of three, one group of three, two groups of three, three groups of three.

So if I know, 21 divided by three is equal to seven I also know that 21 divided by seven is equal to three because of the commutative law.

And if I know that my division equations, then I know my multiplication equations, for the same array, because they are the inverse operation.

I know that three times seven is equal to 21, and because of the commutative law, I know that seven times three is equal to 21.

So with arrays, you have four known facts.

Some representations are not like arrays, and they don't show commutativity on their own.

Here, if you look at the bottom, we've got two bar models.

Now, I'm trying to represent my division equations using bar models.

The first one is got 21 shared equally by three is equal to seven.

I need the second bar model to show the commutative law because I need seven bars, 21 shared equally by seven is equal to three.

Have a look at the top one now it says 21 shared equally by three is equal to seven.

Can you draw the next bar, the next sorry, the next number line to show the commutative law of division.

Have a go.

Pause the video now to have a go.

Fantastic, you should have a number line with seven equal parts with the value of three.

Now it's your turn to write the known facts for the representations one and two.

Pause the video and write the equations.

Remember, arrays you have four known facts because we can group the counters in different ways.

But on your bar model, you'll only have two known facts.

Pause the video now.

Let's look at the first array.

I have four groups of five or five groups of four, which is equal to 20.

And we have 20 counters shared equally by five, or equally by four.

For number two, it does not represent four equations because there are only five equal groups.

So my equation could be five times seven is equal to 35, or 35 divided by five is equal to seven.

Take your answers if you've got them correct.

And if you made any mistakes, don't worry, but now's your time to correct them.

Next, we're going to write down our known multiplication and division facts.

If you know that seven times six is equal to 42.

What else do you know? Pause the video and write down your four known multiplication facts.

You could have had seven times six is equal to 42.

And then because of the commutative law, it means you could have had six times seven is equal to 42.

Because division is the inverse to multiplication, you could have had 42 divided by six is equal to seven, and 42 divided by seven is equal to six, because of the commutative law.

Now we're looking at deriving multiplication and division facts from known facts.

This time the array is already grouped into columns of seven.

If you look carefully, you can see those lines between the counters, and that that shows that they're already in groups.

I know that seven times six is equal to 42.

I have used 10 counters in my array, so my whole is going to be 10 times greater.

I could derive the fact that seven times 60 is equal to 420.

One group of six, two groups of six and one group of 60, 2 groups of 60, 3 groups of 60, 4 groups of 60, 5 groups of 60, 6 groups of 60, 7 groups of 60 and that's equal to 420.

Pause the video now and complete the missing number equations.

Brilliant, here are the equations the array could represent because multiplication and division are the inverse operations.

Now we have counters with the value of 100.

I know my answer will be 100 times greater than 42.

So it will be 4,200.

I'm trying to find out 4,200 divided by seven, I can count how many tens counters.

Sorry how many hundreds counters are in each group.

If you look carefully at this array, you can see that there are lines already grouping the counters.

Pause the video and count one of the groups.

Brilliant, so there are one, two, three, four, five, six, seven equal groups and each group has 100, 200, 300, 400, 500, 600.

You might have noticed too that 100 times greater than our known facts.

Next, so here's our first one.

4,200 divided by seven is equal to 600, because we've got seven groups, and each group has six the value of 600.

So we know that seven multiply by 600 is 4,200 because division and multiplication are the inverse operation.

Next, you need to complete the equations using the arrays to help you remember, check and see how the arrays are grouped.

Pause the video now to complete the missing number equations.

Great job you may have noticed the arrays are the same but one is 10 times greater than the other.

In the first where the counters have the value of 10, here are your answers.

In the second where the counters have the value of 100.

Here are answers, there are still six equal parts in each array, but the value of the counters is 10 times greater in the blue array than the orange array.

Brilliant work, you're now ready if you're independent task.

Let's begin.

We have known facts in the middle of the main map.

we need to decide what multiplication facts we can derive from our known fact.

42 divided by seven is equal to six.

Step one, derive facts and represent this by drawing an array that has the counter values of 100 or 10.

Step two derive facts from the known fact use the given arrays on your sheet or on your slides.

Remember, in these arrays, the counters have already been grouped if you looked very carefully at the lines.

See what facts you can derive from the known facts.

Pause the video now and complete your independent task.

Fantastic work, let's check through our answers together.

When we read the equation 42 divided by seven is equal to six, we should think of it as 42 equally shared between seven.

So we know that we need seven equal groups in our array, these are the arrays and the equations you could have had, tick and correct them now.

Fantastic work today you can now derive facts from known facts 10 times and 100 times greater.

Now let's complete our quiz to show just how much we've learned.

And we have reached the end of the math lesson.

You should be feeling very pleased with yourselves well done for all of your hard work.

Have a wonderful rest of your day and I will see you next time.

Well done.