# Lesson video

In progress...

Hello and welcome.

My name is Miss Thomas and I'm really looking forward to going through our maths lesson with you today.

But before we start, I wanted to talk to you about things that we're pleased with.

Something that I've been really pleased with is some seeds that I grew recently.

A few weeks ago I planted some herb seeds and here I've got some parsley, I've got some thyme, and I've got some chive.

I'm really pleased because they've come along loads recently and I think that my chive's going to be very tasty in a ham sandwich.

What have you been pleased with recently? I bet there's a lot.

Let's get ready to begin our maths lesson for today.

In today's lesson agenda, first we will be exploring pictorial representations to show multiplication and division equations.

Then we will move on to our talk task where you can have a practise.

After that, we will develop our understanding of how to find the inverse of division and multiplication equations.

Finally, we will finish off with a quiz where you can test yourself on the learning.

For today's lesson, you will need a pencil, paper, and a ruler.

Pause the video now if you need to get your equipment.

Let's get going.

Let's read the equation four times three is equal to 12.

Four times three means four groups of three or four lots of three.

This is equal to 12.

I can see this from the array because there are 12 counters in total.

Our new star word is commutative.

My turn, commutative.

Commutative means to get the same result whatever order the values are in.

I have the equations four times three is equal to 12 and 12 is equal to three times four.

I can swap the three and the four around because multiplication is commutative.

Notice as well, where my equals sign is.

12 is equal to three times four and four times three is equal to 12.

It doesn't matter if the whole comes first in the equation or last.

Does one of the equations belong with array A and the other belong with array B? Pause the video now and have a think.

You might have noticed, it's actually the same array.

It has just been grouped differently.

This is because multiplication is commutative and it doesn't matter which order you write the factors, as the product, the answer, will be the same.

So the array actually matches both equations.

Now, if you're feeling confident, it's time for you to have a go.

If not, we'll go through the answers together.

So match the pictorial representation with the equations.

Remember that more than one equation can be represented because of the commutative law.

Pause the video now.

Let's look at the first array.

I can see that there are seven groups of four or four groups of seven, depending on which way you look at it.

So I'll match these equations.

So I'll match it with these equations.

Next, the array below has three groups of four.

So I'll match with these equations.

Finally, let's take a look at the bar model.

This shows four groups of nine is equal to 36, so I'll match with these equations.

Now, let's create our own pictorial representations for the equation six multiplied by three.

We will represent six multiplied by three using an array.

Looking at six times three, I know that I will have six groups of three, so let's draw my array.

So I've got one group of three, two groups of three, three groups of three, four groups of three, five groups of three, and finally, six groups of three.

Let's move on to my sentence stem.

Listen carefully because it'll be your turn to do a sentence stem next.

There are six groups which represents the number of equal parts.

Each group has three counters which represents the value of the parts.

Altogether there are 18 counters which represents the whole.

Now it's your turn to create your own array for the equation five times two.

I want to hear you saying your sentence stem.

If you say it clear enough, I might just hear you.

Great work, everybody.

Let's have a look at the answers together.

Five times two is like saying five groups of two.

So let's have one group of two, two groups of two, three groups of two, four groups of two, five groups of two.

Give yourselves a pat on the back for your array.

Now let's have a look at the sentence stem.

There are five groups which represents the equal parts.

Each group has how many counters? That's right, two counters which represents the value of the parts.

And altogether there are, great job, 10 counters which represents the whole.

We're going to create different pictorial representations now for the equation six times three.

In my array, there are three rows which represents the number of equal parts.

Each column has three counters which represents the value of the parts.

Altogether there are 18 counters which represents the whole.

Next we have a bar model.

There are three bars with a value of six.

Altogether the bars equal 18, which matches my equation six times three because it's equal to 18.

Let's have look at the number line.

On the number line, there are three jumps of six.

Altogether the jumps equal to 18.

Again, this representation matches my equation of six times three because it's like saying six groups of three.

Now it's your turn to draw your own representations for three times four is equal to 12 and 12 is equal to four times three.

Have a look at my examples to give you some ideas.

Pause the video now and have a go.

Welcome back.

Great work.

Here are some examples of the answers.

Let's take a look at the bar model with bars with the value of three.

Can you spot them for me? Well spotted.

The bars have a value of three which represents the value of the bars.

There are four equal parts, each with a value of three, so what is the value of the whole? You've got it.

It's 12 because three lots of four is equal to 12.

I want you to choose your favourite representation either out of my examples or the ones you've done and explain out loud how it represents the equations.

Pause the video now and explain.

Excellent explaining.

Well done.

Our new star word is, my turn, inverse.

The definition of inverse is the opposite operation.

We're going to explore how multiplication and division are the inverse operations, the opposite operations.

Meet Amirdhini and Stefan.

They're learning too.

Amirdhini has asked what will you look for in a representation of this equation? 20 divided by four is equal to five.

Stefan's replied, I will look for a whole of 20 with four equal parts or five equal parts of four.

Amirdhini is left wondering.

How can the same array represent division and multiplication equations? Stefan explains that it's because multiplication and division are the inverse operations, one array can model four equations that have the same whole and the same number of equal parts.

This is a picture of the same array, but depending on how you group the counters, you can represent four equations.

Have a think what the equations could be for this array.

Remember that we can use multiplication and division.

Pause the video now.

Welcome back.

Great job.

Here are some answers that you may have got.

Let's have a go at matching the representation to the correct equation.

Have a think about which equation the array matches with.

There is only one.

Pause the video and decide.

Excellent work.

Let's take a look.

So first, let's look at seven times 21 is equal to three.

We know that this is incorrect as we do not have seven groups of 21 and it does not equal three.

Next let's look at 21 divided by seven is equal to three.

Within our array, we have 21 counters, they are shared equally into seven columns, and in each group there are three.

This is the correct representation for the equation.

Lastly, let's take a look at seven is equal to three divided by 21.

This is incorrect as the array does not represent three divided equally into 21 groups.

Give yourselves a thumbs up because you're now ready for the independent task.

It's time for you to show off just how much you've learned.

You need to match the equations with the image that could be used to represent it.

Each representation matches with one equation, so think carefully about how they are grouped so you match the correct equation.

Good luck.

Great work, everybody.

Let's have a look at the answers.

Compare yours to mine and see if you've got them correct.

If you make a mistake, now is the time to correct it.

Give yourselves a pat on the back for all your hard work.