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Hello and welcome to today's Math lesson.

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

I've just got back in from a run outside so I'm feeling really energised and ready to get going.

I hope you've done something today that's made you feel energised and ready to learn.

If not, if you haven't done something yet, there's plenty of time after the lesson to find something refreshing and energising to do.

Have a think, see what you could do.

Let's get started with our maths lesson today.

In today's lesson agenda.

First, we'll be representing multiplication word problems. Then we'll be carrying out some matching activities and say it out loud sentence stems in our talk task.

After that, we'll learn what it means to derive facts from known facts and finally, you'll complete the end of lesson quiz.

During the lesson, you're going to need a pencil, paper and a ruler.

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

Okay, my equation here says three multiplied by seven is equal to 21.

I want to write a word problem to match this equation.

So, let me think about what this equation means.

I've got here, three lots of seven or seven three times.

So, this is the word problem I've come up with.

Reem shopping three pencils on Monday.

On Tuesday, she sharpened seven times as many.

How many did she sharpen on Tuesday? I know that my amount has to be multiplied seven times in order to find my final answer.

Now, you have a go at creating your own word problem.

Pause the video now to have a go with this.

Let's look at two new star words for today.

Factor.

Factors are numbers that you can multiply to get another number.

Next one, product.

Product.

The product is the answer when two factors are multiplied.

Have a look at our equation, which numbers would you consider to be factors and which number would be the product? See if you can label your own equation.

Three and seven are the factors.

They are the numbers we multiply together to get a product.

21 in this instance is our product.

The result of two factors being multiplied together.

We've got another star word.

My turn, commutative.

Let's say that one again, that's a tricky one.

My turn, commutative.

Commutative means getting the same multiplication whatever order the digits are in.

So remind me, what's the factor? Call it out loud.

Brilliant.

Numbers you can multiply to get another number.

So, remind me, what's the product? Call it out loud.

Great job.

The answer when factors are multiplied.

Now, I would like you to read the definition of commutative out loud once more.

Brilliant.

Getting the same product, whatever order the digits are in.

Now, we're going to look at what happens when we change the order of 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.

It's all the same thing.

So, let's have a go.

I've got one group of seven or one lot of seven, two, lots of seven, three lots of seven.

Here is the exact same array.

Can you group the array so that the factors three and seven are in a different order? So, instead of saying three lots of seven, you could say seven lots of three.

Pause the video now and have a go.

You may have found that you can 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.

So, I've got one lot of three, two lots of three, three lots of three, four lots of three, five lots of three, six lots of three, seven lots of three.

That's right.

You can change the order of the factors and the answer will be the same.

Here, both the arrays have 21 counters.

So, if three times seven is equal to 21 and seven times three is equal to 21.

Multiplication is communicative.

Their ratio is more commutativity on its own depending on which way we group the counters.

However, some representation do not show commutativity on their own like an array does.

Here, the blue bar model shows three groups of seven but it doesn't show seven groups of three.

So, we have to have the yellow bar more do on top to show commutativity.

And the same with the number line.

The first number line shows three groups of seven but it doesn't show three lots of seven.

It doesn't show.

Sorry, it doesn't show seven lots of three, we have to have the other number line next to it.

Here, I've got a bar model that shows three lots of seven.

Can you have a go now at drawing your own bar model to show the commutativity law with three and seven? Pause the video now and have a go.

Great job, check your bar model against mine.

You should have a bar with seven equal parts with a value of three.

Well done if you got that.

We are now at the talk task.

The question says, what could these represent? What are the factors and what are the products? I can see here, I have a number line.

There are five jumps or five equal parts, each for the value of nine.

I'm going to complete my say it out loud sentence turn.

Listen carefully because you'll need to do yours in a moment.

Number one, the factor is five because there are five equal groups.

Number two.

The other factor is nine because nine is the value of each equal group.

Number three, final one.

The product is 45 because there are five equal groups with the value of nine.

My number line represents five groups of nine, which is equal to 45.

So, I can say five times nine is equal to 45.

Look carefully at the bar model, decide how many equal parts they are and decide what is the value of each part.

Then, complete your say it out loud sentence then after that, write down the equation to match the bar model.

Great job, let's go through the answers.

First, there are seven equal parts on my bar model, each with the value of four.

Let's read the say it out loud together.

Number one.

A factor is seven because there are seven equal groups.

The other factor is four because four is the value of each group.

Number three, the product is 28 because there are seven equal groups of four.

Finally, let's write our equation, check yours against mine.

Here we have seven groups of four which is equal to 28.

So, we now know the factors are seven and four.

So, seven times four which is equal to the product 28.

Check yours, correct it if you made any mistakes and let's keep going.

Well done.

Let's recap.

We've got some matching now.

Match the green pictorial representations to the correct pink.

Pause the video to match the green to the pink.

Okay, welcome back.

Let's look at the answers together.

These matches because here we have two columns of five counters.

Say two lots of five.

Next, we have six bars of two or six groups of two.

After that, we have an array of squares which is three groups of four or three times four.

Finally we have five equal parts with the value of three so we match our continuous addition three plus three plus three plus three plus three.

In maths, we have many known facts, many of which we know mentally just like how you might know some of your times tables.

That is going to be one of our star phrases today.

My turn, known facts.

But from these known facts, we can derive facts.

My turn, derived facts.

Your turn, derived facts are facts that we make using our known facts.

So, we don't have those already in our head but from the known facts, we can derive new facts.

We're going to explore what that means now.

We're going to use our knowledge of multiplication tables and place value to find other multiplication facts, to derive other multiplication facts.

She's wondering, "If I know that three times seven is equal to 21, what else can I work out?" Stefan says, "If each counter has a value of 10, then the array would represent three groups of 70 because there are seven counters in each group." I've got one group of 70, two groups of 70, three groups of 70.

Three groups of 70 is the same as three times 70, which is equal to 210.

So, if I know three times seven is equal to 21, I can derive that three times 70 is equal to 210.

The product is 10 times greater because our factor was 10 times greater.

Let's practise driving facts from known facts.

The word problem says.

By the end of June, a sunflower is 30 centimetres tall.

By the end of August, the sunflower is five times as tall.

How tall is the sunflower by the end of August? Think about your known facts.

Stefan says, pause the video now and draw your own array to represent the word problem with each counter having the value of 10.

Pause the video now and have a go.

Excellent, let's look at Stefan's array.

You can compare his to yours.

He says each counter has the value of 10.

So, we need three counters to represent 30.

And we will need five groups because there's some flower grew five times bigger than 30 centimetres by the end of August.

So, I've got one group of 30, two groups of 30, three groups of 30, four groups of 30, five groups of 30.

"Well, I could do that mentally.

I know that five times three is equal to 15.

So, I also know that five times 30 is equal to 150." If the factor or if a factor rather is 10 times greater, the product will be 10 times greater.

Now, it's your turn to create an array to represent the word problem.

This time we're looking at 100 counters.

So, they've got the value of 100 each counter.

Pause the video to complete your array.

Brilliant, let's look at the answers.

Jo sells 300 ice creams every day.

We want to find out how many she sells in one week.

That is the missing hole we want to find.

One of my parts 300 and the other is seven because there are seven days in one week.

I need seven groups of 300.

One group of 300, two groups is 300, three groups of 300, four groups of 300, five groups of 300, six groups of 300, seven groups of 300.

Seven times 300 is equal to 2,100.

You could use your known facts because we know that three times seven is 21 and 300 is a hundred times greater than three.

So, our product needs to be a hundred times greater than 21, so it's 2,100.

We're going to practise deriving facts, 10 and 100 times greater than known multiplication facts.

Here you have a multiplication fact.

Three multiplied by seven is equal to 21.

Using this, derive your own facts.

Use 100 counters and 10s counters to derive new facts.

Remember to swap the factors because multiplication is commutative.

Once you've completed your arrays, write the equations to match.

Time to check through the answers together.

First, let's look at deriving facts using the 10s counters.

Here we have three groups of seven but the counters have a value of 10.

So, the equation is 30 times seven is equal to 210 or with the commutative law, seven times 30 is equal to 210.

I just swapped the factors.

Next, we could have seven groups of three with counters with a value of 10, the equation could be 70 times three is 210 or three times 70 is equal to 210 because of the commutative law, we can swap the factors and the product will be the same.

Now, let's look at the 100 counters.

We could have three groups of seven where the counters have a value of 100.

So, from three multiplied by seven, we know that 300 times seven is equal to 2,100.

Because of the commutative law, we can also derive seven times 300 is equal to 2,100.

Lastly, we could have seven groups of three and the counters have a value of 100.

So, the equation is 700 times three is equal to 2,100 or say three times 700 is equal to 2,100.

We know the factors can be switched and the product is still the same because multiplication is commutative.

Well done, we've learned to derive facts 10 and 100 times greater than known multiplication facts.

Give yourselves a pat on the back.

Well done for today.

It's time to show off your learning and go and complete your quiz.

And we have come to the end of the lesson.