Lesson video

Hello, I'm Ms. Miah, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be able to represent equal groups as repeated addition and multiplication.

Your keywords are on the screen now, and I'd like you to repeat them after me.

Multiplication.

Group.

Fantastic.

And we're going to be using these keywords throughout the lesson.

Now this lesson is all about representing equal groups as repeated addition and multiplication.

We have two lesson cycles here.

Our first lesson cycle is all to do with looking at multiplication.

We then go on to looking at different representations for multiplication as well in the second cycle.

So are you ready? Let's begin.

In this lesson, you will meet Alex and Jacob.

And here and there, I might also drop in.

So let's begin.

I'm organising a dessert stall for the Easter fair.

You can see here that I've got some desserts that I've arranged in groups.

Jacob says he can see four bundles each with three cake pops.

That is the same as saying 3 plus 3 plus 3 plus 3.

Now from another lesson, you may remember that this equation here is known as a repeated addition expression.

So we can represent the groupings as a repeated addition expression, but you can also write this as 4 multiplied by 3, or you might say times.

So 4 times 3.

The 4 represents the number of groups.

The 3 represents the number of cake pops in each group.

This is the multiplication sign.

So it looks like the X from the alphabet, but actually, in the mathematical world, this symbol represents multiplication.

You can represent repeated addition using multiplication.

Now Alex makes a prediction.

I add another bundle of cake pops.

Is that the same as 5 times 3 or 5 multiplied by 3? What do you think? I'd like you to explain your thinking to your partner.

Well, Jacob says, I can see five bundles each with three cake pops.

That is the same as saying 3 plus 3 plus 3 plus 3 plus 3.

So there are five groups of three.

That is the same as 5 times 3.

So you've got your repeated addition expression on the left, which shows 3 plus 3 plus 3 plus 3 plus 3, which is equal to 15 cake pops altogether.

And then you've also got 5 times 3.

So these are two different ways that you can represent equal groups.

The 5 represents the number of groups and the 3 represents the number of cake pops in each group.

So that means Alex is correct.

3 plus 3 plus 3 plus 3 plus 3 is the same as 5 times 3.

Over to you, I'd like you to gather some pencils and show 3 times 2, and I'd like you to complete the sentence below.

So that is the same as something times something or something add something, add something.

You could pause the video here.

So how did you do? Well, you may have arranged your pencils like this.

That is the same as 3 times 2 or 2 plus 2 plus 2.

Ms. Miah is now setting up the cake slices.

Jacob says, "I can see four groups, each with four slices of cake." That is the same as saying 4 plus 4 plus 4 plus 4.

You could also write this as 4 times 4.

Now the 4 represents the number of groups.

This 4 represents the number of cake slices in each group.

Now we've got five groups, so that is five groups of four, which is the same as 5 times 4.

Let's move on.

As the day progresses, we're adding on more groups of desserts.

Alex says that the display table is not big enough.

I will have to reduce the amount.

I'll remove some.

There we go.

Perfect.

So Jacob says that that is two groups of four, which is the same as 2 times 4.

Over to you, I'd like you to gather some pencils and show 2 times 5, and then complete the sentence.

You can pause the video here.

So how did you group the pencils? Well, you may have grouped them like this.

That is the same as 2 times 5 or 5 plus 5.

Onto the main task for your lesson cycle.

For question one, you're going to fill in the gaps using the images to help you.

So you've got some milkshakes on the left, and what I'd like you to do is write the repeated addition expression first, followed by the multiplication equation, and then you've got some sweets on the right.

So what I'd like you to do is do the same.

So you're going to write the repeated addition, followed by the multiplication expression.

Now for question two, lollipops come in packets of three.

Jacob says he has two packets, so that means there are two equal groups of three lollipops.

He can represent this as multiplication or addition expressions.

So for example, two equal groups of three is the same as saying 2 times 3 or 3 plus 3.

I'd like you to do the same for Izzy.

She's got four packets and Jun has six packets.

You could pause the video here.

Off you go.

Good luck.

So how did you do? Well, for question one, this is what you should have got.

The first addition expression, we can see that there are three groups of three milkshakes.

So that's 3 plus 3 plus 3 or 3 times 3.

Then we've got three groups of four milkshakes, so that's the same as 4 plus 4 plus 4 or 3 times 4.

After that, we've got four groups of four milkshakes, which is the same as saying 4 plus 4 plus 4 plus 4 or 4 times 4.

And lastly, we've got three groups of five milkshakes.

So that's the same as saying 5 plus 5 plus 5 or 3 times 5.

Now let's look at the groupings for sweets.

We've got four groups of two sweets.

That's the same as saying 2 plus 2 plus 2 plus 2 or 4 times 2.

Next, we've got four groups of four sweets.

So that's the same as saying 4 plus 4 plus 4 plus 4 or 4 times 4.

And lastly, we've got four groups of six sweets.

So that's the same as saying 6 plus 6 plus 6 plus 6 or 4 times 6.

Now for question two, this is what you should have got.

So we know that lollipops come in packets of three.

Now if Izzy has four packets, that's the same as saying four equal groups of three.

So we can represent that as 4 times 3 or 3 plus 3 plus 3 plus 3.

Now Jun had six packets, so two more groups than Izzy.

So that could have been represented as 6 times 3 or 3 plus 3 plus 3 plus 3 plus 3 plus 3.

Well done if you managed to get that correct.

Let's move on.

Now for this lesson cycle, we're going to be having a look at different representations to represent equal groups.

Alex and Jacob have both represented three groups of five in different ways.

So Alex has written 3 times 5 and Jacob's written 5 plus 5 plus 5.

So you know that multiplication is another way to represent repeated addition.

You know that 3 times 5 can be said as three groups of five or 5 plus 5 plus 5, and this is also three groups of five.

So the symbol that you see there, the equal sign, means is equal to.

It's a way of writing equals without saying or writing the word.

That means we can write that 3 times 5 is equal to 5 plus 5 plus 5.

So that's how we would represent this.

So 3 times 5 is equal to 5 plus 5 plus 5.

Now it looks a bit scary because they're combining different operations together.

So in this case, multiplication and addition.

But, really, we know what we are saying here.

This is our mathematical language.

So 3 times 5 is equal to 5 plus 5 plus 5.

Now Alex and Jacob have both represented two groups of six in different ways.

Alex has got 2 times 6 and Jacob's written 6 plus 6.

So you know that multiplication is another way to represent repeated addition.

You know 2 times 6 can be said as two groups of six and 6 plus 6 is also two groups of six.

Now remember, the equal symbol means equal to.

It's a way of writing equals without saying or writing the word.

So let's join these equations together.

That means we can write that 2 times 6 is equal to 6 plus 6, and this is how we would represent it.

So 2 times 6 is equal to 6 plus 6.

Over to you.

Alex is representing 4 times 5.

Tick the correct expression.

You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, if you got C, you are correct.

Let's move on.

Alex and Jacob are playing a maths game.

Alex writes a multiplication expression and Jacob needs to represent this using repeated addition.

Ooh, this is a good game.

All right, okay, so they take a couple of turns, let's see what happens.

Alex says 6 times 3 and Jacob says 3 plus 3 plus 3 plus 3 plus 3 plus 3.

And he's correct because he's represented 6 times 3 as being equal to this repeated addition.

He has added 3 six times to represent 6 times 3.

Now Alex says 3 times 6 and Jacob responds 6 plus 6 plus 6.

And he's correct because 3 times 6 is equal to 6 plus 6 plus 6.

Back to Alex, he says 4 times 5 and Jacob says 4 plus 4 plus 4 plus 4.

Hmm.

Is Jacob correct? Explain your thinking to your partner.

You can use the sentence then below to help you.

Well, Jacob is incorrect because 4 multiplied by 5 or four times five, or four groups of five, is actually equal to 5 plus 5 plus 5 plus 5, not 4 plus 4 plus 4 plus 4.

And that's because there are four groups of five.

Now Alex and Jacob swap.

Alex draws the representation using dots and Jacob writes the multiplication expression.

So let's see what Alex draws first.

Ooh.

Okay.

So Jacob says 1 times 4.

Ooh.

Okay.

Jacob says 2 times 4.

And now we've got another group of four.

3 times 4.

Is Jacob correct? Explain your thinking to your partner.

Well, Jacob is correct because three 3 times 4 is equal to 4 plus 4 plus 4.

Later, Alex, Jacob, and Izzy create different representations of two groups of six.

So let's have a look.

We've got multiplication, we've got repeated addition, a drawing and a bar model.

And in the middle, we're representing two groups of six.

I want you to think about what's the same and what's different.

Hmm.

Now, I'm looking at this.

I see sixes in each section and I see two groups.

So each representation does show two groups of six.

The drawing shows two groups of six dots.

The bar model shows two groups, and each bar represents six.

The difference between them all is the way they look.

Over to you.

What I'd like you to do is choose a multiplication equation below for this representation.

So there are, mm, groups of.

That is something times something.

Is it A, 2 times 5, B, 6 times 2, or C, 4 times 2? Use your knowledge of groupings to help you with this.

You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, if you got C, you are correct.

There are four groups of two.

That is 4 times 2.

And I know that's correct because there are four equal groups of two.

And the repeated addition expression for this would be, 2 plus 2 plus 2 plus 2, which is four groups of two.

Back to you again.

Jacob now represents 5 times 4.

Is Jacob correct? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, Jacob is incorrect.

He has represented 6 times 4.

There are six groups of four here and he needs to show five groups.

So actually, how would we correct that? Well, we would have to remove one group of four to show five groups of four.

Onto the main task for your lesson.

So you are going to match the multiplication and addition expressions.

So first, you're going to match 3 plus 3, then you're going to match 2 plus 2 plus 2 plus 2, then you're going to match 4 plus 4 plus 4 plus 4, then 6 plus 6 plus 6, and lastly, 7 plus 7 plus 7 to the correct multiplication expression.

For question two, you're going to circle the correct expression for the statements and write the multiplication expression.

So for A, I have two bags of five lollipops.

Is that 2 plus 2 plus 2 or 5 plus 5? 2B, I have three bags of four sweets.

Is that equal to 3 plus 3 plus 3 plus 3 or 3 plus 3 plus 3, or 4 plus 4 plus 4? 2C, I have five boxes of four doughnuts.

Now is that equal to 4 plus 4 plus 4 plus 4 plus 4 or 5 plus 5 plus 5 plus 5.

And lastly, 2D, I have three boxes of seven cupcakes.

Now is that equal to 3 plus 3 plus 3 plus 3 plus 3 plus 3 plus 3 or 7 plus 7 plus 7, or 5 plus 5.

For question three, you're going to use your knowledge of grouping and complete the Frayer model below.

So we've got two groups of seven there.

First, you're going to write a multiplication expression, then move on to write it a repeated addition for this, then a drawing.

So you could use circles for the groupings and dots to show the number of items in each group.

And lastly, a bar model.

So each representation should show two groups of seven.

And lastly, for question four, you're going to prove that 4 plus 4 plus 4 is equal to 3 times 4.

Now you could draw a picture or use cubes.

You could explain how you know to a friend.

You can pause the video here and click play when you're ready to rejoin us.

So how did you do? For question one, this is what you should have got.

So 3 plus 3 is equal to 2 times 3.

2 plus 2 plus 2 plus 2 is equal to 4 times 2.

4 plus 4 plus 4 plus 4 is equal to 4 times 4.

6 plus 6 plus 6 is equal to 3 times 6.

And 7 plus 7 plus 7 is equal to 3 times 7 because there are three groups of seven.

Well done if you managed to match those correctly.

For question two, this is what you should have got.

So for 2A, you should have got 5 plus 5, and that's equal to 2 times 5.

For question 2B, you should have got 4 plus 4 plus 4.

That is equal to 3 times 4.

For 2C, you should have got 4 plus 4 plus 4 plus 4 plus 4, which is equal to 5 times 4.

And lastly, for 2D, you should have got 7 plus 7 plus 7, and that is equal to 3 times 7.

For question three, this is what you should have got for two groups of seven.

So the multiplication expression that you should have got is 2 times 7, and that's because two groups of seven is equal to 2 times 7.

For repeated addition, you should have got 7 plus 7, and that's because there are two groups of seven.

So we're adding 7 two times.

For the drawing, you should have shown two groups with seven items in each group.

So your drawing may have looked like this.

And lastly, your bar model should have shown two bars, each with a value of seven, because there are two groups of seven.

For question four, you may have proven that 4 plus 4 plus 4 is equal to 3 times 4 by showing that there are three groups of four.

So for example, you may have had three groups with four items in each group, or you may have written that 4 plus 4 plus 4 is three lots of four.

Well done.

We've made it to the end of the lesson.

So in this lesson, you were representing equal groups as repeated addition and multiplication.

So you should now understand that repeated addition can be written as a multiplication expression and represented in different ways.

You should also understand that the times symbol represents times.

For example, three groups of five can be represented as 5 plus 5 plus 5 or 3 times 5.

3 represents the number of groups and 5 represents the number in each group.

Well done, I'm super proud of you, and I can't wait to see you in the next lesson.

Bye.