Lesson video

Hello, I'm Miss Mia 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 multiplication.

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

Groups, grouping.

Multiplication.

Fantastic.

Let's move on.

Now, this lesson is all about representing equal groups as multiplication.

Now, there are two lesson cycles in this lesson, and the first lesson cycle is grouping as multiplication.

The second lesson cycle then focuses on reasoning.

So we're going to apply everything we've learned from the first cycle to the second cycle.

And, in this lesson, you will meet Alex and Jacob who are going to be helping us with our mathematical thinking.

Let's begin.

Jacob has six counters and he organises them into equal groups.

So Jacob says, "This is known as an array." So you can see that the counters have been placed in a specific way.

Now, "An array is when items are arranged in rows and columns." So, we can see here that there are two columns of three.

Now, remember, columns are vertical.

And we can see that there are three rows.

Now, rows are horizontal, okay? So, two columns and three rows.

Here, we can see that there are two columns.

Now, columns are vertical.

Each column has three counters.

This is also the same as saying two threes.

So this array shows two groups of three, which is 2 times 3.

Now, Alex says, "I'm looking at two columns.

I can see two equal groups of four counters.

I can show equal groups using multiplication." So, the array shows that there are two groups of four, which is 2 times 4.

Now if I added on another counter to each column, that would show me two groups of five because each column would have five counters.

So, coming back to what Alex said, two groups of four is also the same as saying 4 plus 4.

I can also see another way of grouping eight into equal groups.

Ooh, look at the change here.

So, if I look at the rows, which are horizontal, I can see four equal groups of two counters.

I can show these equal groups using multiplication two.

Ooh, I wonder what the multiplication would be.

Well, this time, there are four groups and we can see four groups there because there are four rows.

So, four groups of two, which is 4 times 2.

Over to you.

What multiplication expression does this representation show? And I'd like to have a go at filling in the blanks.

So, there are something equal groups of something counters.

Is it, A, 2 times 6? B, 2 times 4? Or C, 2 times 5? You can pause the video here.

So, what did you get? Well, there are two equal groups of four counters.

And that's because I can see that there are two rows, and in each row, there are four counters.

Jacob has 10 counters and he organises them into equal groups.

Ooh, okay, well, something definitely doesn't look right there.

What advice would you give to Jacob? Well, the groups need to be equal.

He could arrange the counters like this.

So now Jacob can see something groups of something counters.

I wonder how he could describe this.

So, "That is five groups of two counters." This shows five groups of two or 5 times 2.

Now, we've got a different arrangement.

So, this is two groups of five.

This shows two groups of five, which is the same as saying 2 times 5.

Over to you.

You can use counters or pencils for this.

So, you're going to now show 5 times 3.

You can pause the video here.

So, how did you do? Now remember, multiplication is all about equal groups.

Now, 5 times 3 is the same as saying five groups of three.

So, five rows which are horizontal, and in each row, there's three counters.

Okay, onto the main task for your lesson.

So question one, you're going to draw lines connecting each picture with the correct multiplication expression.

So you've got a group of counters, groups of slices of cake.

Then you've got bundles of sweets and then groups of pencils.

And for question two, you're going to complete the Frayer model using your knowledge of multiplication and grouping for the multiplication 4 times 3.

So you're going to complete the sentence.

There are something groups of something.

Then you're going to show 4 times 3 as repeated addition.

Then you're going to show it as a Bar model.

And lastly, a drawing.

Think about how many equal groups there are and how many items you might need to draw in each group.

You can pause the video here.

Off you go.

Good luck.

So, how did you do? Well, this is what you should've got.

For question one, the counters show two groups of three, which is the same as 2 times 3.

The slices of cake.

Well, we've got four groups of three, which is 4 times 3.

Then, for the sweets, we've got three groups of three sweets, which is the same as 3 times 3.

And then lastly, we've got five groups of three pencils, which is the same as saying 5 times 3.

Well done if you manage to match those correctly.

For question two, you should've completed the Freya model.

So we'll start with the sentence stem first.

So, 4 times 3 is the same as saying there are four groups of three.

For repeated addition, you should've got 3 plus 3 plus 3 plus 3 because there are four groups of three, and we need to add three, four times.

For the Bar model, you should've got four bars each with a value of three.

And lastly, your drawing may have looked like this.

So you four rows with three counters in each.

Now we're going to move on to the second part of this lesson cycle.

Jacob is at a school trip on a farm.

He spots groups of chicks.

He uses multiplication to describe how many groups he can see, but he is confused.

Hmm, he asks, "Is this 3 times 5 or 5 times 5?" What do you think? Explain your thinking to your partner.

Now, you may have looked at the multiplication equation separately, so let's have a look.

The three represents the amount of groups and the five represents the amount of chicks in each group.

So, this shows 3 times 5 because there are three groups of five chicks.

Later, at the farm, Jacob also sees groups of rabbits.

Hmm.

"Is this 4 times 5 or 5 times 5?" What do you think? I'd like you to explain your thinking to your partner.

Well, you may have said something like this.

Now, the four represents the amount of groups and the five represents the amount of rabbits in each group.

So, this shows 4 times 5 because there are four groups of five rabbits.

And notice how they have been arranged in rows.

So, each row has five rabbits and there are four rows altogether.

So, four rows of five rabbits is the same as saying 4 times 5.

Over to you.

What I'd like you to do is use your knowledge of multiplication and also of arrays to help you identify the correct representation, which shows 2 times 8.

Think about what the two might represent and think about what the eight might represent to help you.

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

So, what did you get? If you got C? You are correct.

And that's because C shows two groups of eight penguins.

So, if we look at this more closely, I can see two rows there.

And in each row, there are eight penguins.

So, two groups of eight is the same as saying 2 times 8.

Back to you.

So, what advice would you give Jacob to change this representation to 6 times 5? Now, on the screen I can see 1, 2, 3, 4.

Four groups of five counters.

How might you change that to 6 times 5? Hmm.

Pause the video and have a think.

So, what did you discuss? Well, this shows 4 times 5 because there are four groups of five dots.

You need to increase the amount of groups by two.

The next day the farmer decides to change the groups of chicks.

How would you make this 4 times 4? On the screen, I can see 3 times 4 because there are three rows of four chicks.

What advice would you give to the farmer? Have a think.

Well, you know that three is the number of groups.

If you want to make it 4 times 4, you need to increase the group by one group.

So, we've added in one more row of four chicks.

That is the same as saying 4 times 4 now because we've got four rows of four chicks.

Now, moving on.

The farmer needs to change the groups of chicks again.

How could you make this 4 times 3? So, on the screen here, we can see four rows of four chicks.

This is the same as saying 4 times 4.

What advice would you give to the farmer? Have a think.

So, let's compare the two multiplication equations.

We've got 4 times 4 on the screen and we need to change it to 4 times 3.

I know that three is one less than four.

So you know that the three represents the number of chicks in each group.

So, if we are making it three chicks, we need to actually remove one chick from each group.

So, have a look carefully.

The four within the equation represents the groups.

So we're going to leave that untouched.

We don't need to remove any groups, but what we are going to do is remove one chick from each group.

So, now we've got groupings that show 4 times 3.

Over to you.

So, you can use counters or pencils or anything that you have on your desk for this part.

So, you're going to change the groups of chicks.

So, the items that you have will represent the number of chicks from 3 times 3 to 3 times 2.

Think about what the two represents.

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

So, how did you do? Well, I used counters.

So, I had nine counters altogether and I arranged it into an array.

I had three rows of counters and in each row there were three counters.

So, I know that the three represents the number of chicks in each group.

So, I know that the first three in the equation represents the groups.

So, I will stick with my groups.

So, the groups stay the same, but what's changing is the number of chicks in each group.

So, because we are making it two chicks, two is one less than three so, we need to remove one chick from each group.

And you should've been left with this arrangement here.

So, and that's 3 times 2.

Well done if you got that correct.

Right, onto the main task for this lesson.

So, for question one, you're going to complete the questions below by changing the amount of groups or animals in each.

You can draw dots or use counters, whatever's easier for you.

So, in our first section of the quadrant, we've got groups of rabbits here.

We've got four groups of four rabbits.

What I'd like you to do is change this to 4 times 3 instead.

So think about what the four represents and think about what the three represents in that equation.

Then let's move over to the other group of rabbits on the right-hand side of the screen.

So, this time, we've got three groups of five rabbits.

I would like you to show 2 times 5.

Let's look at the image on the bottom left screen.

So, you're going to change this to show 3 times 6.

And here, we've got three groups of five.

And lastly, you've got three groups of four chicks there.

I'd like you to change this to show 4 times 4.

You can pause the video here.

Remember to think about what each number in the equation represents.

The first number here is representing the groups, and the second number is representing the amount of animals or items in each group.

You can pause the video here.

Off you go.

Good luck.

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

For the first question, there were four groups of four rabbits, so that would've represented 4 times 4, but we need 4 times 3.

So, the number of groups would've stayed the same, which is four groups, but the number of rabbits in each group would've changed.

And that's because three is one less than four so we would've had to remove one rabbit from each group, leaving us with 4 times 3.

For the second question, there were three groups of five rabbits.

So, you could've removed one group of the rabbits to show 2 times 5.

So, here on the screen, we can see two rows of five, which is the same as 2 times 5.

Okay, now let's look at the groupings of the chicks.

So, we needed to change three groups of five to 3 times 6.

So, at the beginning, there were three groups of five chicks.

So, you could've added one chick to each group to show 3 times 6.

So, the groups remained the same, but we added on one more chick to each group.

And lastly, we needed to change three groups of four to 4 times 4.

Now remember, three groups of four is the same as saying 3 times 4.

Now, when it comes to 4 times 4, I know that the three represents the number of groups.

And for it to change to 4 times 4, I would've had to add one more group of chicks.

And I know that in each group there are four, so I would've drawn four more chicks in one group.

Well done if you managed to get that correct.

I'm super proud of you because sometimes it can be a bit confusing knowing what to add and rowing, whether to take away a group or add a group or remove an item, object, or animal from the group.

So, if you managed to get those correct, fantastic work.

You've now shown that you understand what each number represents in a multiplication equation.

Well done, we've made it to the end of this lesson.

I am super proud of you.

So, to summarise our learning, today, you were able to represent equal groups as multiplication.

You should now understand that multiplication can be used to represent equal groups.

You should also understand that the times symbol or the multiplication represents times.

I know that sometimes we can get a bit confused with the X in the alphabet, but in the mathematical world, this symbol represents times.

So you should also understand that one number in the multiplication represents the number of groups.

So, for example, if we were looking at 3 times 5, the three would represent the number of groups, and the other number represents the items or objects in each group.

Well done for making it to the end of this lesson, and I cannot wait to see you in the next lesson.

Bye.