Lesson video

Hi, I'm Mr. Taziman.

Today I'm gonna teach you a lesson from a unit that's all about multiplying and dividing by two digit numbers.

There might be lots of steps that you encounter here, but it's really important for you to understand not just the steps but the maths behind those steps as well.

So sit back, listen well, it's time to learn, let's go.

Here's the outcome for today's lesson then.

By the end, we want you to be able to say, "I can explain how to use factorization and the associative law to multiply efficiently." The key words or phrases are as follows, associative law, composite number.

I'm gonna say them and I want you to repeat them back to me.

So I'll say my turn, say the phrase.

And then I'll say your turn and you can repeat it back.

Okay, ready, here we go.

My turn associative law.

Your turn! My turn, composite number.

Your turn.

Okay, here's what those phrases mean.

If you're not totally sure about these as I explained them, don't worry 'cause we're going to touch on them throughout the lesson.

The associative law states that it doesn't matter how you group or pair values i.

e.

which we calculate first.

The result is still the same.

It applies for addition and multiplication.

A composite number is an integer with more than two factors.

All integers greater than one are either composite or prime.

Here's the outline then for today.

We're gonna start by looking at using the associative law.

Then we're gonna move on to some missing factors questions.

Sam and Andeep are here today to help us.

They've been really helpful throughout this unit and they're gonna give us some hints and tips and discuss the maths involved.

Okay, sit comfortably.

Be ready to listen 'cause here we go.

A composite number is a number that has more than two factors, whereas prime numbers have exactly two factors.

"So 6 is a composite number because it has more than two factors," says Sam.

"I can see 1 group of 6 or 1, 6 times.

I can also see 3 groups of 2 or 2, 3 times." The factors of six are 1, 2, 3, and 6.

Sam and Andeep look at another number, 7.

Sam says, "7 is a prime number.

Its only factors are 1 and itself." "I can see 1 group of 7 or 1, 7 times." 7 has exactly two factors, 1 and 7.

Okay, let's check your understanding of what we've learned about so far then.

Which of the following are composite numbers and how do you know? We've got A 8, B 21, and C 29? Pause the video and decide whether you think any of those are composite numbers, good luck.

Welcome back.

A and B are both composite numbers.

Remember, a composite number is a number that has more than two factors, whereas prime numbers have exactly two factors.

Here's a worded problem then.

Athlete snack packs contain 12 snacks per pack.

How many snacks are needed for 23 packs? What's known and what's unknown? Well, we know there are 23 packs and each pack contains 12 snacks.

These are the factors.

What's unknown is the total number of snacks, which is the product.

23 x 12 = an unknown.

We can use factors to multiply more efficiently.

We can factorised one or both factors.

What are the factors of 23 and 12? 12 is a composite number.

Its factors are 1, 12, 2, 6, 3 and 4.

23 is a prime number.

Its factors are 1 and 23.

It only has two factors.

That's what makes it prime.

Sometimes it is easier to add or multiply in a different order.

You can simplify this multiplication equation by factorised the composite number.

A factor pair of 12 is 6 and 2.

We can multiply by these in either order.

So you can see there that we've changed that area model.

Now we've got 6 lots of 23 multiplied by 2.

I can multiply 23 by 2, and then multiply it by 6.

23 x 12 = 23 x 2 x 6.

That's the same as 46 x 6 = 276.

You can also reorder the factors and calculate it as 23 x 6 x 2.

So, we've got 2 lots of 23 multiplied by 6 now.

23 x 12 = 23 x 6 x 2.

23 x 6 = 138.

So we can take 138 and multiply it by 2 to give us 276.

Rearranging the groupings can make it easier for us to calculate the answer.

This is known as the associative law.

What do you notice? Have a look at both of these methods, compare them.

Multiplication is commutative.

You can multiply the factors in any order and still get the same number.

Both of these methods ended with the product of 276.

Here's another worded problem.

Olympic programmes are distributed around the Olympic village.

Each box contains 41 programmes and there are 15 boxes.

How many programmes are there in total? What's known and what's unknown? Well, we know there are 15 boxes each containing 41 programmes and these are the factors.

What is unknown is the total number of programmes.

That's gonna be the product.

41 x 15 = an unknown.

We can use factors to multiply more efficiently.

We can factorised one or both factors.

What are the factors of 41 and 15? Well, 41 is a prime number.

Its factors are 1 and 41.

15 is a composite number.

Its factors are 1, 15, 3 and 5.

Sam says, "Rearranging the groupings can make it easier for us to calculate the answer.

This is known as the associative law." You can simplify this multiplication equation by factorising the composite number.

3 and 5 are factors of 15, so these can be used.

So we've now got in our area model 41 x 3, 5 times.

And you can see the jottings underneath.

41 x 15 = 41 x 3 x 5.

41 x 3 = 123.

Then we can take that and multiply it by 5.

That gives us an answer of 615.

And at the bottom it says you can also reorder the factors and calculate it as 41 x 5 x 3.

Can you see the change in the area model there? We've now got 3 lots of 41 x 5.

The product though is still the same.

Sam says, "I got the same answer each time.

There are 615 programmes.

I preferred to multiply by 3 first because I could do it mentally, then multiply by 5." It's time to check your understanding then.

For this, I'd like you to identify the composite number in each of these expressions.

You can see there's a pair of factors in each of these multiplication expressions below A, B, and C.

One of those pair of factors is a composite number, but which one? Pause the video and see if you can find out which.

Welcome back.

Here are the three composite numbers identified in A, B and C.

28, 34 and 32 are composite numbers because they have more than two factors.

Here's your first practise task then.

Represent each expression using a grid model.

Show how you would use factors and the associative law to calculate the product.

We've got A, 23 x 18 and B, 29 x 14.

Here's number two.

Andeep has represented 37 x 24.

Is he correct? Why or why not? Okay, pause the video, have a go at those and I'll be back in a little while for some feedback, enjoy.

Welcome back, let's do some marking then.

You may have used 9 and 2 as factors of 18 and calculated like this.

So you can see we've got 23 x 18 and there's a grid model underneath in which we've got 9 lots of 23 x 2.

The jottings below show this in equation form.

23 x by 18 = 23 x 2 x 9.

That's equal to 46 x 9, which is equal to 414.

That was the product.

Here's another way of doing it though.

You can see in this grid model we've got 23 x 9, 2 times.

And you can see that in the equation form, the factors 9 and 2 have swapped positions within the multiplication expression.

The product is still the same though, 414.

For B, here's one way of doing it, 29 x 14.

You might have done 29 x 2, 7 times, giving a product of 406.

Or, you might have done 29 x 7, 2 times giving still a product of 406.

For number two, was he correct or incorrect? Well, Andeep has factorised incorrectly.

6 x 6 = 36, not 37.

37 is a prime number, not a composite number.

Okay, let's move on to the second part of the lesson then, missing factors.

Sam and Andeep are solving problems using the associative law to find the missing numbers.

29 x 14 = 29 x 7 x by something.

What advice would you give to both Sam and Andeep to solve this problem? Hmm, well, Sam says 14 is a composite number, so it can be factorised.

Something multiplied by 7 is 14.

I know that 2 x 7 = 14.

2 is the missing number.

Really good reasoning, Sam, well done.

Okay, let's look at this one this time then.

Same sort of question, but different numbers.

We've got 53 x 21 = 53 x by an unknown x by an unknown.

So we've got two unknowns this time.

Sam says, "21 is a composite number, so it can be factorised.

Something x by something is 21.

I know that 3 x 7 = 21, so 7 and 3 can be used." Remember, multiplication is commutative, so you can swap the order of the factors.

The product will remain unchanged.

So we could have written it in this order, 3 and 7.

7 and 3 could be the missing numbers.

"Ah, yes, but I know that 1 and 21 are also factors.

Could they work?" "Yes, but if you were calculating, this wouldn't be any more efficient." Okay, let's check your understanding then.

Look at the equation.

What is the missing number? 29 x 24 = 29 x 6 x by something.

Sam gives us a tip here.

"Remember, you can only factorised composite numbers." So start by looking for the composite number in the factor pair.

Okay, pause the video here and have a go, good luck.

Welcome back, 24 was the composite number and we knew that 6 x 4 = 24, so the missing number was 4.

Sam and Andeep are solving problems using the associative law still.

We've got another problem.

This time, there are three unknowns.

53 x 16 = to something x by something x by something.

What advice would you give to both Sam and Andeep to solve this problem? Hmm, well, Sam says, "53 is a prime number, so it will remain as the same factor.

16 is a composite number, so it can be factorised." Something x by something is 16.

You know that 2 and 8 are factor pairs of 16.

There we go, 8 and 2 have been put as the missing numbers.

Because of commutativity though, we know we can swap those around.

The order doesn't matter, the product will remain unchanged.

"You also know that 4 and 4 are factor pairs of 16." The missing numbers can be 4 and 4 or 2 and 8.

Okay, let's look at this one then.

Find the missing factors.

This time, we've got 3 factors in the expression on the right hand side, but we are missing 2 factors on the left.

An unknown x by an unknown = 47 x 8 x 4.

Andeep says, "47 is a prime number, so it will remain as the same factor." He puts 47 into one of the missing number boxes.

"We can multiply the other 2 factors to find the missing factor.

8 x 4 = 32." Let's check your understanding then.

Look at the equation.

What could the missing number be? An unknown x by 12 = 3 x 43 x 4.

Sam says, "What stayed the same and why?" Okay, pause the video and give that a go.

Welcome back, the missing number then was 43.

It's the missing number because it's a prime number and it will stay the same.

You can see the other 2 factors of 3 and 4 can be multiplied together to give the factor of 12.

In a sense, the left hand expression, the 12, has been factorised to become 3 and 4 in the right hand expression.

All right, let's have a go then at a second practise task.

using knowledge of the associative law and commutative law fill in the missing numbers.

We've got A to J.

For number two, how many different ways can you make the following equation true? Pause the video here.

Have a go at those two questions.

I'll be back in a little while with some feedback, enjoy.

Welcome back, let's look at some answers then.

For A, we had 21 x 18 = 21 x 9 x 2.

18 is not included in the second expression, but there is a 9.

9 x 2 = 18.

So 2 is the missing factor.

It's using that associative law again.

For B, 21 x 20 = 21 x 1 x 2.

20 is not included in the second expression, but there is a 2.

2 x 10 = 20.

So 10 is the missing factor.

Here are all the rest of them then.

I'll read out the equations.

C, 22 x 2 x 10 = 22 x 20.

D, 35 x 15 = 15 x 7 x 5.

For E, 43 x 54 = 43 x 6 x 9.

For F, 29 x 6 x 3 = 29 x 3 x 6.

For G, 29 x 24 = 29 x 12 x 2.

For H, 24 x 5 x 7 = 24 x 35.

For I, 48 x 2 x 9 = 18 x 48.

For J, 44 x 53 = 11 x 4 x 53.

Okay, if you need to pause here to take some time to finish marking those carefully, then please do so.

Finally then question two.

How many different ways can you make the following equation true? Well, here are some of the ones that you may have got.

30 x 24 = 3 x 10 x 24.

Or 15 x 2 x 24.

Or 6 x 5 x 24.

Or 2 x 12 x 30.

Or 3 x 8 x 30.

Or 6 x 4 x 30.

Factors of 30 were 1 30, 2, 15, 3, 10, 5, and 6.

And factors of 24 are 1, 24, 2, 12, 3, 8, 4, and 6.

This means lots of combinations are possible, so just because yours isn't listed here, it doesn't mean that it's incorrect.

If you need to pause the video to do some pairing and sharing of your answers, then please do so now.

Here's a summary then for today's lesson.

We understand that composite numbers can be factorised and that multiplication is commutative.

We can also use the associative law of multiplication.

We understand that factors can be grouped in different ways and the product remains the same.

My name is Mr. Taziman.

Hope you enjoyed that lesson.

I certainly did.

Maybe I'll see you again soon.

Bye for now.