Lesson video

Hi everyone.

My name is Ms. Kuh, and today we're going to have a really interesting and fun lesson.

I'm so happy to be learning with you today and it might be hard in places, but I will be here to help.

You're going to come across some keywords that you are familiar with as well as some new keywords to build on that previous knowledge.

It's going to be a great lesson, and I'm really happy to be landing with you today.

In today's lesson from the unit Properties of Number Factors, Multiples, Squares and Cubes, we'll be looking at securing understanding of factors, multiples, squares and cubes, and by the end of the lesson you'll be able to use multiplication tables to identify factors and multiples.

So let's go through our key words for this lesson, starting with the word multiple.

Now, a multiple is the product of a number and an integer.

For example, 10, multiply by 2 equals 20.

This means 20 is a multiple of both 2 and 10.

We'll also be looking at the word numerical factor, and a numerical factor is a factor that is an integer.

For example, 20 divide by 2 is 10.

Because 20 divide by 2 equals an integer, in other words, there's no remainder, this also identifies that 2 and 10 are factors of 20.

Knowing that factors and multiples are inverse concepts, this means we can look at our first example and identify our factors.

10 and 2 are factors of 20 and our multiple.

20 is a multiple of 2 and 10.

We'll be looking at these keywords a lot through the lesson, so don't worry if it seems like a lot of information now.

Now our lesson will be broken into two parts, so we can secure our understanding of factors, multiple, squares, and cubes.

The first part will be looking at multiplication tables to identify multiples, and the second part will be using multiplication tables to identify factors.

So let's start by using multiplication tables to identify multiples.

Here's a 5 by 5 multiplication table, and what I want you to do is identify where are all the multiples of 2 from this table? See if you can give it a go.

Well, hopefully you've spotted the multiples of 2 are here.

This means multiples of 2 aren't just in the row or column of 2, but they're also in the row and column of 4.

This is because 2 is a factor of 4.

My next question asks, does the table show all the multiples of 2? What do you think? Well, hopefully you can spot it doesn't, as there are an infinite number of multiples.

We're only using a 5 by 5 times table here.

Now let's have a check for understanding question.

Here I've put a 9 by 9 multiplication table and I want you to identify what's the largest multiple of 4 you can see using this table? And then I want you to explain how you found it.

See if you can give it a go and press Pause if you need.

So let's see what you've got.

While I'm hoping you've identified the largest multiple of 2 and you can see in this multiplication table is 72, and this is because we're looking at the row or column of 8, because 4 is a factor of 8.

So this means all the multiples of 4 will also be in the row or column of 8.

A huge well done if you've got that question.

Now let's have a look at your task.

Question 1 shows a 6 by 6 multiplication table and it wants us to answer if it's true or false for each statement and making sure we do provide a justification for your answer.

So using the 6 by 6 multiplication table, is the statement 12 is a factor of 4 true or false? And provide a justification.

For B, it says 36 is a multiple of 3.

Is that true or false? And provide a justification.

For C, it states all the multiples of 6 can be seen in this table.

Do you think this is true or false? And make sure you provide a justification.

Press Pause if you need more time.

Well done.

So let's move on to the second question.

Here we have at 12 by 12 multiplication table and you're asked to find the largest multiple of seven using this 12 by 12 multiplication table.

Part B wants you to find the largest multiple of 3, and part C wants you to find the largest multiple of 5, and part D wants you to find the lowest multiple of 3 and 5.

See if you can give this a go and press Pause if you need.

So let's go through our answers.

Question 1 gives us a 6 by 6 multiplication table and wants us to use this to identify if the statements are true or false for each statement and provide a justification.

For A, it says 12 is a factor of 4.

Is that true or false? Hopefully you've spotted it's false, because 12 is a multiple of 4 or 4 is a factor of 12.

That's a great question using those keywords.

For B, 36 is a multiple of 3, true or false? Well, it's true because 3 multiply by 12 is 36, or 36 is a multiple of 3 and you can see 36 is in the row or column of 6, and we know 3 is a factor of 6.

So that means we know all the multiples of 3 are also seen in the row or column of 6.

For C, all the multiples of 6 can be seen in this table.

That's false because our table is only a 6 by 6 multiplication table and there are an infinite number of multiples.

Well done if you got this one right.

Now let's look at Question 2 using our 12 by 12 multiplication table.

Were you able to find the largest multiple of seven from this table? Hopefully you spotted it's 84, well done.

B wants you to find the largest multiple of 3.

Well the largest multiple of 3 will be 144 because you're looking at the row or column of 12.

We know 3 is a factor of 12.

So that allows us to look at all multiples of 12 because there'll also be multiples of 3.

For C, we're asked to find the largest multiple of 5.

Hopefully you can spot it's 120, because we're looking at the row or column of the tens.

We know 5 is a factor of 10, which means all the multiple of tens will also be a multiple of 5.

For D, we're asked to find the lowest multiple of 3 and 5, and that would be 15.

It's the lowest number in the 3 times table as well as the 5 times table.

Huge well done if you've got that one right.

Now let's move on to the second part of our lesson.

We'll be looking at multiplication tables to identify factors.

In this multiplication table I'm showing you a 6 by 6, and I want to see how you can use a multiplication table to identify factor pairs of 6.

And then I want you to identify how many factor pairs of 6 can you find? See if you can give it a go.

Well done.

So let's see what you've got.

Well, using the 6 by 6 multiplication table, we have the following factor pairs to make 6.

Here's my 6, and I've made it by multiplying one and 6.

So there's my first factor pair.

I also spot my 6 here, which is made by multiplying 2 by 3.

You may have also got 3 multiply by 2 or 6 multiply by one.

Remember, multiplication is commutative, so the order does not matter.

So it doesn't matter if you did one and 6, or 6 and one or if you did 2 and 3, and 3 and 2.

They are still a factor pair, well done.

Now let's move on to a 10 by 10 multiplication table.

Can you find all the factor pairs of 9? Press Pause if you need more time.

Let's see how you've done.

Yes, you can find all those factor pairs of 9.

We have 1 and 9, or 9 and 1, and we also have 3 and 3.

Now, 9 is quite a special number, because when we have a factor pair, which is a repeated integer, this means we know the product is a square number.

So this tells me that 9 is a square number.

Well done.

Moving on to a check question.

Here we have a 10 by 10 multiplication table, and we're asked to find as many factor pairs of 24 as you can.

Then the second part, I want you to explain why you cannot find all the factors of 24 using this table.

See if you can give it a go and press Pause if you need.

Well done.

So let's identify these factor pairs using our 10 by 10 table.

Well, hopefully you can spot all of these 24s.

So how does this help us find our factor pairs? Well, we've got 8 multiply by 3, or 3 multiply by 8, and we have 4 multiply by 6, or 6 multiply by 4.

So we have our factor pairs.

Now why can't we see all the factors of 24 using this table? Well, you need at least a 24 by 24 multiplication table to see all the factors of 24.

For example, we're missing the factor pair 1 and 24.

We're also missing the factor pair of 2 and 12.

So there are more factor pairs out there.

We just couldn't see them using a 10 by 10 multiplication table.

Well done if you've got that one right.

Now let's move on to our task.

Here it shows an 8 by 8 multiplication table.

Question 1A wants you to find all the factors of 8.

B wants you to find all the factors of 5, C wants you to find all the factors of 4, and D wants you to find all the factors of 7.

E then asks, what is their common factor? See if you can give this one a go and press Pause if you need more time.

Well done.

So let's move on to Question 2.

Question 2 says, using a 6 by 6 multiplication table, are the following true or false? And we must provide a justification for our answer.

So using the 6 by 6 table, do you think 4 only has 3 factors, true or false? And please do justify.

For B, do you think all the factors of 6 are seen on our 6 by 6 multiplication table, true, false? And please justify.

For C, 3 has an infinite number of factors, true, false and justify.

And for D, are there 5 square numbers seen in our 6 by 6 multiplication table? Do you think it's true or false? And do justify.

See if you can give it a go and press Pause if you need more time.

Well done.

So let's move on to the third question.

Here the question wants us to identify what number is remaining when we eliminate first of all, all the multiples of 5.

Second of all, all the factors are 24, third, all the multiples of 3, 4th, all the multiples of 4.

And then lastly, all the factors of 14.

Once we eliminate all of those numbers, we will be left with one number remaining.

Can you work it out? See if you can give it a go and press Pause if you need.

Really well done.

So let's go through these answers starting with question 1A.

We had to identify all the factors of 8.

So you need to look for the number 8 in our grid.

Hopefully you would've spotted the factor pairs of 8 are 1 and 8, 2 and 4, because one multiply by 8 is 8, 2 multiply by 4 is 8.

For B, all the factors of 5.

Using our multiplication grid, you can see 5 appears twice, 1 multiplied by 5 or 5 multiply by 1.

C, identify all the factors of 4.

So where do you see 4 on our multiplication grid? Well you can see we by one multiplied by 4 or 2 multiply by 2.

For D, we're asked to identify all the factor pairs of seven.

Well, hopefully you can only spot one pair 1 and 7.

Lastly, let's have a look at E.

What is their common factor? Well, the common factor for A, B, C, and D is simply 1.

Just to extend that a little bit more, do you think you can see why their common factor is 1? There's something very special about the number 5 and 7.

While 5 and 7 each only have one factor pair, and that makes those numbers very special.

Now let's move on to Question 2.

Question 2 shows a 6 by 6 multiplication table and wants us to answer true or false and justify our answer.

So for 2A, does 4 only have 3 factors? Yes it does, because those factors are 1, 2, and 4.

For 2B are all the factors of 16? Yes, they are 1, 6, 2, and 3 in any order.

For C, does 3 have an infinite number of factors? No, it doesn't, it's false, because the only factors of 3 are 1 and 3.

Lastly, 2D.

There are 5 square numbers seen, true or false? It's false.

There are actually 6 square numbers seen, 1, 4, 9, 16, 25 and 36.

A huge well done if you got that one right.

Question 3 is a great question, as you'll need to eliminate in order to find what the final number would be.

So let's have a look at 3A, identifying and eliminating all those multiples of 5.

To eliminate all the multiples of 5, you need to make sure you eliminate all the numbers in the row and column of 5, as well as the row and column of 10, because we know 5 is a factor of 10, and we also know that all the multiples of 10 will also be a multiple of 5.

Well done if you've done that.

Part B wants us to eliminate all the factors of 24.

So what you need to do is think about the numbers and think, well, what numbers are factors of 24? I'm going to cross them all out as there are quite a few factors there.

We know 1, 2, 3, 4, 6, 8, 12, and 24 are all factors of 24.

They need to be crossed out.

Well done if you've done that.

For C, we need to cross out all the multiples of 3.

So that means we need to, so eliminating all our multiples of 3 means we eliminate all the numbers in the row and column of 3, all the numbers in the row and column of 6, and all the numbers in the row and column of 9.

This is because 3 is a factor of 6 and 9.

For D, eliminate all the multiples of 4.

This means we need to eliminate all the numbers in the row and column of 4, all the numbers in the row and column of 8, because we know 4 is a factor of 8.

Now we're left with eliminating all the factors of 14.

The only factors of 14 we have on the screen are 7 and 14, thus leaving us with a final answer of 49.

A huge well done if you've got that one right.

That was a great question.

I really hope you've enjoyed this lesson today on securing understanding of factors, multiples, squares, and cubes.

Who would've thought when the multiplication table was invented approximately 4,000 years ago it'd be such a powerful tool? And this fantastic resource doesn't just allow us to find the product of two entities using rows and columns of the table, but multiplication tables can also be used to identify multiples and factors of a number.

But it is important to remember multiplication tables can never find all the multiples of a number as there are an infinite number of multiples.

It's also important to remember a multiplication table must be large enough to find all the factors of a number.

I hope this lesson has introduced you to the other uses of a multiplication table.

And multiplication tables are such powerful tools that they have many different uses which can help in different topics of mathematics, such as division and even helping us with fractions.

So in summary, we've looked at using multiplication tables to find factors and multiples.

Great work today, we've done so much.

I really do hope you've enjoyed this lesson and it was great learning with you.