Lesson video

Hi, everyone, my name is Miss Coo, and I'm really excited to be learning with you today.

It's going to be an interesting and fun lesson.

We'll be building on some previous knowledge as well as looking at some keywords that you may or may not know.

It might be easy or hard in some places, but I'll be here to help.

I'm really excited to be learning with you so we can learn together.

In today's lesson from the unit properties of number, factors, multiples, squares, and cubes, we'll be looking at square and cube numbers, and by the end of the lesson you'll be able to explain the concept of a squared and cubed number as well as being able to calculate them.

So let's have a look at some keywords, starting with a square number.

Now, a square number is the product of two repeated integers.

For example, four is a square number as it is the result of two multiplied by two.

Another square number is 25 because it's the result of five multiplied by five.

Now let's have a look at a cube number.

Now, a cube number is the product of three repeated integers.

For example, eight is a cube number because it's the result or product of two, multiplied by two, multiplied by two.

We also have 125 is a cube number because it's the product or the result of five, multiplied by five, multiplied by five.

So it's important to know the definitions of a square number and a cube number, but we will be looking at these a little bit more in depth in our lesson.

Our lesson will be broken into two parts.

The first part will be looking at square numbers, and the second part will be looking at cube numbers.

So let's make a start looking at square numbers.

So a square number is the product of two repeated integers.

I showed you four as a square number, and 25 as a square number.

But what I want you to do is use four dots and 25 dots to show why they are called square numbers.

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

Well, hopefully you've created squares using these dots, so the four dots has made a two by two array, and the 25 dots has made a five by five array.

So you can see why they're called square numbers because we can make squares from them.

Now let's have a look at a table.

I'm going to summarise all our information in one place.

I'm going to look at the integers, one, two, three, four.

and make an array, identify the calculation, and then from there, identify our square number.

So let's start with the number one.

Well, simply means we have an array of one by one.

So that means one multiplied by one gives us the square number one.

It's the product of a repeated integer.

Now let's have a look at the integer two.

I'm going to make a two by two array, so hopefully you can count or you can see the calculation.

This means it's two multiplied by two, which gives me the square number four.

The next array we're going to make is using the integer three.

So a three by three array is formed here.

The calculation would be three multiplied by three, which we can see is nine.

And you can see that from the array we have nine dots.

What do you think using the integer four our array would look like, and our calculation, and our square number? Well, hopefully you've spotted we'd have a four by four array, and the calculation would be four multiplied by four, and our square number would be 16.

Well done if you got that one right.

Now let's see if you can fill in the rest of this table.

You can copy it down and press pause if you need more time.

So let's have a look at the integer five, making a five by five array, so our calculation would be five multiplied by five, thus giving us the square number of 25.

A six by six array would look like this.

Six multiplied by six is our calculation, thus giving us the square number of 36.

The integer, using the integer seven, we have a seven by seven array with the calculation being seven multiplied by seven, giving us the square number of 49.

Well done if you've got this one right.

So you can see all our square numbers are listed here, a nice way for you to identify the square numbers using an array and a calculation.

Now let's have a look at a check for understanding.

Izzy drew this array.

She then says, "I've made a square because I've used an array with 3.

5 dots by 3.

5 dots.

So this means 12.

25 is a square number." Is she correct? And can you explain why? See if you can give it a go and press pause if you need.

Well, hopefully you've spotted she's not correct because a square number is the product of two repeated integers, so we have to be using whole numbers in our array.

Now let's have a look at what Lucas says.

Lucas drew this array and he says, "The array shows three is the square number." Is he correct? And can you explain why? Well, hopefully you've spotted he's not correct.

Nine is the square number as it's the product of three and three.

Well done if you've got that one right.

So let's see if we can move on to our task.

All I've done on question one is draw some arrays, and what I'd like you to do is match the arrays with the correct square number.

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

Well done, so let's move on to question two.

Question two wants us to work out the age given these clues.

We have to work out how old the teacher is and how old is Alex.

Now, the teacher's age is a square number.

It's also a multiple of three and less than 70.

We know Alex is a student at Oak Academy and Alex's age is four less than a square number, and it's even.

Can you work out how old the teacher is and how old is Alex? See if you can give it a go and press pause if you need.

Well done, so let's move on to the next question, question three.

We need to identify if the following statements are true or false and provide a justification.

So our first statement states, "121 is a square number." Do you think this is true, false? And I'd like you to justify.

The second statement says, "13 multiplied by 13 is 169, so 13 is a square number." Is this true or false? And provide a justification.

The next statement says, "Four, add three, then multiply by seven gives a square number." Is this true or false? And explain with a justification.

The last statement says, "Seven multiplied by four, add three, gives a square number." Is this true or false? And make sure you provide that justification.

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

Well done, so let's move on to question four.

Question four states that Jun discovers he can sum two different square numbers to make a third square number.

Now, can you find the missing square numbers to complete the table? The first one's been done for you.

So the first square number he thinks of is nine, a second square number he thinks of is 16, and if you add nine and 16 together, it gives the resulting square number, which is 25.

The second row, we don't know what one square number is, and we don't know what the second square number is, but we do know when we sum them together, we have a resultant square number of 100.

And the third row, we don't know what the first square number is, we don't know what the second square number is, but we do know when we add them together, the resulting square number is 169.

Question B wants you to find another set of two different square numbers to make a third square number.

See if you can give this a go and press pause if you need more time.

So let's move on to the last question.

This is a great question and shows an eight by eight chess board, and the question wants you to find how many squares do you see on this eight by eight chess board? I'm going to give you a hint.

It's not 64.

There are a lot more squares than 64 squares on this chess board.

See if you can find out how many squares there are and press pause if you need.

Really well done.

These are great questions, so let's go through our answers.

For question one, hopefully you've identified the square number 49 links to the seven by seven.

Then you should have had the square number of 25 links to the five by five, the square number of 64 links to the eight by eight, and the square number of 16 links to the four by four.

Really well done.

For question two, so let's see if we can figure out the teacher's age and Alex's age.

To do this, I'm going to list my square numbers just so I can quickly refer to them.

Let's have a look at the teacher's age.

Well, we know the teacher's age is a square number, a multiple of three, and less than 70.

We know the teacher can't be a one-year-old, a four-year-old, a nine-year-old, or a 16-year-old, so let's have a look at anything past 16.

25 is an option, but unfortunately 25 is not a multiple of three.

36 is a multiple of three and less than 70, so that's a possibility.

49 is not a multiple of three, but is less than 70.

And 64 is not a multiple of three.

So that means we know the teacher must be 36 years old.

Now let's have a look at Alex.

Alex is a student at Oak Academy, and we know his age is four less than a square number and is even, so we need to figure out how old is Alex.

Well, we can't use the square number one because one subtract four means we have a negative age.

We can't use the square number four because four subtract four is zero.

Nine subtract four is five, and five is not an even number.

16 subtract four is 12, and 12 is an even number.

We don't want to be going anything past 25 as Alex is a student at Oak Academy, so that means we know Alex is 12 years old because the square number is 16, 16 subtract four gives us an even number.

Huge well done if you got that one right.

Now let's have a look at question three.

We have to identify true or false with a justification.

Is 121 a square number? Yes, it is, because 11 multiplied by 11 is 21.

13 multiplied by 169 means 13 is a square number.

True or false? It's false.

169 is the square number as it's the product of 13 multiply by 13.

Four add three, then multiply by seven gives a square number.

Yes, it's true because four add three is seven, and seven multiplied by seven is 49.

And we know 49 is a square number.

Next, seven multiplied by four and add three gives a square number.

This is false because seven multiplied by four is 28, 28 add three is 31, and 31 is not a square number.

Well done if you've got this one right.

Question four was a great question.

Summing the first square number with a second square number, 36 add 64 is 100.

You can have them in either position.

64 add 36 is equal to 100.

The next answer would be 25 add 144 is 169.

Same again, you could have written it as 144 add 25 is 169.

A huge well done if you got 4A correct as that was tricky.

For B, there are many different answers out there.

I'm just gonna give some more examples.

81 add 144 is 225.

You may have even got 64 add 225 is 289.

Great work if you found any two different square numbers to make a third square number.

Question five was a fantastic question, and if you got this one right, a huge well done.

There are 204 squares in total.

This is because you need to look at the different types of squares you have on the board.

So if we're looking at one by one squares, we have 64 one by one squares.

If we have two by two squares, how many two by two squares do we have? Well, we have 49 two by two squares.

Next, three by three squares.

How many three by three squares do we have? 36, so on and so on forth.

These numbers end up being square numbers.

64, add the 49, add the 36, add the 25, add the 16, 9, 4, and 1.

And summing those together gives 204 squares on our chess board.

Fantastic work if you got close all that answer.

Great work so far, so let's move on to the second part of our lesson, which is cube numbers.

A cube number is the product of three repeated integers, so I've put some examples on the screen.

Eight is a cube number as it's the product of two, multiplied by two, multiplied by two.

27 is a cube number as it's the product of three, multiplied by three, multiplied by three.

80 is not a cube number because there's no three repeated integers which make 80.

So now I'm going to use the cube number eight and the cube number 27.

And what I want you to do is use eight cubes and 27 cubes to show why are they called cube numbers.

Can you arrange them in a particular way to justify why they're called cube numbers? See if you can give it a go and press pause if you need.

Well, let's see what you found.

Hopefully you've spotted the cube number eight is called a cube number because we can arrange them to make a cube, a two by two by two cube.

And 27.

27 can be arranged to make a cube.

As you can see here, I'm arranging them to make a three by three by three.

So you can see why a cube number is the product of three repeated integers, and why it's called a cube number, because they make a cube.

Now let's have a look at a table summarising the information on our cube numbers.

Here I've filled in part of the table identifying the integer, the calculation, and the cube number.

And what I want you to do is see if you can find all the cube numbers up to 250 and fill in the table below.

I've done the first two for you.

So using the integer one, the calculation would be one, multiplied by one, multiplied by one.

So that means our cube number is one.

Using the integer two, two, multiplied by two, multiplied by two gives us the cube number of eight.

See if you can fill in the rest and press pause if you need.

Let's see how you got on.

Well done if you identified the calculation to be three, multiplied by three, multiplied by three to give you 27, because three multiplied by three is nine, multiplied by three is 27.

The next calculation is four, multiplied by four, multiplied by four.

Well, four multiplied by four is 16.

Multiply this by four gives us 64.

Next, let's use the integer five.

Five, multiplied by five, multiplied by five is our calculation, so five multiplied by five is 25.

Multiply this by five gives me 125.

So that's our cube number.

Now let's have a look at six.

Well, the calculation would be six, multiplied by six, multiplied by six.

Six times six is 36.

36 multiplied by six is 216.

This table is really helpful as it identifies the calculation to make a cube number.

Well done if you got any of those correct.

What I'm going to do now is look at a quick check question.

Laura put these cubes together and she counted them, and she said, "I've made a cube with 48 cubes so 48 is a cube number." Where is her mistake? See if you can find it and press pause if you need.

Well, it certainly looks like a cube, but it's not a cube because what Laura has made is a four by four by three, and that is not a cube, it's a cuboid.

She made a cuboid with lengths four by four by three.

Next, Laura's put together these cubes, and she's counted them.

And she said, "27 is not a cube number because I don't have a cube." Can you explain why she's wrong? See if you can give it a go and press pause if you need.

Well done, she did not arrange them correctly.

All the lengths should be the same.

So she should be creating a cube, which is a three by three by three.

So 27 is a cube number, as it makes this cube.

Well done if you've got that one right.

Now let's move on to the task.

Here, you've been given some numbers, and all you need to do is identify the cube numbers from the list below.

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

Well done, so let's move on.

Question two gives you a Venn diagram, and you need to insert the numbers one, three, four, eight, nine, 16, 25, 27, 36, 40, 49, 64, 125, 216, and 1,000 in the Venn diagram.

Now, the numbers to the left of the Venn diagram are square numbers, and the numbers to the right of the Venn diagram are cube numbers.

See if you can insert these numbers in their correct position into the Venn diagram.

Press pause if you need more time.

Moving on to question three, we're asked to fill in the number to make the calculation correct.

Now, the number in the square is a square number, and the number in the cube is a cube number.

So question 3A states we have a square number, add a cube number must make 31.

For B, we have a square number, add a cube number makes 33.

For C, we have a square number, add a cube number makes 225.

For D, we have a square number, add a square number, add a cube number makes 104.

And for E, we have three cube numbers make 36.

See if you can give this a go.

This is a great question using your knowledge on both square and cube numbers.

Well done, so let's move on to the answers to question one, identifying all our cube numbers.

We have one, eight, 27, 64, 125, and 1,000.

Well done if you've got those right.

Make sure you know the difference between cube numbers and square numbers.

For question two, we needed to insert the numbers into our Venn diagram, knowing that we have some square numbers and some cube numbers and some numbers which are both square and cube numbers.

Let's see how you got on.

One is a square number and cube number.

Three is neither a square or cube.

Four is only a square number.

Eight is only a cube number.

Nine is only a square number.

16 is only a square number.

25 is only a square number.

27 is only a cube number.

36 is only a square number.

40 is neither a square or cube number.

49 is only a square number.

64 is a square and cube number.

125 is a cube number.

216 is a cube number.

And 1,000 is a cube number.

Really well done if you've got this.

This Venn diagram is a lovely way to illustrate square numbers, cube numbers, and numbers which are both square and cube numbers.

So let's see how you got on with question three, which wanted you to identify the square and cube numbers.

For A, you should have got 4 and 27.

For B, you should have got 25 and 8.

For C, 100 and 125.

For D, 36, 4, and 64.

Remember, 36 and 4, they're the two square numbers.

You can have them either way round.

And for E, a cracking answer 1, 8, and 27.

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

Fantastic work today.

Let's have a look at our summary page.

When there are two repeated integers, the product is a square number, and forming a square array can help you identify a square number.

And when there are three repeated integers, the product is a cube number.

And forming a cube using blocks can help you identify a cube number.

Great work today, a huge well done.