Lesson video

Hi, my name is Ms. Coe.

I'm really looking forward to learning with you today, and I know that you're going to try really hard and also really enjoy this lesson.

If you're ready, let's get going.

Welcome to this lesson in the place value unit.

The outcome of this lesson is by the end of the lesson, you can compose 100 in 10s and ones.

We've got some keywords for this lesson.

I'm going to say them and then I would like you to say them back.

My turn.

Equivalent.

Your turn.

Great job.

My turn.

Numeral.

Your turn.

Now let's look at what those words mean.

Equivalent means when two or more things have the same value.

So for example, you can say that three plus two is equivalent to two plus three.

They have the same value, and we use a special symbol called the equal sign to show when things are equivalent.

A numeral is a symbol or a name that stands for a number.

So as you can see there, we have a numeral for the number 100, which is made up of digits.

Today's lesson is all about the composition of 100 in 10s and ones.

In the first part of our lesson, we're going to look at how 100 is composed of 10s, and then in the second part of our lesson, we are going to look at how 100 is composed of ones.

Let's get going.

We are going to meet the following characters in our lesson: Aisha, Alex, Andeep, and Sofia.

They're going to help us with our learning, but they're also going to ask us some tricky questions to help us deepen our understanding.

I'd like you to take a moment to think, what do you know about the number 100? Well, Andeep knows that his house number is 100.

He can see it's on his door.

Sofia knows that there are 100 pennies in one pound.

Aisha knows that in a metre stick, there are 100 centimetres in one metre, so one metre is equal to, is equivalent to 100 centimetres.

And Alex knows that there are 100 ones in a base 10 100 block, and you may have seen and used these blocks before.

Sofia knows that she can write 100 in different ways and we're going to have a look at how we can write 100 using this, a place value chart.

Let's start with the number one.

Here we can see the digit one and it is positioned in the place value chart in the ones column.

So what does this digit one represent? Well, in this case, because it is in the ones column, the one represents one one.

Now, this is the number 10 written as a numeral, and this time, we have two digits, a one and a zero.

So what do the digits represent this time? Well, in this case, the one is in the 10s column of the place value chart.

So it represents one 10.

And the zero is in the ones column as a placeholder to show that it represents no additional ones.

This is how we write 10 as a numeral.

So now if we think of the number 100, we can see that we have three digits and you might spot something similar about one, 10 and 100, but this time, the one represents 100 because it is in the 100s column of the place value chart.

This zero represents there are no additional 10s and this one represents there are no additional ones.

This is how we write 100 as a numeral using digits, and you might want to remember that for later in our lesson.

Now let's think about how many 10s there are in 100.

So I can see here that we have a number line.

There is zero on one side and 100 on the other side.

Hmm, how many equal parts are there in my number line? Well, let's count together and find out.

We're going to start our count at zero and our first number is going to be 10.

Are you ready? 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

So we can see here that we have counted in 10s from zero to 100.

How many 10s are there in 100? Well, I can see that there are 10 10s in 100.

We can also think about and count this relationship in a different way.

We have the same number line here, but this time, instead of counting in groups of 10, so 10, 20, 30 and so on, we are going to count in 10s.

So this time, we start our count at zero 10s and our first number is one 10.

Let's count together.

Are you ready? Zero 10, one 10, two 10s, three 10s, four 10s, five 10s, six 10s, seven 10s, eight 10s, nine 10s, 10 10s.

10 10s are in 100.

10 10s is equal to 100.

Now, you may have seen this piece of equipment in the classroom.

This is a bead string.

A bead string contains 100 beads.

As we can see with the bead string, they are colour coded and there are 10 equal parts or equal groups of 10 beads.

So we can say that 10 groups of 10 beads is equivalent to 100 beads.

Let's count together to check.

Are you ready? Zero 10s, one 10, two 10s, three 10s, four 10s, five 10s, six 10s, seven 10s, eight 10s, nine 10s, and 10 10s, which is 100.

We can clearly see here that one 10 is equal to 10, two 10s is equal to 20, three 10s is equal to 30 and so on.

So therefore, 10 groups of 10 beads is equivalent to, is equal to 100 beads.

There are 10 equal parts.

We can also show this relationship using a bar model and you may have seen bar models before.

The top bar shows our whole, which is 100 and the bottom has been split into 10 equal parts to show us that 10 groups of 10 are equivalent to 100.

I'd like you to say that top sentence with me.

Are you ready? 10 groups of 10 are equivalent to 100.

Great job.

It's time for you to check your understanding.

Hmm groups of 10 squares is equivalent to 100 squares.

Look at the image.

There are 10 equal parts.

I would like you to count the parts in 10s and then I would like to say that sentence to your partner, or you can say it to me.

Pause the video here and have a go.

How did you get on? Let's count together.

We start our count at zero and we say 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

So we can say 10 groups of 10 squares is equivalent to 100 squares and there are 10 equal parts.

Well done if you told your partner that and well done if you counted in 10s, such as one 10, two 10, three 10s instead of counting 10, 20, 30.

Another opportunity for you to check your understanding.

Mm groups of 10 blocks is equal to 100 blocks.

There are 10 equal parts.

Count the parts in groups of 10 this time and complete the sentence.

Pause the video now and have a go.

How did you get on? Shall we count together? We start our count at zero 10s and we say one 10, two 10s, three 10s, four 10s, five 10s, six 10s, seven 10s, eight 10s, nine 10s, 10 10s.

So that means 10 groups of 10 blocks is equal to 100 blocks.

10 groups of 10 blocks is equivalent to 100 blocks.

Well done if you got that.

I'd like you to take a moment to have a look at the three pictures on the screen.

There are 100 small squares in each square, but are we still showing 10 equal parts of 10 that make 100? Hmm.

Well, yes, we are.

10 groups of 10 squares is equivalent to 100 squares and it doesn't matter how we show those 10 groups of 10 squares.

If we look at the image on the right, we can see quite an unusual way of showing 10 equal parts.

But if we count the number of small squares in each part, we can see that there are 10 small squares in each part.

And if we count each part, we can see that there are 10 equal parts.

So we can still say that 10 groups of 10 squares is equivalent to 100 squares, no matter how those parts are divided up.

You can make 100 from lots of things.

So we are going to have a look at some straws.

This is a group or a bundle of 10 straws.

I wonder how many groups of 10 straws is equal to 100 straws.

Let's count together.

One 10, two 10s, three 10s, four 10s, five 10s, six 10s, seven 10s, eight 10s, nine 10s, 10 10s.

10 groups of 10 straws is equal to or equivalent to 100 straws.

So it doesn't matter what we are making 100 from, as long as we have 10 equal parts of 10, we will have 100.

Time to check your understanding here.

Mm groups of 10 p coins is equal to 100 pence.

There are 10 equal parts.

I would like you to complete that sentence and then I would like you to tell your partner mm 10s is equivalent to mm.

100 pence is equivalent to mm 10 pence coins.

Pause the video here and have a go.

How did you get on? Hopefully by now you are realising that 10 groups of 10 is equal to 100 and it doesn't matter if those groups of 10 are blocks or squares or in this case, pennies.

10 groups of 10 pence is equal to 100 pence.

There are still 10 equal parts and hopefully you said to your partner, 10 10s is equivalent to 100, 100 pence is equivalent to 10 10 pence coins.

Well done if you got that.

We can also represent 100 with an equation.

So if you remember, this bar model shows us that 100 is equal to 10 equal parts of 10.

We can write that as 100 equals 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10 plus 10.

Goodness, that's a lot of 10s.

Now, that just shows us that if we add together 10 groups of 10, that is equivalent to or equal to 100.

So here Aisha has represented it with an addition equation.

We know it's an addition equation because we are using the add symbol or the plus symbol between each group of 10.

We can also represent it in a different way.

So Alex is saying that 100 is equal to 10 multiplied by 10.

Hmm, that's interesting.

So Andeep knows that Alex is correct because we can say that multiplied by means groups of, so we can read Alex's equation as 100 is equal to 10 groups of 10, and Andeep can see 10 groups of 10 in the bar model.

So he knows that Alex is correct.

Time for a check for your understanding.

We've seen this image before and we know that 10 groups of 10 pence coins is equal to 100 pence.

We know that there are 10 equal parts here.

I would like you to write an addition and a multiplication equation to show this.

Pause the video now and have a go.

How did you get on? So the addition equation looks like this.

10 p plus 10 p plus 10 p plus 10 p plus 10 p plus 10 p plus 10 p plus 10 p plus 10 p plus 10 p equals 100 pence or 100 pennies.

Now, you may have written that the other way round, so you may have written 100 pence equals, followed by 10 lots of 10 pence.

That's absolutely fine.

We can also say that 10 groups of 10 pence is equal to 100 pence.

And remember, we can use the multiplication sign to show groups of, so we can also write 10 multiplied by 10 pence is equal to 100 pence.

Well done if you wrote either of those equations down.

Great work.

Now we're going to move on to our first practise tasks of the lesson.

So for your first task, I would like you to fill in the missing values on the number line.

So on the top of the number line, we have one 10, then hmm something, then three 10s, then another blank, then five 10s and so on.

What are the missing values there? And on the bottom of the number line, we start off with two blanks, but then we have 30 represented as a numeral.

So please have a think and fill in the missing values on that number line.

For the second question, I'd like you to fill in the missing values on the table.

So there are two tables here.

On the left-hand column, we have the numeral.

So you can see 10, 20, 30 and so on.

But there are some gaps in that column for you to fill in.

And on the right-hand side, you have number of 10s.

So the first row is completed for you.

The numeral is 10 and the number of 10s is one 10.

So you need to fill in the blanks.

Pause the video here and have a go at those questions.

How did you get on? Should we have a look at some answers? So for your first task, we asked you to fill in the missing values on the number line.

The completed number line is here.

So pause the video and have a look at those answers.

Well done if you started to see a pattern.

So for example, we knew that nine 10s had to be written as 90 because if we imagined our place value chart, the nine would be in the 10s column and the zero would represent no additional ones.

Question two, we asked you to fill in the missing values in the table.

So again, pause the video here and give yourself a tick if you've got all of these answers.

I think the pattern here is really obvious.

So we can see, for example, that the numeral is 70 and it represents seven 10s and we know this because of the place value and you can see that pattern happening all over.

The only real change and the thing to be careful of is when we get to 10 10s and we write that as 100.

So the numeral has three digits, one which will be in the 100s column and two zeros, which represent no additional 10s and no additional ones.

Well done if you got all of that correct.

Let's move on to the second part of our learning where we're learning that 100 is composed of ones.

Are you ready? Let's get going.

This is a hundred square.

Now, you may have seen these before and you may have seen them with numbers in, you may have seen them with shading in, but this is a 100 square and there are 100 equal parts.

So this is one way of showing 100 in 100 equal parts.

Andeep is saying, "What could you find to count 100?" Hmm.

Now he might find some cubes, so you'd need 100 equal parts, 100 cubes.

You might find counters or you might find pennies.

Now, all of these and lots of other things could be used to count to 100, but we, for now, are going to use the hundred square.

Now, I have told you that this hundred square is in 100 parts, but I don't expect you to believe me.

So let's check the number of small squares.

We're going to count together.

Are you ready? We start our count at one because we've coloured in that first square.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

(instructor sighing) Well done if you kept up with me with all of that counting.

So there are 100 small squares inside the larger square.

There are 100 ones in 100.

We counted 100 different numbers.

We said 100 different numbers when we were counting.

So that means that there are 100 equal parts in this hundred square.

So that also means that 100 ones are equivalent to 100.

Can you say that sentence with me? 100 ones are equivalent to 100.

Well done.

So Aisha's asking us, "How could we write that as a calculation?" So think about how we wrote 100 composed of 10s, And can we apply that to thinking about 100 ones, which are equivalent to 100? Hmm.

Wow.

Andeep starts writing an addition equation.

So he writes 100 equals one plus one plus one plus one plus one plus one plus one.

(instructor sighing) How many ones would you need to write? Well, there are 100 ones in 100, so Andeep would be there forever writing one plus one plus one.

He would need to write 100 ones.

I think that would take a very long time and I think it would be hard to do accurately.

I know that I would lose count and I'd have to start all over again.

So Aisha thinks there might be a more efficient way to write this.

Should we have a look? Aisha says that we could write 100 multiplied by one equals 100.

Hmm.

Do we think she's right? Well, if we remember that the multiplication symbol can be read as groups of, we could say that 100 groups of one is equal to 100.

We can see on this hundred square 100 groups, which are made up of one.

So Aisha's absolutely right.

We could write one plus one plus one 100 times, but it is much more efficient to write 100 multiplied by one equals 100.

Well done, Aisha.

We can look at this on a bead string as well.

So remember that a bead string is made up of 100 beads.

We can see very clearly that they are in 10 equal parts because of the colours, but because there are 100 beads, that means there are 100 equal parts and we can see that 100 ones are equivalent to 100.

So how would we write this as a calculation? Well, remember that multiplication is more efficient.

There are 100 groups of one.

So we can write this as 100 multiplied by one is equal to 100.

Well done, Andeep.

You're not writing out one 100 times anymore.

Time to check your understanding.

This is a base 10 block and you may have seen it before.

How many ones are there in the 100 base 10 block? Can you write that as a calculation? Pause the video now and have a go.

How did you get on? We know that there are 100 ones in the 100 block.

So we can write this as 100 multiplied by one is equal to 100 because remember, the multiplication sign means groups of.

So 100 groups of one is equal to 100.

Well done if you wrote that.

Time for our second practise now.

The first thing I'd like you to do is complete the one to 100 number square by filling in the numerals.

So we counted them out loud earlier.

Now can you write the numerals? How many numerals will you need to write? Then I would like you to write about your number square using the word equivalent.

So can you write some sentences to explain your hundred square using that keyword of the day equivalent? Remember, equivalent means equal to.

Then I would like you to have a go at filling out the equation.

Hmm multiplied by hmm is equal to 100.

Pause the video here and come back in a few moments for some feedback.

How did you get on? So first of all, your 100 square should now look like mine.

We can see that we had to write 100 different numerals.

Hopefully you saw some patterns in those numerals and remembered that the multiples of 10, the groups of 10 go on the right-hand side in that last column.

We knew that we wrote 100 numerals.

Then I asked you to write about your number square where using the word equivalent.

Now, you may have written slightly different sentences, but hopefully you also wrote 100 is equivalent to 100 ones.

And then finally, I asked you to write the equation.

So hopefully, you wrote 100 multiplied by one is equal to 100 because remember, we have 100 groups of one, which make 100.

Well done if you got all of that right and particularly well done if you filled out your hundred square with all of those numerals.

We have come to the end of our lesson and I have really enjoyed working with you today.

So let's summarise our learning.

We now know that there are 10 10s in 100, so we can say that 100 is equivalent to 10 10s.

We can also say that 100 is equivalent to 100 ones because there are 100 ones in 100.

You have worked incredibly hard today and you've done an excellent job.

I can't wait to see you next time.