Counting and Place Value

What you will learn

• Count forwards and backwards to $100$ in ones and in tens.
• Say how many tens and how many ones are in a number up to $100$.
• Say what a digit is worth from the place it sits in.

Before you start: you only need to be able to count a small group of things, one for each number you say.

The idea

Counting is saying the numbers in order while you point at things, one number for each thing. The last number you say tells you how many there are. If you count a row of pebbles “one, two, three, four, five”, there are $5$ pebbles.

That works for a handful of pebbles. For a whole bucket of them, counting in ones takes forever and it is easy to lose your place. So people invented a better way: bundle the pebbles into groups of ten.

Counting to 100

The numbers from $1$ to $9$ each have their own name. Then comes $10$, and the pattern starts again with a new first part.

• $11$ to $19$ are the awkward ones. “Eleven” and “twelve” have their own names. “Thirteen” to “nineteen” end in “-teen”, which is an old way of saying “and ten”.
• From $20$ onwards, the names are tidy. “Twenty-one, twenty-two, twenty-three” all the way to “twenty-nine”, then “thirty”.
• The tens are “twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety”, and then “one hundred”.

Practise counting out loud past the tricky corners: $29$ to $30$, $59$ to $60$, $99$ to $100$. Those are the places where counting most often goes wrong.

Counting in tens

If you only say the tens, you can get to $100$ in ten words: $10, 20, 30, 40, 50, 60, 70, 80, 90, 100$. Counting in tens is fast, and it is the key to the rest of this lesson.

Making a ten

Take $10$ loose counters and pile them up. Now they are one group, one ten, instead of ten separate ones. Nothing has been added or taken away. You have just bundled them.

Sort $36$ counters into tens and you get $3$ bundles with $6$ left over. That is why we write it as $36$: the $3$ means three tens and the $6$ means six ones.

What each digit is worth

A digit is one of the ten symbols $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$. A number like $36$ is made of two digits. Each digit’s worth depends on its place.

• The digit on the right is in the ones place. It is worth itself.
• The digit to its left is in the tens place. It is worth itself times ten.

So in $36$ the $6$ is worth $6$, but the $3$ is worth $30$. Swap them and you get $63$, which is a very different number. Same digits, different places, different worth. This is called place value.

Zero as a place holder

What about $40$? There are four tens and no ones. We still have to write something in the ones place, or $40$ would look like $4$. Zero holds the place open and says “nothing here”. Without zero, place value would not work.

Worked examples

Example 1: Counting a big pile

Nia tips out a tin of $52$ buttons. How can she count them without losing track?

1. Slide buttons into lines of ten. Each line is one ten.
2. She makes $5$ full lines, with $2$ buttons left over.
3. Count the lines in tens: “ten, twenty, thirty, forty, fifty”.
4. Count on the leftovers in ones: “fifty-one, fifty-two”.

Answer: $52$ buttons, which is $5$ tens and $2$ ones.

Example 2: Reading a number

What is the $7$ worth in $71$, and what is the $1$ worth?

1. Find the ones place. It is the digit on the right, the $1$. It is worth $1$.
2. Find the tens place. It is the digit on the left, the $7$. It is worth $7$ tens.
3. Seven tens is $70$.

Answer: The $7$ is worth $70$ and the $1$ is worth $1$. Together, $70 + 1 = 71$.

Example 3: Building a number

Ravi has $8$ ten-sticks and $4$ single cubes. What number has he built?

1. Count the ten-sticks in tens: “ten, twenty, thirty, forty, fifty, sixty, seventy, eighty”.
2. Count on the single cubes: “eighty-one, eighty-two, eighty-three, eighty-four”.
3. Write $8$ in the tens place and $4$ in the ones place.

Answer: $84$.

Do not read $84$ as “eight, four”. Read it as “eighty-four”. The $8$ is not eight things, it is eight tens. Saying the full name reminds you what each digit is really worth.

Why it matters

Place value is the reason we only need ten digits to write any number at all. Prices in a shop, page numbers in a book, the score in a game and the age of your grandparents are all written this way. Once you know that the left-hand digit is worth tens, you can read numbers at a glance, see which of two numbers is bigger, and add and subtract without counting in ones. Later on, the same pattern stretches to hundreds and thousands, and even past the decimal point.