Unit 5 — Understanding Place Value

Welcome back!

Today we will discover one of the most important ideas in mathematics.

It is called place value.

Place value helps us understand how numbers are built.

Once you understand place value, larger numbers become much easier to read, write, and use.

Ones

Let's begin with numbers from 1 to 9.

Each number has one digit.

Examples:

1

4

7

9

These numbers all have only ones.

Tens

When we count past 9, something exciting happens.

We begin making groups of ten.

10 means:

• 1 group of ten
• 0 ones

11 means:

• 1 ten
• 1 one

15 means:

• 1 ten
• 5 ones

19 means:

• 1 ten
• 9 ones

Building Numbers

Let's look at a few more examples.

23 means:

• 2 tens
• 3 ones

47 means:

• 4 tens
• 7 ones

82 means:

• 8 tens
• 2 ones

Every two-digit number is made from tens and ones.

Using Groups

Imagine you have 34 blocks.

Instead of counting every block one at a time, you can organize them into:

• 3 groups of ten
• 4 extra blocks

Grouping objects makes counting faster and easier.

Comparing Numbers

Place value helps us compare numbers.

Which number is greater?

36 or 63?

Look at the tens.

36 has 3 tens.

63 has 6 tens.

Since 6 tens is greater than 3 tens,

63 is greater than 36.

Activity

Choose any two-digit number.

Write:

• the number
• how many tens
• how many ones

Example:

58

5 tens

8 ones

Now try several different numbers.

Number Puzzle

Can you guess the number?

It has:

• 7 tens
• 2 ones

The answer is:

72

Now try these.

4 tens and 9 ones

9 tens and 5 ones

2 tens and 6 ones

Can you create your own puzzles?

Practice

Write each number as tens and ones.

18 = _____ tens _____ ones

41 = _____ tens _____ ones

56 = _____ tens _____ ones

73 = _____ tens _____ ones

90 = _____ tens _____ ones

Review

Today you learned:

• numbers are built from tens and ones
• place value helps us understand numbers
• grouping makes counting easier
• place value helps us compare numbers
• every digit has an important place

Place value is one of the building blocks of mathematics.

Looking Ahead

Next we will begin adding larger numbers.

You will learn how addition uses the ideas of:

• tens
• ones
• number patterns
• careful thinking

Understanding place value makes addition much easier.