Grade by Grade
B. Number · Number Sense: Numbers to 200 and Fractions

Hundreds, Tens and Ones: Building and Breaking Apart Numbers

B1.1About 35 minutes
Learning goals
  • I know that 10 ones make 1 ten and 10 tens make 1 hundred.
  • I can tell the value of each digit in a number to 200.
  • I can build (compose) a number from hundreds, tens and ones.
  • I can break apart (decompose) a number in more than one way.

Words to know

place value
The value a digit has because of where it is in the number. In 152, the 5 is in the tens place, so it is worth 50.
hundreds place
The first digit of a three-digit number. It tells how many hundreds.
compose
To put parts together to make a number. 100 + 20 + 3 makes 123.
decompose
To break a number into parts. 123 can be broken into 100 + 23.
expanded form
A number written as the sum of its place values, like 100 + 40 + 7 for 147.

Remember from Grade 1

In Grade 1 you learned that 10 ones make 1 ten. The number 34 is 3 tens and 4 ones.

Now we need a new, bigger group. What happens when we have 10 tens?

=10 tens1 hundred
10 ten rods are the same as 1 hundred flat. 10 tens = 100.

10 tens make 1 hundred. That is the same as 100 ones!

So now a number can have three parts:

  • Hundreds (big flats)
  • Tens (long rods)
  • Ones (small cubes)
HundredsTensOnesNumber
147147
109109
190190
08686
200200
A place value chart. Each digit sits in its own place.

What is each digit worth?

In 147:

  • the 1 means 1 hundred, worth 100
  • the 4 means 4 tens, worth 40
  • the 7 means 7 ones, worth 7

We can write it as adding parts: 147 = 100 + 40 + 7. This is called expanded form.

1 hundred, 4 tens, 7 ones
147 is 1 hundred, 4 tens and 7 ones.

Zero holds a place

107 and 170 use the same digits, but they are very different!

  • 107 = 1 hundred, 0 tens, 7 ones = 100 + 7
  • 170 = 1 hundred, 7 tens, 0 ones = 100 + 70

The 0 shows that a place is empty.

Worked example

Example 1: Build a number

Lila has 1 hundred flat, 6 ten rods and 2 ones cubes. What number did she build?

  1. Hundreds: 1, so write 1 first.
  2. Tens: 6, so the next digit is 6.
  3. Ones: 2, so the last digit is 2.
  4. Check with expanded form: 100 + 60 + 2 = 162.

Lila built 162.

Worked example

Example 2: Too many tens

Owen has 12 tens and 6 ones. What number is that?

  1. 10 of the tens can be traded for 1 hundred.
  2. 12 tens = 1 hundred and 2 tens left over.
  3. Now we have 1 hundred, 2 tens, 6 ones.

126. (Count by 10s to check: 10, 20, ... 120, then 121 ... 126.)

10 tens = 1 hundred13 tens, 5 ones = 135
135 can also be shown as 13 tens and 5 ones. 10 of these tens make 1 hundred.
Worked example

Example 3: Break apart a number many ways

Show 135 in three different ways.

  1. Hundreds, tens and ones: 100 + 30 + 5
  2. Hundred and the rest: 100 + 35
  3. Only tens and ones: 13 tens and 5 ones (130 + 5)
  4. There are more ways too, like 120 + 15 or 50 + 50 + 35.

135 = 100 + 30 + 5 = 100 + 35 = 13 tens and 5 ones. All of these are the same amount.

Just for fun

Riddle: I am really 10 tens wearing a disguise. Who am I?

One hundred! My disguise is a big, flat square.

Hands-on activity

Bundle it up

You need: about 150 popsicle sticks, straws or toothpicks (or use dry spaghetti broken in half), and some elastic bands.

  1. Count out 10 sticks and put an elastic around them. That's 1 ten.
  2. Make lots of bundles of ten.
  3. When you have 10 bundles, put a big elastic around them. That's 1 hundred!
  4. A grown-up says a number, like 128. Build it with the bundles and loose sticks.
  5. Now trade: take the elastic off one ten bundle. Can you still show 128 a different way? (1 hundred, 1 ten, 18 ones.)

Math talk: "Why is it faster to count bundles than single sticks?"

Your turn

1

What number is 1 hundred, 5 tens and 8 ones?

2

In 174, what is the 7 worth?

3

Write 193 in expanded form.

4

What number is 100 + 6?

5

How many tens are in 100?

6

What number is 14 tens and 2 ones?

7

Break apart 150 in two ways.

More practice: warm-up

1

What number is 1 hundred, 2 tens and 3 ones?

2

100 + 40 + 1 = ?

3

In 186, which digit is in the tens place?

4

How many ones make 1 ten?

5

How many hundreds are in 200?

More practice: on your own

1

What is the value of the 1 in 61? In 116?

2

Ben says 105 has 5 tens. Is he right?

3

What number is 1 hundred, 3 tens and 12 ones?

4

Fill in: 167 = 100 + __ + 7

5

Fill in: 184 = __ tens and 4 ones

Challenge

1

I have 1 hundred and 0 tens. My ones digit is 3 more than my hundreds digit. What number am I?

2

Find two ways to make 120 using only ten rods and hundred flats. Then find a third way that also uses ones cubes.

3

Ana builds 132 with blocks. She adds 3 ten rods and 4 ones. What number does she have? Then she adds 10 more ones. What number is it now?

Check your understanding

Quiz

1.

What number is 1 hundred, 3 tens, 9 ones?

2.

In 158, what is the 5 worth?

3.

Which is the expanded form of 120?

4.

What number is 100 + 4?

5.

How many tens are in 160?

6.

Which is not a way to make 145?

For parents and teachers

Big idea: Our number system groups by tens. 10 ones make a ten, and 10 tens make a hundred. The place of a digit tells its value. A number can be broken apart in many ways and still be the same amount.

Common difficulties:

  • Reading 12 tens as 12 or writing 1 hundred 2 tens 6 ones as 10026. Use bundles or blocks and have your child trade 10 tens for a hundred.
  • Thinking a number can only be split one way. Ask, "Can you show it a different way?"
  • Forgetting zero as a placeholder (104 vs 14). Point at the empty tens place: "How many tens? Zero. We write 0."

How to help: Bundles of straws or popsicle sticks are the best tool. Free base ten blocks apps and printable paper blocks also work. Ask, "What is the 6 worth in 163?" and let your child show it.

Note: The Grade 2 curriculum goes to 200. If your child is curious about bigger numbers, the same pattern continues.