Numbers and Sequence to 120

Rote Counting 11 to 20

Today we will learn how to say the numbers from 11 to 20 in order.

This is called rote counting. Rote counting means saying numbers in the correct order from memory.

The teen numbers are a little tricky because some of their names do not sound exactly like the small numbers you already know. That is why we practice them again and again.

Here are the numbers from 11 to 20:

$$11,\ 12,\ 13,\ 14,\ 15,\ 16,\ 17,\ 18,\ 19,\ 20$$

Let’s say their names together:

eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty

When we count forward, we say one number after another in order.

1. 11 — eleven
2. 12 — twelve
3. 13 — thirteen
4. 14 — fourteen
5. 15 — fifteen
6. 16 — sixteen
7. 17 — seventeen
8. 18 — eighteen
9. 19 — nineteen
10. 20 — twenty

Listen for the pattern. Many teen numbers end with "-teen".

• thirteen
• fourteen
• fifteen
• sixteen
• seventeen
• eighteen
• nineteen

But the first two teen numbers are special:

• 11 is eleven
• 12 is twelve

These are important numbers to remember because they do not end with "-teen".

Counting forward from 11 to 20 means each new number is 1 more than the number before it.

We can show that like this:

$$11 \rightarrow 12 \rightarrow 13 \rightarrow 14 \rightarrow 15 \rightarrow 16 \rightarrow 17 \rightarrow 18 \rightarrow 19 \rightarrow 20$$

If you know one number, you can say the next number.

• After 11 comes 12.
• After 12 comes 13.
• After 13 comes 14.
• After 14 comes 15.
• After 15 comes 16.
• After 16 comes 17.
• After 17 comes 18.
• After 18 comes 19.
• After 19 comes 20.

Worked Example 1

Say the numbers from 11 to 15.

Start at 11 and count forward:

$$11,\ 12,\ 13,\ 14,\ 15$$

We say: eleven, twelve, thirteen, fourteen, fifteen.

Worked Example 2

What number comes after 16?

Count forward one step:

$$16 \rightarrow 17$$

The number after 16 is 17.

Worked Example 3

Fill in the missing numbers: $$13,\ \_,\ 15,\ \_,\ 17$$

Count in order from 13:

$$13,\ 14,\ 15,\ 16,\ 17$$

The missing numbers are 14 and 16.

Worked Example 4

Say the numbers from 18 to 20.

Count forward:

$$18,\ 19,\ 20$$

We say: eighteen, nineteen, twenty.

Tips to help you remember teen numbers

• Say them slowly in order every day.
• Remember that 11 = eleven and 12 = twelve are special.
• Listen for "-teen" in many of the numbers from 13 to 19.
• Practice starting at different numbers, like 14 or 17, and keep counting forward.

Let’s practice together

• Start at 11: 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
• Start at 14: 14, 15, 16, 17, 18, 19, 20
• Start at 17: 17, 18, 19, 20

Quick check

• What comes after 11? 12
• What comes after 18? 19
• What comes after 19? 20
• What number comes between 15 and 17? 16

Summary

Rote counting means saying numbers in the correct order from memory.

The numbers from 11 to 20 are:

11, 12, 13, 14, 15, 16, 17, 18, 19, 20

We say them like this: eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty.

Keep practicing so the teen numbers become easy to say in order.

Counting Objects 11 to 20

Sometimes we count small groups of things. Sometimes we count bigger groups. In this lesson, we will learn how to count objects from 11 to 20.

When there are many objects, it can be easy to lose track. That is why good counters use strategies to help. A strategy is a smart way to do something.

By the end of this lesson, you will be able to count objects up to 20 and know that the last number you say tells how many objects there are.

1. Count one object at a time

When you count, touch or point to one object for each number word you say.

• Say one number for each object.
• Do not skip objects.
• Do not count the same object twice.

This is called counting carefully.

2. Say the numbers in order

To count objects from 11 to 20, we say the numbers in the correct order:

\(11, 12, 13, 14, 15, 16, 17, 18, 19, 20\)

If you know the number order, it is easier to count bigger groups.

3. Move counted objects

A very helpful strategy is to move each object after you count it.

You can:

• slide counted objects to one side,
• put counted objects in a line,
• touch each object as you say the next number.

Moving counted objects helps you see which ones you already counted and which ones you still need to count.

4. The last number tells how many

When you finish counting all the objects, the last number you say is the total number of objects.

For example, if you count:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\)

then there are 12 objects.

5. Objects can be in a line or mixed up

Sometimes objects are in a straight line. These can be easier to count.

Sometimes objects are mixed up or spread out. These can be trickier. That is when moving objects or pointing carefully helps a lot.

No matter how the objects are arranged, we still count one by one.

Worked Example 1: Counting objects in a line

Sam sees a row of buttons. He points to each button and says:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\)

The last number Sam says is 11.

So there are 11 buttons.

Worked Example 2: Counting a bigger line of objects

Ava counts crayons in a line. She says:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14\)

The last number is 14.

So Ava counted 14 crayons.

Worked Example 3: Counting mixed-up objects

Leo has some blocks that are not in a line. They are mixed up on the table.

Leo moves each block to the left after he counts it. He says:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16\)

The last number is 16.

So there are 16 blocks.

Moving the blocks helped Leo not count any block twice.

Worked Example 4: Counting all the way to 20

Mia counts a group of shells. She touches each shell once and says:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\)

The last number is 20.

So Mia counted 20 shells.

Helpful counting tips

• Start at 1 when counting a group of objects.
• Touch or move each object as you count it.
• Say the numbers in order.
• Stop when every object has been counted.
• Remember: the last number tells how many.

If you make a mistake

That is okay. You can try again.

Here are some things to check:

• Did I skip an object?
• Did I count one object two times?
• Did I say the numbers in the right order?
• Did I move or touch each object?

Practice thinking

If you count a group and the last number you say is \(13\), then there are 13 objects.

If you count a group and the last number you say is \(18\), then there are 18 objects.

This is true because the last number tells the total.

Summary

To count objects from 11 to 20:

1. Start at 1.
2. Count one object at a time.
3. Touch or move each object as you count.
4. Say the numbers in order up to 20.
5. The last number you say tells how many objects there are.

With practice, you can count lines of objects and mixed-up groups too. Careful counting helps you get the right answer every time.

Writing Numerals 11 to 20

Let’s learn how to write the numbers 11 to 20. These numbers are called teen numbers.

Teen numbers can be tricky because sometimes we say them in a different way than we write them. For example, fourteen is written as 14, not 41.

In this lesson, we will practice reading, saying, and writing the numerals from 11 to 20 the right way.

Meet the teen numbers:

• eleven = 11
• twelve = 12
• thirteen = 13
• fourteen = 14
• fifteen = 15
• sixteen = 16
• seventeen = 17
• eighteen = 18
• nineteen = 19
• twenty = 20

Big idea: A teen number has 1 ten and some extra ones.

For example:

• 11 means 1 ten and 1 one
• 14 means 1 ten and 4 ones
• 19 means 1 ten and 9 ones

This helps us remember why teen numbers start with the digit 1. The 1 tells us there is 1 ten.

The second digit tells us how many ones there are.

So:

• 13 has 1 ten and 3 ones
• 16 has 1 ten and 6 ones
• 18 has 1 ten and 8 ones

How to write teen numerals:

1. Listen to the number name.
2. Remember that teen numbers from 11 to 19 start with 1.
3. Write the ones digit second.

For 20, we write a 2 and a 0. That means 2 tens and 0 ones.

Be careful! Sometimes children switch the digits. This is called a reversal error.

For example:

• 14 is correct for fourteen
• 41 is not fourteen

Why? In 14, the 1 comes first because there is 1 ten. Then the 4 shows 4 ones.

Here are more examples of numbers that should not be flipped:

• fifteen = 15, not 51
• seventeen = 17, not 71
• nineteen = 19, not 91

A helpful pattern: Most teen numbers end with teen.

When you hear thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, or nineteen, think: 1 ten and some ones.

Worked Example 1

Write the numeral for eleven.

Eleven has 1 ten and 1 one.

So we write $$11$$

Worked Example 2

Write the numeral for fourteen.

Fourteen has 1 ten and 4 ones.

Write the 1 first, then the 4.

So we write $$14$$

Worked Example 3

A student wrote 61 for sixteen. Is that correct?

No. Sixteen means 1 ten and 6 ones.

So the digits must be written as $$16$$

16 is correct. 61 is not correct.

Worked Example 4

Write the numeral for twenty.

Twenty has 2 tens and 0 ones.

So we write $$20$$

Let’s practice thinking about digits:

• In 12, the 1 means 1 ten and the 2 means 2 ones.
• In 15, the 1 means 1 ten and the 5 means 5 ones.
• In 20, the 2 means 2 tens and the 0 means 0 ones.

Tips to help you remember:

• Teen numbers from 11 to 19 start with 1.
• The second digit tells the extra ones.
• Do not flip the digits.
• Say the number slowly, then write it.

You can also check your work by asking:

• Did I start with 1 for a teen number?
• Did I put the ones digit second?
• If the number is twenty, did I write 20?

Summary

Numbers from 11 to 19 are teen numbers. They all have 1 ten and some ones, so they usually start with 1.

When writing a teen numeral, write the 1 first, then the ones digit. For example, fourteen is 14, not 41. Twenty is written as 20.

Counting Forward from a Given Number means starting at a number you already know and saying the next numbers in order.

You do not always have to start at 1. If someone says 6, you can keep counting: 7, 8, 9, 10.

This is an important skill because numbers stay in the same order every time. When we know the order, we can start anywhere and count forward.

Let’s remember: counting forward means the numbers get bigger by 1 each time.

For example:

$$5,\ 6,\ 7,\ 8,\ 9$$

Each number is 1 more than the number before it.

When you count forward from a given number, follow these steps:

1. Say the starting number.
2. Think: “What number comes next?”
3. Keep going one number at a time.

Here are some number order examples:

• After 3 comes 4.
• After 9 comes 10.
• After 14 comes 15.
• After 29 comes 30.

Sometimes counting forward crosses into a new ten. That is okay. You still just say the next number.

For example:

$$8,\ 9,\ 10,\ 11$$

And:

$$18,\ 19,\ 20,\ 21$$

Notice how after 9 comes 10, and after 19 comes 20. The numbers are still going forward by 1.

Worked Example 1

Start at 4. Count forward 3 numbers.

We begin with 4.

The next numbers are 5, 6, and 7.

So the count is:

$$4,\ 5,\ 6,\ 7$$

Worked Example 2

Start at 11. Count forward 5 numbers.

We begin with 11.

Then we count on: 12, 13, 14, 15, 16.

So the count is:

$$11,\ 12,\ 13,\ 14,\ 15,\ 16$$

Worked Example 3

Start at 27. Count forward 4 numbers.

We begin with 27.

The next numbers are 28, 29, 30, and 31.

So the count is:

$$27,\ 28,\ 29,\ 30,\ 31$$

Did you see what happened? We moved from 29 to 30. That is still counting forward by 1.

Worked Example 4

What number comes next?

$$58,\ 59,\ \_\_$$

After 59 comes 60.

So the answer is:

$$58,\ 59,\ 60$$

Helpful Tips

• Say the numbers slowly and in order.
• Remember: each new number is 1 more.
• Do not start over at 1 unless the starting number is 1.
• When you reach 9, the next number is 10.
• When you reach 19, the next number is 20.
• When you reach 29, the next number is 30.

You can also use a number line in your mind. Start on the number you are given, then hop forward one step at a time.

Example:

Start at 32 and count forward 3 numbers:

$$32 \rightarrow 33 \rightarrow 34 \rightarrow 35$$

Each hop moves forward by 1.

Let’s practice thinking about “what comes next”:

• After 7 comes 8.
• After 15 comes 16.
• After 39 comes 40.
• After 99 comes 100.

No matter what number you start with, counting forward means you keep the number order going.

Summary

Counting forward from a given number means you start at that number and say the next numbers in order. The numbers get bigger by 1 each time. You can start at 4, 18, 27, 58, or any number, and keep counting on without going back to 1.

Counting Backward from 20 means saying numbers in reverse order, starting at 20 and going down to 0.

This is an important number skill because when we count backward, each new number is 1 less than the number before it.

Counting backward helps us get ready for subtraction. If we know how to go back by 1, we can understand taking away.

Let’s look at the backward counting path from 20 to 0:

$$20,\ 19,\ 18,\ 17,\ 16,\ 15,\ 14,\ 13,\ 12,\ 11,\ 10,\ 9,\ 8,\ 7,\ 6,\ 5,\ 4,\ 3,\ 2,\ 1,\ 0$$

When we count backward, we do not go up. We go down. We say the number that comes just before.

For example:

• Before 20 comes 19
• Before 19 comes 18
• Before 10 comes 9
• Before 1 comes 0

Main Idea: Counting backward means taking away 1 each time.

We can think about it like this:

$$20 \to 19 \to 18 \to 17$$

Each arrow means “go back 1.”

If we start at any number, we can count backward by saying the numbers that are 1 less each time.

Tips for counting backward from 20

• Start at the number given.
• Say the number that comes before it.
• Keep going one number at a time.
• Go slowly if you need to.
• Listen for the change from 10 to 9. That is an important step.

Worked Example 1: Count backward from 5 to 0

Start at 5. Each time, say 1 less.

$$5,\ 4,\ 3,\ 2,\ 1,\ 0$$

We stopped at 0.

Worked Example 2: Count backward from 12 to 7

Start at 12 and go back by 1.

$$12,\ 11,\ 10,\ 9,\ 8,\ 7$$

Notice that after 10 comes 9.

Worked Example 3: Fill in the missing numbers

$$20,\ 19,\ \underline{\ \ },\ 17,\ 16,\ \underline{\ \ },\ 14$$

Let’s count backward carefully:

$$20,\ 19,\ 18,\ 17,\ 16,\ 15,\ 14$$

So the missing numbers are 18 and 15.

Worked Example 4: Start at 20 and count backward to 0

We say every number, going back by 1 each time.

$$20,\ 19,\ 18,\ 17,\ 16,\ 15,\ 14,\ 13,\ 12,\ 11,\ 10,\ 9,\ 8,\ 7,\ 6,\ 5,\ 4,\ 3,\ 2,\ 1,\ 0$$

This is the full backward count from 20.

How to practice

1. Say 20 out loud.
2. Tap your finger once for each new number.
3. Go back by 1 each time.
4. Keep going until you reach 0.

You can also practice from smaller starting numbers like 10, 8, or 15. Then try again from 20.

Things to remember

• Backward means go from a bigger number to a smaller number.
• Each step is 1 less.
• After 20 comes 19.
• After 10 comes 9 when counting backward.
• The backward count can end at 0.

Quick check

• Count backward from 6: $$6,\ 5,\ 4,\ 3,\ 2,\ 1,\ 0$$
• What comes before 14? 13
• What comes before 1? 0

Summary

Counting backward from 20 means starting at 20 and saying numbers that are 1 less each time until 0.

The full count is:

$$20,\ 19,\ 18,\ 17,\ 16,\ 15,\ 14,\ 13,\ 12,\ 11,\ 10,\ 9,\ 8,\ 7,\ 6,\ 5,\ 4,\ 3,\ 2,\ 1,\ 0$$

If you remember to go back by 1 each time, you can count backward correctly.

Counting to 100 by Ones

Today we will learn how to count to 100 by ones. Counting by ones means we say one number at a time in order.

When we count by ones, each new number is 1 more than the number before it. For example, after 4 comes 5. After 19 comes 20.

Counting to 100 helps us read numbers, say numbers in order, and see number patterns. It is an important math skill.

Let’s start with the counting pattern.

The numbers from 1 to 9 are:

$$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9$$

After 9, we start a new group of ten. Then we say:

$$10,\ 11,\ 12,\ 13,\ 14,\ 15,\ 16,\ 17,\ 18,\ 19$$

After 19 comes 20. Then the ones pattern starts again.

Look at these numbers:

$$21,\ 22,\ 23,\ 24,\ 25,\ 26,\ 27,\ 28,\ 29$$

Do you see the pattern? The tens part stays the same for a little while, and the ones part changes from 1 to 9.

This happens again and again:

• 32, 33, 34, 35, 36, 37, 38, 39
• 41, 42, 43, 44, 45, 46, 47, 48, 49
• 51, 52, 53, 54, 55, 56, 57, 58, 59

At the end of each group, the next number changes to a new ten:

• After 9 comes 10
• After 19 comes 20
• After 29 comes 30
• After 39 comes 40
• After 49 comes 50
• After 59 comes 60
• After 69 comes 70
• After 79 comes 80
• After 89 comes 90
• After 99 comes 100

Here is the full count to 100 by ones.

$$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9,\ 10$$

$$11,\ 12,\ 13,\ 14,\ 15,\ 16,\ 17,\ 18,\ 19,\ 20$$

$$21,\ 22,\ 23,\ 24,\ 25,\ 26,\ 27,\ 28,\ 29,\ 30$$

$$31,\ 32,\ 33,\ 34,\ 35,\ 36,\ 37,\ 38,\ 39,\ 40$$

$$41,\ 42,\ 43,\ 44,\ 45,\ 46,\ 47,\ 48,\ 49,\ 50$$

$$51,\ 52,\ 53,\ 54,\ 55,\ 56,\ 57,\ 58,\ 59,\ 60$$

$$61,\ 62,\ 63,\ 64,\ 65,\ 66,\ 67,\ 68,\ 69,\ 70$$

$$71,\ 72,\ 73,\ 74,\ 75,\ 76,\ 77,\ 78,\ 79,\ 80$$

$$81,\ 82,\ 83,\ 84,\ 85,\ 86,\ 87,\ 88,\ 89,\ 90$$

$$91,\ 92,\ 93,\ 94,\ 95,\ 96,\ 97,\ 98,\ 99,\ 100$$

Main ideas to remember

• Counting by ones means saying numbers in order, one at a time.
• Each number is 1 more than the number before it.
• The ones digits follow a pattern: 1, 2, 3, 4, 5, 6, 7, 8, 9.
• After a number ending in 9, we go to the next ten.
• After 99 comes 100.

Worked Example 1: Count on from a small number

Start at 3 and count by ones to 8.

We say one number at a time:

$$3,\ 4,\ 5,\ 6,\ 7,\ 8$$

Each number is 1 more than the one before it.

Worked Example 2: Count through a ten

Start at 17 and count by ones to 22.

First count to 19:

$$17,\ 18,\ 19$$

After 19 comes 20. Then keep counting:

$$20,\ 21,\ 22$$

So the full count is:

$$17,\ 18,\ 19,\ 20,\ 21,\ 22$$

Worked Example 3: Find the missing numbers

Fill in the blanks:

$$45,\ 46,\ \square,\ 48,\ \square,\ 50$$

Let’s count by ones:

$$45,\ 46,\ 47,\ 48,\ 49,\ 50$$

The missing numbers are 47 and 49.

Worked Example 4: Count to 100

Suppose we are at 96. What numbers come next until 100?

Count by ones:

$$96,\ 97,\ 98,\ 99,\ 100$$

Remember, after 99 comes 100.

Helpful counting tips

• Say the numbers slowly and in order.
• Listen for the pattern in the ones digits.
• Be extra careful when you move to a new ten, like 29 to 30.
• If you get stuck, start again from a number you know and count on by ones.

Let’s practice the decade pattern

These groups show how the pattern repeats:

• $$31,\ 32,\ 33,\ 34,\ 35,\ 36,\ 37,\ 38,\ 39$$
• $$41,\ 42,\ 43,\ 44,\ 45,\ 46,\ 47,\ 48,\ 49$$
• $$51,\ 52,\ 53,\ 54,\ 55,\ 56,\ 57,\ 58,\ 59$$

In each group, the ending digits go up the same way:

$$1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9$$

That is why counting to 100 is easier when you notice the pattern.

Summary

Counting to 100 by ones means saying every number in order from 1 to 100. Each number is 1 more than the number before it. The pattern of 1 through 9 repeats in each group of ten, and after numbers like 19, 29, and 39, we move to the next ten. After 99 comes 100.

Counting to 100 by Tens

Today we will learn how to count by tens all the way to 100.

Counting by tens means we do not say every number. We skip ahead by 10 each time. This helps us count faster and see number patterns.

When we count by tens, the numbers are:

$$10,\ 20,\ 30,\ 40,\ 50,\ 60,\ 70,\ 80,\ 90,\ 100$$

These numbers are called decade numbers. They all end in 0.

Let’s say them together slowly:

• 10
• 20
• 30
• 40
• 50
• 60
• 70
• 80
• 90
• 100

What pattern do you see?

Each number is 10 more than the number before it.

We can show that like this:

$$10 \rightarrow 20 \rightarrow 30 \rightarrow 40 \rightarrow 50 \rightarrow 60 \rightarrow 70 \rightarrow 80 \rightarrow 90 \rightarrow 100$$

If we start at 10 and add 10 each time, we keep making the next number in the pattern.

For example:

• \(10 + 10 = 20\)
• \(20 + 10 = 30\)
• \(30 + 10 = 40\)

This keeps going until we reach 100.

A helpful idea: the ones digit stays 0 when we count by tens. The tens digit changes: 1, 2, 3, 4, and so on.

Look at these numbers:

• 10 has 1 ten
• 20 has 2 tens
• 30 has 3 tens
• 40 has 4 tens
• 50 has 5 tens
• 60 has 6 tens
• 70 has 7 tens
• 80 has 8 tens
• 90 has 9 tens
• 100 has 10 tens

So when we count by tens, we are really counting how many groups of ten we have.

Worked Example 1

Count by tens from 10 to 50.

Start at 10. Add 10 each time:

$$10,\ 20,\ 30,\ 40,\ 50$$

So the answer is 10, 20, 30, 40, 50.

Worked Example 2

What number comes after 60 when counting by tens?

We add 10 to 60:

\(60 + 10 = 70\)

So the next number is 70.

Worked Example 3

Fill in the missing numbers:

$$20,\ 30,\ \underline{\quad},\ 50,\ \underline{\quad},\ 70$$

We are counting by tens.

After 30 comes 40. After 50 comes 60.

So the full pattern is:

$$20,\ 30,\ 40,\ 50,\ 60,\ 70$$

Worked Example 4

Count by tens all the way to 100.

Start at 10 and keep adding 10:

$$10,\ 20,\ 30,\ 40,\ 50,\ 60,\ 70,\ 80,\ 90,\ 100$$

The last number is 100.

Tips for counting by tens

• Say the numbers in order.
• Remember that each number ends in 0.
• Think: 10 more, 10 more, 10 more.
• If you get stuck, start again at 10 and go step by step.

Let’s practice saying them one more time:

$$10,\ 20,\ 30,\ 40,\ 50,\ 60,\ 70,\ 80,\ 90,\ 100$$

Great job! Counting by tens helps us count quickly and understand big numbers.

Summary

Counting by tens means adding 10 each time.

The numbers we say are 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

All of these numbers end in 0, and each number is 10 more than the one before it.

Extending the Sequence to 120 means counting forward, reading numbers, and writing numbers all the way up to 120.

When we count, numbers go in order. Each new number is 1 more than the number before it.

We already know how to count to 100. Now we will keep going past 100 and learn the numbers up to 120.

Let’s look at the counting pattern:

$$1, 2, 3, 4, 5, \dots, 98, 99, 100, 101, 102, 103, \dots, 119, 120$$

The important part is what happens after 99.

After 99, we do not go back to 1. We say 100.

Then we keep counting by ones:

$$100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120$$

How to think about 100

The number 100 is a special number. It comes right after 99.

Then each next number is just 1 more:

• 101 is 1 more than 100

• 102 is 2 more than 100

• 110 is 10 more than 100

• 120 is 20 more than 100

Reading the numbers after 100

Here are some numbers and how to say them:

• 100 = one hundred

• 101 = one hundred one

• 105 = one hundred five

• 110 = one hundred ten

• 117 = one hundred seventeen

• 120 = one hundred twenty

Writing the numbers after 100

When you hear a number, write the digits in order.

Listen carefully to the part after 100.

• one hundred three = 103

• one hundred twelve = 112

• one hundred twenty = 120

Notice the pattern

The ones digit changes as we count by ones.

For example:

$$101, 102, 103, 104, 105, 106, 107, 108, 109$$

Then after 109, the next number is 110.

Now the tens digit changes:

$$110, 111, 112, 113, 114, 115, 116, 117, 118, 119$$

Then after 119, the next number is 120.

This is just like other counting patterns. The numbers keep going in order, one at a time.

Worked Example 1: What comes next?

Fill in the next number:

$$98, 99, \underline{\qquad}$$

We count one more after 99.

The next number is 100.

Answer: $$100$$

Worked Example 2: Count on from 100

Fill in the missing numbers:

$$100, 101, \underline{\qquad}, \underline{\qquad}, 104$$

Count by ones:

100, 101, 102, 103, 104

Answer: $$102, 103$$

Worked Example 3: What number is missing?

$$108, 109, \underline{\qquad}, 111$$

After 109 comes 110.

Answer: $$110$$

Worked Example 4: Count to 120

Fill in the missing numbers:

$$116, 117, \underline{\qquad}, \underline{\qquad}, 120$$

Count by ones:

116, 117, 118, 119, 120

Answer: $$118, 119$$

Tips to help you count to 120

• Say the numbers slowly and in order.

• Remember: after 99 comes 100.

• After 100, keep counting by ones.

• Look for what number is 1 more.

• If you get stuck, start at 100 and count on: 100, 101, 102, 103, and so on.

Let’s practice reading a full set after 100

$$100, 101, 102, 103, 104, 105, 106, 107, 108, 109$$

Then:

$$110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120$$

Quick check

1. What comes after 100?

2. What comes after 109?

3. What comes before 120?

4. Say these numbers: 101, 115, 120

Answers:

1. 101

2. 110

3. 119

4. one hundred one, one hundred fifteen, one hundred twenty

Summary

Counting to 120 means we keep going in order, one number at a time.

After 99 comes 100, and after that we count on: 101, 102, 103, all the way to 120.

When you read or write these numbers, listen for the part after 100 and remember that each new number is 1 more.

Skip Counting by 5s and 2s

Sometimes we do not count every number one by one. Sometimes we count by jumping over numbers in a pattern. This is called skip counting.

In this lesson, we will learn how to skip count by 5s and by 2s. We will look for patterns that help us know what number comes next.

What is skip counting?

Skip counting means we add the same number each time. If we skip count by 2s, we add 2 again and again. If we skip count by 5s, we add 5 again and again.

Here is skip counting by 2s:

$$2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14$$

Each number is 2 more than the number before it.

Here is skip counting by 5s:

$$5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35$$

Each number is 5 more than the number before it.

Skip counting by 2s

When we count by 2s, we say every other number. We can start at 0 or at 2.

Starting at 0 looks like this:

$$0,\ 2,\ 4,\ 6,\ 8,\ 10,\ 12,\ 14,\ 16,\ 18,\ 20$$

Look at the ones digits: 0, 2, 4, 6, 8. Then the pattern repeats.

• \(2\) ends in 2
• \(4\) ends in 4
• \(6\) ends in 6
• \(8\) ends in 8
• \(10\) ends in 0

Then it starts again:

$$12,\ 14,\ 16,\ 18,\ 20$$

So when we skip count by 2s, the ones place follows a pattern:

$$2,\ 4,\ 6,\ 8,\ 0,\ 2,\ 4,\ 6,\ 8,\ 0$$

This pattern helps us know what number comes next.

Skip counting by 5s

When we count by 5s, we add 5 each time. We can start at 0 or at 5.

Starting at 0 looks like this:

$$0,\ 5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45,\ 50$$

Look at the ones digits. They make an easy pattern: 0, 5, 0, 5, 0, 5.

• \(5\) ends in 5
• \(10\) ends in 0
• \(15\) ends in 5
• \(20\) ends in 0

So when we skip count by 5s, the ones place goes back and forth:

$$5,\ 0,\ 5,\ 0,\ 5,\ 0$$

This is a great pattern to remember.

How skip counting helps

Skip counting helps us count faster. It also helps us see number patterns.

We use skip counting when we count things in pairs and groups of 5.

• 2 shoes at a time
• 2 socks at a time
• 5 fingers on one hand
• 5s on a clock

Worked Example 1: Count by 2s

Fill in the missing numbers:

$$2,\ 4,\ \underline{\hspace{1cm}},\ 8,\ \underline{\hspace{1cm}},\ 12$$

We are counting by 2s, so we add 2 each time.

After \(4\) comes \(6\). After \(8\) comes \(10\).

The full pattern is:

$$2,\ 4,\ 6,\ 8,\ 10,\ 12$$

Worked Example 2: Count by 5s

Fill in the missing numbers:

$$5,\ 10,\ \underline{\hspace{1cm}},\ 20,\ \underline{\hspace{1cm}},\ 30$$

We are counting by 5s, so we add 5 each time.

After \(10\) comes \(15\). After \(20\) comes \(25\).

The full pattern is:

$$5,\ 10,\ 15,\ 20,\ 25,\ 30$$

Worked Example 3: Use the ones-digit pattern

What number comes next?

$$20,\ 25,\ 30,\ 35,\ \underline{\hspace{1cm}}$$

We are counting by 5s. The ones digits are:

$$0,\ 5,\ 0,\ 5$$

The next ones digit should be \(0\).

After \(35\), add 5:

$$35 + 5 = 40$$

So the next number is 40.

Worked Example 4: Start at a different number

Count by 2s starting at \(6\):

$$6,\ 8,\ 10,\ 12,\ 14,\ 16$$

We keep adding 2 each time.

Look at the ones digits:

$$6,\ 8,\ 0,\ 2,\ 4,\ 6$$

The pattern still helps us.

Tips to remember

• Skip counting by 2s means add 2 each time.
• Skip counting by 5s means add 5 each time.
• By 2s, the ones digits follow a pattern: 2, 4, 6, 8, 0.
• By 5s, the ones digits follow a pattern: 5, 0, 5, 0.
• Say the numbers out loud to hear the pattern.

Let’s practice thinking

If you count by 2s, what comes after \(16\)? Add 2. The answer is \(18\).

If you count by 5s, what comes after \(45\)? Add 5. The answer is \(50\).

If you see \(10, 12, 14, 16\), you know the pattern is counting by 2s.

If you see \(25, 30, 35, 40\), you know the pattern is counting by 5s.

Summary

Skip counting means counting by the same number each time.

When we skip count by 2s, we add 2 and the ones digits follow a pattern like 2, 4, 6, 8, 0.

When we skip count by 5s, we add 5 and the ones digits follow a pattern like 5, 0, 5, 0.

These patterns help us count faster and know what number comes next.

Identifying Missing Numbers

Let’s learn how to find missing numbers in a number sequence. A number sequence is a list of numbers in order.

Sometimes a number is hidden, and we need to figure out what goes in the empty spot. We can do that by counting forward or backward.

If numbers are getting bigger, we count forward. If numbers are getting smaller, we count backward.

Here are two simple number sequences:

• Counting forward: \(3, 4, 5, 6\)
• Counting backward: \(9, 8, 7, 6\)

When one number is missing, we look at the numbers we can see and think: What number comes next? or What number comes before?

Main Ideas

• Numbers in order can go up by 1.
• Numbers in order can go down by 1.
• The missing number must fit in the correct place.
• We can use counting to check our answer.

How to Find a Missing Number

1. Look at the numbers you know.
2. Decide if the numbers are going forward or backward.
3. Count to find the number that belongs in the empty spot.
4. Read the whole sequence again to make sure it sounds right.

Worked Example 1

Find the missing number:

$$4,\ \square,\ 6$$

The numbers are going forward. After \(4\) comes \(5\), then \(6\).

So the missing number is \(5\).

The full sequence is:

$$4,\ 5,\ 6$$

Worked Example 2

Find the missing number:

$$10,\ 9,\ \square,\ 7$$

The numbers are going backward. We count down: \(10, 9, 8, 7\).

So the missing number is \(8\).

The full sequence is:

$$10,\ 9,\ 8,\ 7$$

Worked Example 3

Find the missing number:

$$18,\ 19,\ \square,\ 21$$

The numbers are going forward. After \(19\) comes \(20\), then \(21\).

So the missing number is \(20\).

The full sequence is:

$$18,\ 19,\ 20,\ 21$$

Worked Example 4

Find the missing number:

$$32,\ \square,\ 30$$

The numbers are going backward. Before \(30\) is \(31\), and before \(31\) is \(32\).

So the missing number is \(31\).

The full sequence is:

$$32,\ 31,\ 30$$

Helpful Tips

• If the numbers get bigger, count up by 1.
• If the numbers get smaller, count down by 1.
• Say the numbers out loud if that helps.
• Start from a number you know and keep counting.

Let’s Look at Bigger Numbers Too

Missing numbers can happen with bigger numbers all the way to \(120\).

Example:

$$58,\ 59,\ \square,\ 61$$

After \(59\) comes \(60\).

So the missing number is \(60\).

Example:

$$84,\ \square,\ 82$$

The numbers are going backward. The number between \(84\) and \(82\) is \(83\).

So the missing number is \(83\).

How to Check Your Work

After you find the missing number, read the whole sequence from start to finish.

Ask yourself:

• Do the numbers go in order?
• Am I counting forward by 1?
• Am I counting backward by 1?

If the sequence sounds right, your answer is probably correct.

Summary

Missing numbers are numbers that belong in an empty spot in a number sequence.

To find them:

• Look at the numbers around the blank.
• Decide if the numbers go forward or backward.
• Count by 1 to find the missing number.
• Check by reading the whole sequence again.

You can find missing numbers with small numbers like \(4, 5, 6\) and with bigger numbers all the way to \(120\). Keep practicing, and you will get better and faster!

Even and Odd Numbers

Let’s learn about even and odd numbers.

We can tell if a number is even or odd by making pairs. A pair means 2 together.

If every object can be put into pairs with no leftovers, the number is even.

If one object is left without a partner, the number is odd.

Think about socks or shoes. They often come in pairs of 2. Numbers that make perfect pairs are even. Numbers that leave 1 alone are odd.

Main idea:

• Even = pairs of 2 and 0 leftovers
• Odd = pairs of 2 and 1 leftover

Here are some even numbers:

\(2, 4, 6, 8, 10, 12, 14, 16, 18, 20\)

Here are some odd numbers:

\(1, 3, 5, 7, 9, 11, 13, 15, 17, 19\)

If you keep counting, even and odd numbers make a pattern:

\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10\)

Odd, even, odd, even, odd, even, odd, even, odd, even.

The pattern keeps going all the way to 120: odd, even, odd, even.

A quick way to check: Look at the last digit.

• If a number ends in 0, 2, 4, 6, or 8, it is even.
• If a number ends in 1, 3, 5, 7, or 9, it is odd.

This works for bigger numbers too, like numbers up to 120.

For example:

• \(24\) ends in \(4\), so it is even.
• \(37\) ends in \(7\), so it is odd.
• \(120\) ends in \(0\), so it is even.

Worked Example 1

Is \(6\) even or odd?

Let’s make pairs:

$$6 = 2 + 2 + 2$$

We made 3 pairs and had 0 leftovers.

So, \(6\) is even.

Worked Example 2

Is \(7\) even or odd?

Let’s make pairs:

$$7 = 2 + 2 + 2 + 1$$

We made pairs, but 1 was left over.

So, \(7\) is odd.

Worked Example 3

Is \(14\) even or odd?

We can look at the last digit. The number \(14\) ends in \(4\).

A number that ends in \(4\) is even.

So, \(14\) is even.

Worked Example 4

Is \(19\) even or odd?

We can look at the last digit. The number \(19\) ends in \(9\).

A number that ends in \(9\) is odd.

So, \(19\) is odd.

Let’s practice thinking about numbers up to 120.

• \(22\) ends in \(2\) → even
• \(35\) ends in \(5\) → odd
• \(48\) ends in \(8\) → even
• \(51\) ends in \(1\) → odd
• \(86\) ends in \(6\) → even
• \(99\) ends in \(9\) → odd
• \(100\) ends in \(0\) → even
• \(117\) ends in \(7\) → odd

Tips to remember

• Even numbers can be split into pairs.
• Odd numbers leave 1 left over.
• When you count, even and odd take turns.
• Look at the last digit to check quickly.

Brief Summary

Even and odd numbers tell us if a number can make pairs.

An even number has pairs with no leftovers.

An odd number has one leftover.

You can also check the last digit: \(0, 2, 4, 6, 8\) mean even, and \(1, 3, 5, 7, 9\) mean odd.