Addition Concepts and Strategies

Addition as Putting Together

Addition means putting groups together to make one bigger group.

When we add, we start with one group, then put another group with it. After we put them together, we count how many there are altogether.

This is called addition as putting together.

We can use pictures, objects, fingers, or numbers to help us add.

What addition looks like

If one group has 2 apples and another group has 3 apples, we can put them together.

Then we count all the apples:

$$2+3=5$$

This means 2 and 3 together make 5.

Important idea

Addition is about finding the total. The total is how many things there are when all the groups are together.

You can think:

• First group
• Second group
• Count all

Words that tell us to add

These words often mean we should put groups together:

• and
• together
• all
• in all
• altogether
• join
• add

How to add by putting together

1. Look at the first group.
2. Look at the second group.
3. Put the groups together.
4. Count everything.
5. Say the total.

Worked Example 1

There are 1 red balloon and 2 blue balloons. How many balloons are there altogether?

Start with the first group: 1 balloon.

Add the second group: 2 balloons.

Put them together and count: 1, 2, 3.

So,

$$1+2=3$$

There are 3 balloons altogether.

Worked Example 2

There are 4 cats on the porch and 3 cats in the yard. How many cats are there in all?

We put the two groups together: 4 cats and 3 cats.

Count all the cats: 1, 2, 3, 4, 5, 6, 7.

So,

$$4+3=7$$

There are 7 cats in all.

Worked Example 3

Mia has 6 crayons. Her friend gives her 5 more crayons. How many crayons does Mia have now?

First group: 6 crayons.

Second group: 5 crayons.

Put them together and count all: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

So,

$$6+5=11$$

Mia has 11 crayons now.

Worked Example 4

There are 8 ducks in the pond and 4 more ducks swim over. How many ducks are there altogether?

We join the groups: 8 ducks and 4 ducks.

Count all to find the total.

$$8+4=12$$

There are 12 ducks altogether.

Ways to help yourself add

• Use counters or small toys.
• Draw circles for each group.
• Use your fingers.
• Count on after the first number.

For example, for \(5+3\), you can say: 5... 6, 7, 8. So \(5+3=8\).

Try to remember

The plus sign, \(+\), means put together.

The equals sign, \(=\), means the same as.

In \(3+2=5\), the two groups are 3 and 2. The total is 5.

Summary

Addition as putting together means joining two groups to make one whole group.

We can find the answer by counting how many there are altogether.

When you see words like together, all, or in all, you are often adding.

Remember:

• Find the two groups.
• Put them together.
• Count all.
• Say the total.

Addition helps us find how many things there are altogether.

Addition as Adding To

Addition means putting more with what you already have. When we add to, we start with one number and then get more.

You can think of addition as a story: Start with some. Add more. Find how many now.

For example, if you have 3 apples and then get 2 more apples, you are adding to 3. Now you have 5 apples.

We can write that with numbers like this:

$$3 + 2 = 5$$

The number 3 is the number we start with. The number 2 tells how many we add to it. The number 5 is the total, or how many there are in all now.

How to think about adding to

• Start with the first number.
• Add the second number.
• Find how many there are now.

You can use objects, pictures, fingers, or counting to help.

Using counters or pictures

If you start with 4 dots and add 3 more dots, you can draw them:

● ● ● ● + ● ● ●

Now count all the dots. There are 7 dots.

$$4 + 3 = 7$$

This shows that addition is adding more to a starting amount.

Using counting on

Counting on is a smart way to add. You say the first number, then count up the number you are adding.

For example, to solve \(5 + 2\):

• Start at 5.
• Count on 2 more: 6, 7.
• The answer is 7.

$$5 + 2 = 7$$

Look for the action in the story

When a story says someone got more, found more, or was given more, that is often addition as adding to.

Words that can mean add to are:

• got more
• added
• joined
• now there are

Worked Example 1

Lina has 2 balloons. She gets 3 more balloons. How many balloons does she have now?

Step 1: Start with 2.

Step 2: Add 3 more.

Step 3: Count all: 3, 4, 5.

$$2 + 3 = 5$$

Lina has 5 balloons.

Worked Example 2

There are 6 birds in a tree. 1 more bird comes. How many birds are in the tree now?

Step 1: Start with 6.

Step 2: Add 1 more.

Step 3: Count on 1: 7.

$$6 + 1 = 7$$

Now there are 7 birds.

Worked Example 3

Sam has 8 toy cars. He gets 4 more toy cars. How many toy cars does he have now?

Step 1: Start with 8.

Step 2: Add 4 more.

Step 3: Count on 4: 9, 10, 11, 12.

$$8 + 4 = 12$$

Sam has 12 toy cars.

Worked Example 4

A jar has 9 marbles. 5 more marbles are put in the jar. How many marbles are in the jar now?

Step 1: Start with 9.

Step 2: Add 5 more.

Step 3: Count on 5: 10, 11, 12, 13, 14.

$$9 + 5 = 14$$

Now there are 14 marbles.

Tips to help you

• Say the first number first.
• Count on the second number.
• You can use fingers to show the extra ones.
• You can draw quick pictures to help count.
• Ask yourself, How many are there now?

Let’s compare

If you start with 7 and add 0 more, the number stays the same.

$$7 + 0 = 7$$

Adding to means more are joining. If no more join, the total does not change.

Summary

Addition as adding to means you start with a number and then get more.

You can solve addition problems by:

1. Finding the starting number,
2. Seeing how many more are added,
3. Counting to find how many there are now.

Remember:

$$\text{start} + \text{more} = \text{now}$$

When you see a story where more things are added, that is addition as adding to.

The Plus and Equals Symbols

Today we will learn about two important math symbols: plus and equals.

The plus symbol looks like this: \(+\).

The equals symbol looks like this: \(=\).

These symbols help us write a math sentence when we join groups together.

When we see \(+\), we can say plus or add. It tells us to put groups together.

When we see \(=\), we can say equals. It tells us that the amount on one side is the same as the amount on the other side.

Let’s look at what each symbol means:

• \(+\) means join or add to.
• \(=\) means is the same as.

If we have 2 apples and then get 1 more apple, we are joining the apples together.

We can write that with symbols like this:

$$2 + 1 = 3$$

This math sentence says, “2 plus 1 equals 3.”

It also means, “2 apples joined with 1 apple is the same as 3 apples.”

How to turn a joining story into a math sentence

1. Find the first group.
2. Find the second group that is joining.
3. Use \(+\) to show the groups are joining.
4. Count all the objects.
5. Use \(=\) to show the total.

So a joining story has three parts:

• a number
• plus another number
• equals the total

It looks like this:

$$\text{first group} + \text{second group} = \text{total}$$

Worked Example 1

There is 1 bird on a fence. Then 2 more birds land on the fence.

First group: \(1\)

Second group: \(2\)

Join them with plus: \(1 + 2\)

Count all the birds: \(3\)

Write the math sentence:

$$1 + 2 = 3$$

This says, “1 plus 2 equals 3.”

Worked Example 2

There are 4 blocks on the floor. A child puts down 3 more blocks.

First group: \(4\)

Second group: \(3\)

Use plus to show joining: \(4 + 3\)

Count all the blocks: \(7\)

$$4 + 3 = 7$$

This says, “4 plus 3 equals 7.”

Worked Example 3

There are 5 fish in a tank. Then 5 more fish are added.

First group: \(5\)

Second group: \(5\)

Put in the plus symbol: \(5 + 5\)

Count all: \(10\)

$$5 + 5 = 10$$

The equals symbol shows that the total number of fish is 10.

Worked Example 4

There are 8 crayons in a box. Then 2 more crayons are put in the box.

First group: \(8\)

Second group: \(2\)

Join them: \(8 + 2\)

Count all the crayons: \(10\)

$$8 + 2 = 10$$

What the equals symbol really tells us

The equals symbol does not just mean “the answer is next.”

It means both sides are the same amount.

In this math sentence,

$$3 + 2 = 5$$

the group \(3 + 2\) is the same amount as \(5\).

Both sides match.

Let’s read math sentences together

• \(2 + 3 = 5\) means “2 plus 3 equals 5.”
• \(6 + 1 = 7\) means “6 plus 1 equals 7.”
• \(9 + 0 = 9\) means “9 plus 0 equals 9.”

When you read a math sentence, say the symbol names out loud:

• \(+\) is plus
• \(=\) is equals

Tips to remember

• Plus means you are putting groups together.
• Equals means the two sides are the same.
• The total goes after the equals symbol in an addition sentence like \(3 + 4 = 7\).

Try thinking about these stories

If you have 2 toy cars and get 2 more toy cars, you can write:

$$2 + 2 = 4$$

If you have 7 stickers and get 1 more sticker, you can write:

$$7 + 1 = 8$$

Each time, the plus symbol shows the groups joining. The equals symbol shows the total is the same as all the objects counted together.

Summary

The plus symbol, \(+\), means to join or add groups.

The equals symbol, \(=\), means is the same as.

When we see a joining story, we can write a math sentence like this:

$$\text{group} + \text{group} = \text{total}$$

Now you can use \(+\) and \(=\) to turn pictures, objects, and stories into addition equations.

Adding Zero is an easy and important idea in math.

When we add zero to a number, the number stays the same.

Zero means nothing. If you have 5 apples and add 0 more apples, you still have 5 apples.

We can say it like this:

$$a + 0 = a$$

This means any number plus 0 equals that same number.

You can also add zero in the other order:

$$0 + a = a$$

That also means the number stays the same.

Let’s think about it with real things.

• If you have 3 toys and get 0 more toys, you still have 3 toys.
• If there are 7 birds on a tree and 0 more birds come, there are still 7 birds.
• If you count 9 blocks and add 0 blocks, you still count 9 blocks.

Main idea: Adding zero does not change the number.

Here are some number sentences:

• \(4 + 0 = 4\)
• \(0 + 6 = 6\)
• \(10 + 0 = 10\)
• \(0 + 1 = 1\)

When you see a zero in an addition problem, you can remember: keep the other number.

Let’s work through some examples together.

Example 1

Find \(5 + 0\).

Start with 5. Add nothing. The number stays 5.

$$5 + 0 = 5$$

Example 2

Find \(0 + 8\).

Start with 8. Zero does not change it.

$$0 + 8 = 8$$

Example 3

Sam has 12 stickers. He gets 0 more stickers. How many stickers does Sam have now?

Sam still has 12 stickers because adding 0 does not change the number.

$$12 + 0 = 12$$

Example 4

There are 0 cats sitting by 9 cats. How many cats are there in all?

Zero more cats means the number stays 9.

$$0 + 9 = 9$$

How to remember it

1. Look for the number 0.
2. Find the other number.
3. Keep that number the same.

So if you see \(7 + 0\), the answer is 7.

If you see \(0 + 14\), the answer is 14.

Try thinking about these:

• \(2 + 0 = 2\)
• \(0 + 15 = 15\)
• \(19 + 0 = 19\)

Summary

Adding zero is simple: the number does not change.

No matter what number you start with, adding 0 means you still have the same amount.

Remember: zero adds nothing.

Commutative Property of Addition

Today we will learn a big idea about addition. It has a long name: Commutative Property of Addition.

This big idea means something simple: when we add, we can switch the numbers around, and the answer stays the same.

For example, \(4+3\) and \(3+4\) both make \(7\).

So, \(4+3=3+4\).

This is helpful because sometimes one order is easier to think about than the other order.

What does "switch the numbers" mean?

In addition, the numbers we add are called addends. If we change the order of the addends, the total does not change.

Look at these two addition sentences:

Both have the same addends: \(2\) and \(5\). They are just in a different order. The sum is still \(7\).

Think about objects

Imagine you have 2 red blocks and 3 blue blocks. That makes 5 blocks.

Now imagine the blue blocks first and the red blocks second. You still have 5 blocks.

The blocks did not change. Only the order changed.

Main idea

• Adding means putting groups together.
• You can add the first group and then the second group.
• Or you can add the second group and then the first group.
• The total stays the same.

This works for addition facts within 20 too.

Here are more examples:

• \(1+6=6+1\)
• \(8+2=2+8\)
• \(10+4=4+10\)
• \(7+5=5+7\)

Worked Example 1

Find the sum: \(3+1\)

Start with 3. Add 1 more.

Now switch the addends:

Both sums are 4. So switching the numbers did not change the answer.

Worked Example 2

Find the sum: \(2+6\)

Put 2 and 6 together.

Now switch the addends:

The answer is still 8.

Worked Example 3

Look at \(9+4\). You can also think of it as \(4+9\).

Both addition sentences have the same sum, 13.

Sometimes \(4+9\) may feel easier to say or think about, but both are correct.

Worked Example 4

Fill in the missing number:

We want the same addends in a different order.

The first sentence has 5 and 7.

So the missing number is 7.

Both sides equal 12.

How this helps you

The commutative property helps you use addition facts you already know.

Maybe you know \(8+1=9\). Then you also know \(1+8=9\).

Maybe you know \(6+3=9\). Then you also know \(3+6=9\).

You do not need to learn them as two different facts, because they have the same total.

Try to notice the pattern

• \(4+2=6\)
• \(2+4=6\)

• \(7+1=8\)
• \(1+7=8\)

• \(3+5=8\)
• \(5+3=8\)

In each pair, the addends switch places, but the sum stays the same.

Important note

This lesson is about addition. When adding, switching the order keeps the same total.

Summary

The Commutative Property of Addition means:

You can change the order of the addends, and the sum stays the same.

For 1st grade, you can remember it like this:

Switch the numbers. Keep the same answer.

Examples:

• \(4+3=3+4\)
• \(2+8=8+2\)
• \(6+5=5+6\)

When you add, if one order feels easier, you can switch the addends and still get the same sum.

Strategy: Counting All

When we add, we put groups together to find how many in all.

One way to add is called counting all. Counting all means we count every object in both groups, starting at 1.

This strategy helps us solve addition problems with toys, pictures, fingers, cubes, or numbers.

What does counting all mean?

Let’s say one group has 2 apples and another group has 3 apples. We join the groups and count every apple:

1, 2, 3, 4, 5

So, $$2 + 3 = 5$$

We counted all the apples. We did not skip any. We started at 1 and counted each object one time.

How to use counting all

1. Look at the first group.

2. Look at the second group.

3. Put the groups together.

4. Count every object, starting at 1.

5. The last number you say is the sum.

Helpful things to remember

• Touch or point to each object as you count.

• Say one number for each object.

• Start at 1 when you count all.

• The last number tells how many there are in all.

Worked Example 1

There are 1 red balloon and 2 blue balloons. How many balloons are there in all?

Write the addition sentence: $$1 + 2$$

Now count all the balloons:

1, 2, 3

So, $$1 + 2 = 3$$

There are 3 balloons in all.

Worked Example 2

There are 4 ducks in the pond. 3 more ducks join them. How many ducks are there in all?

Write the addition sentence: $$4 + 3$$

Count all the ducks:

1, 2, 3, 4, 5, 6, 7

So, $$4 + 3 = 7$$

There are 7 ducks in all.

Worked Example 3

Mia has 5 blocks. Sam has 5 blocks. How many blocks do they have in all?

Write the addition sentence: $$5 + 5$$

Count all the blocks:

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

So, $$5 + 5 = 10$$

They have 10 blocks in all.

Worked Example 4

There are 6 stars on one page and 2 stars on another page. How many stars are there in all?

Write the addition sentence: $$6 + 2$$

Count all the stars:

1, 2, 3, 4, 5, 6, 7, 8

So, $$6 + 2 = 8$$

There are 8 stars in all.

Let’s think about objects and numbers

You can use counting all with real things, pictures, or just numbers.

• If you see 3 circles and 4 circles, count every circle: 1, 2, 3, 4, 5, 6, 7

• If you use your fingers for $$2 + 3$$, hold up 2 fingers and 3 fingers, then count all 5 fingers

• If you see $$7 + 1$$, you can imagine 7 things and 1 more thing, then count all 8 things

Common mistakes to watch for

• Counting too fast and skipping an object

• Counting one object two times

• Not joining both groups before counting

• Stopping too soon

If you make a mistake, that is okay. Go back, point to each object, and count again slowly.

Try this idea

For $$3 + 2$$, you can draw 3 dots and 2 dots:

● ● ●    ● ●

Count all the dots:

1, 2, 3, 4, 5

So, $$3 + 2 = 5$$

Why counting all helps

Counting all is a good first strategy for addition. It helps you see that addition means putting groups together.

It also helps you practice careful counting and finding the sum.

Summary

Counting all means counting every object in both groups, starting at 1.

To use this strategy, join the groups, count each object one time, and listen for the last number you say.

That last number is the sum, or how many there are in all.

Strategy: Counting On

Today we will learn a smart addition strategy called counting on.

Counting on means you start with one number and then count forward to add more. This helps you add quickly without starting at 1 every time.

When we use counting on, it is best to keep the bigger number in our head and count on the smaller number. That makes the counting easier.

For example, in \(8+3\), we start with 8 in our head. Then we count on 3 more: 9, 10, 11. So \(8+3=11\).

Why counting on helps

• You do not have to count all the way from 1.
• It is faster and easier.
• It works well for addition facts within 20.

How to count on

1. Look at the two numbers.
2. Pick the larger number.
3. Say that larger number in your head.
4. Count forward the amount of the smaller number.
5. The last number you say is the sum.

Example 1

Find \(5+2\).

Start with the bigger number: 5.

Count on 2 more: 6, 7.

So, $$5+2=7$$

Example 2

Find \(3+6\).

The bigger number is 6, so start with 6.

Count on 3 more: 7, 8, 9.

So, $$3+6=9$$

Notice something important: even though \(3\) comes first, we can still start with \(6\) because it is bigger. That makes counting on easier.

Example 3

Find \(9+4\).

Start with 9.

Count on 4 more: 10, 11, 12, 13.

So, $$9+4=13$$

Example 4

Find \(7+5\).

The bigger number is 7, so start with 7.

Count on 5 more: 8, 9, 10, 11, 12.

So, $$7+5=12$$

Try to think like this

• \(6+1\): start at 6, count on 1 → 7
• \(10+3\): start at 10, count on 3 → 11, 12, 13
• \(2+8\): start at 8, count on 2 → 9, 10

Helpful tips

• Say the bigger number first.
• Use your fingers for the smaller number if you need help counting how many jumps to make.
• Each number you say is one count forward.
• Stop when you have counted on the right number of times.

Watch out!

• Do not start back at 1.
• Do not count the starting number as a new count.

For example, with \(8+2\), start at 8. Then count on: 9, 10. The answer is 10.

You do not say 8 as one of the extra counts. You start at 8, then move forward two numbers.

Let’s compare

For \(4+9\):

• Counting all: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
• Counting on: start at 9, then 10, 11, 12, 13

Counting on is much faster!

Summary

Counting on is a smart way to add.

Remember these steps:

1. Find the bigger number.
2. Keep it in your head.
3. Count forward by the smaller number.
4. The last number you say is the answer.

When you practice counting on, addition gets quicker and easier!

Using a Number Line to Add

Addition means putting more with a number. One way to add is to use a number line.

A number line shows numbers in order. The numbers get bigger as you move to the right.

When we add on a number line, we start at the first number. Then we make jumps to the right for the second number. Each jump is 1 step.

So if we add \(3 + 2\), we start at 3 and jump right 2 times.

Here is a number line to 10:

$$0\quad 1\quad 2\quad 3\quad 4\quad 5\quad 6\quad 7\quad 8\quad 9\quad 10$$

How to use a number line to add:

1. Find the first number.

2. Put your finger there.

3. Look at the second number.

4. Jump to the right that many times.

5. The number where you land is the sum.

Remember:

• Adding means jump right.

• Each jump is 1.

• The last number you land on is the answer.

Worked Example 1

Let's solve \(2 + 3\).

Start at 2.

Now make 3 jumps right:

• 1st jump: 3

• 2nd jump: 4

• 3rd jump: 5

You land on 5.

So, $$2 + 3 = 5$$

Worked Example 2

Let's solve \(4 + 1\).

Start at 4.

Make 1 jump right:

• 1 jump: 5

You land on 5.

So, $$4 + 1 = 5$$

Worked Example 3

Let's solve \(6 + 2\).

Start at 6.

Make 2 jumps right:

• 1st jump: 7

• 2nd jump: 8

You land on 8.

So, $$6 + 2 = 8$$

Worked Example 4

Let's solve \(7 + 5\).

Start at 7.

Make 5 jumps right:

• 1st jump: 8

• 2nd jump: 9

• 3rd jump: 10

• 4th jump: 11

• 5th jump: 12

You land on 12.

So, $$7 + 5 = 12$$

Tips to help you

• Say the numbers as you jump.

• Do not count the number where you start as a jump.

• If the problem is \(5 + 0\), do not jump at all. The answer stays 5.

Common mistake

Sometimes children start at the first number and count that number as jump 1. That gives the wrong answer.

Example: for \(3 + 2\), start at 3. Then jump to 4 and jump to 5. The answer is 5, not 4.

Let's think about one more

Solve \(9 + 3\).

Start at 9.

Jump right 3 times:

• 10

• 11

• 12

You land on 12.

So, $$9 + 3 = 12$$

Summary

A number line helps us see addition. To add, start at the first number and jump right by the second number. Count each jump carefully. The number where you land is the answer.

When you see an addition problem like \(a + b\), remember:

• Start at \(a\)

• Jump right \(b\) times

• Land on the sum

You can use a number line anytime you want help with addition within 20.

Doubles Facts within 20

Today we will learn about doubles facts. A double is when we add the same number to itself.

For example, \(3+3\) is a double because both numbers are 3. When we know doubles facts, we can add faster and more easily.

Doubles facts within 20 are doubles that have sums up to 20. Here are some doubles facts:

• \(1+1=2\)
• \(2+2=4\)
• \(3+3=6\)
• \(4+4=8\)
• \(5+5=10\)
• \(6+6=12\)
• \(7+7=14\)
• \(8+8=16\)
• \(9+9=18\)
• \(10+10=20\)

You may notice a pattern. As the number gets bigger by 1, the sum gets bigger by 2.

For example:

• \(4+4=8\)
• \(5+5=10\)
• \(6+6=12\)

This happens because we are adding one more to both parts.

You can think of doubles as two equal groups. If you have 4 apples in one group and 4 apples in another group, you have 8 apples altogether.

Here is another way to see a double:

This means 5 and 5 more makes 10.

Knowing doubles facts can help with many addition problems. They are important facts to remember.

Ways to learn doubles facts

• Say them out loud: “1 plus 1 equals 2.”
• Use fingers to show the same number on both hands.
• Draw two matching groups of dots.
• Look for the pattern in the sums.

Worked Examples

Example 1: Find \(2+2\).

Both addends are the same, so this is a doubles fact.

Start with 2 and add 2 more:

So, \(2+2=4\).

Example 2: Find \(5+5\).

This is a double of 5.

If you have 5 in one group and 5 in another group, that makes 10.

So, \(5+5=10\).

Example 3: Find \(7+7\).

This is a double of 7.

You can count on: 7, 8, 9, 10, 11, 12, 13, 14.

So, \(7+7=14\).

Example 4: Find \(10+10\).

This is the double of 10.

Two groups of 10 make 20.

So, \(10+10=20\).

Tips to remember doubles

• Doubles have the same number both times.
• Think: “double 4” means \(4+4\).
• Practice the doubles facts often so you can remember them quickly.

Let's review the doubles facts within 20:

• Double 1 is 2
• Double 2 is 4
• Double 3 is 6
• Double 4 is 8
• Double 5 is 10
• Double 6 is 12
• Double 7 is 14
• Double 8 is 16
• Double 9 is 18
• Double 10 is 20

Summary

Doubles facts are addition facts where both numbers are the same. When you add a number to itself, you are finding its double. Learning doubles facts from \(1+1\) to \(10+10\) helps you add quickly within 20.

Near Doubles Strategy

Sometimes two addends are almost the same. When the numbers are close together, we can use a near doubles strategy to add.

A double means adding the same number to itself. For example, \(4+4\) is a double. So is \(7+7\).

With near doubles, the numbers are only 1 apart. That means one number is just a little bigger or a little smaller than the other number.

For example:

• \(5+6\) is a near double because 5 and 6 are 1 apart.
• \(8+7\) is a near double because 8 and 7 are 1 apart.
• \(3+3\) is a double, not a near double.

Near doubles are helpful because doubles are easy to remember. If you know a double, you can solve a near double fast.

How to use the near doubles strategy

When you see a near double, follow these steps:

1. Find the double you know.
2. Add the extra 1, or take away 1 if needed.
3. Say the answer.

You can think of it like this:

\(6+7\) is almost \(6+6\). One addend is 1 more, so the answer is 1 more than the double.

$$6+7=6+6+1$$

If you know \(6+6=12\), then:

$$6+7=12+1=13$$

Worked Example 1

Solve \(2+3\).

The numbers 2 and 3 are 1 apart, so this is a near double.

Use the double \(2+2\).

$$2+2=4$$

But \(2+3\) has one more than \(2+2\), so add 1.

$$2+3=4+1=5$$

Answer: \(2+3=5\)

Worked Example 2

Solve \(4+5\).

The numbers are 1 apart, so use a double.

Use \(4+4\).

$$4+4=8$$

Now add 1 more.

$$4+5=8+1=9$$

Answer: \(4+5=9\)

Worked Example 3

Solve \(6+7\).

These numbers are near doubles because 6 and 7 are 1 apart.

Use the double \(6+6\).

$$6+6=12$$

Then add 1 more.

$$6+7=12+1=13$$

Answer: \(6+7=13\)

Worked Example 4

Solve \(9+8\).

The numbers 9 and 8 are 1 apart.

You can use the double \(8+8\).

$$8+8=16$$

Now add 1 more because 9 is 1 more than 8.

$$9+8=16+1=17$$

Answer: \(9+8=17\)

Another way to think

You can use either smaller double or bigger double, if it helps you.

For \(5+6\):

• Use smaller double: \(5+5=10\), then add 1, so \(5+6=11\).
• Or use bigger double: \(6+6=12\), then take away 1, so \(5+6=11\).

Both ways give the same answer.

Look for near doubles

These are near doubles:

• \(1+2\)
• \(3+4\)
• \(7+8\)
• \(9+10\)

These are not near doubles:

• \(2+5\)
• \(3+7\)
• \(4+4\) because that is a double

Why this strategy helps

• Doubles are easy to remember.
• Near doubles are fast to solve.
• You only need to add 1 or take away 1.

Let’s remember some doubles

• \(1+1=2\)
• \(2+2=4\)
• \(3+3=6\)
• \(4+4=8\)
• \(5+5=10\)
• \(6+6=12\)
• \(7+7=14\)
• \(8+8=16\)
• \(9+9=18\)
• \(10+10=20\)

If you know these doubles, near doubles will be much easier.

Quick practice ideas

• For \(3+4\), think \(3+3\), then add 1.
• For \(7+6\), think \(6+6\), then add 1.
• For \(10+9\), think \(9+9\), then add 1.

Summary

The near doubles strategy helps you add numbers that are almost the same.

First, find a double you know. Then add 1 more, or take away 1 if needed.

When numbers are 1 apart, near doubles can help you solve the problem quickly and correctly.

Making Ten to Add is a smart way to solve addition problems. It helps us add numbers more easily by first making a 10.

We use this strategy when one number is close to 10. Then we can take part of the other number, use it to make 10, and add what is left.

For example, in \(8+5\), the number 8 needs 2 more to make 10. We can split 5 into 2 and 3. Then we add in a new way:

$$8+5=8+2+3=10+3=13$$

Making 10 is helpful because adding to 10 is easy.

Why making ten works

When we add, we are joining numbers together. We can break one number into two smaller parts. This is called splitting a number.

When we split a number, the total stays the same. So we can move parts around to make an easier problem.

For example, \(9+4\) can be thought of as 9 and 1 more to make 10, with 3 left over.

$$9+4=9+1+3=10+3=13$$

How to make ten

1. Look at the first number.

2. Ask: How many more does it need to make 10?

3. Split the second number into two parts.

4. Use one part to make 10.

5. Add the leftover part.

Numbers that make 10

It helps to know these pairs:

• \(1+9=10\)

• \(2+8=10\)

• \(3+7=10\)

• \(4+6=10\)

• \(5+5=10\)

If you know these pairs, making ten becomes faster.

Worked Example 1

Solve \(8+4\).

First, ask: how many does 8 need to make 10? It needs 2.

Now split 4 into 2 and 2.

$$8+4=8+2+2=10+2=12$$

So, \(8+4=12\).

Worked Example 2

Solve \(9+6\).

First, ask: how many does 9 need to make 10? It needs 1.

Now split 6 into 1 and 5.

$$9+6=9+1+5=10+5=15$$

So, \(9+6=15\).

Worked Example 3

Solve \(7+5\).

First, ask: how many does 7 need to make 10? It needs 3.

Now split 5 into 3 and 2.

$$7+5=7+3+2=10+2=12$$

So, \(7+5=12\).

Worked Example 4

Solve \(6+8\).

First, ask: how many does 6 need to make 10? It needs 4.

Now split 8 into 4 and 4.

$$6+8=6+4+4=10+4=14$$

So, \(6+8=14\).

Tips for making ten

• Look for a number close to 10, like 8 or 9.

• Think about the number needed to get to 10.

• Split the other number into two parts.

• Make 10 first, then add the rest.

Let’s think together

If you see \(8+7\), 8 needs 2 more to make 10.

Split 7 into 2 and 5.

$$8+7=8+2+5=10+5=15$$

This is often easier than trying to add 8 and 7 all at once.

Summary

Making ten is an addition strategy that helps us solve problems within 20.

We do it by:

• finding how many more to make 10,

• splitting the other number,

• making 10 first,

• and then adding what is left.

Remember: 10 is a friendly number. When you make 10 first, addition can feel easier and faster.

Adding Three Single-Digit Numbers

Today we will learn how to add three one-digit numbers. A one-digit number is a number from 0 to 9.

When we add three numbers, we are joining all of them together to find the sum. The sum is the answer to an addition problem.

Sometimes adding three numbers can feel tricky. But there are smart ways to make it easier!

Smart way 1: Look for a friendly pair

A friendly pair is a pair of numbers that is easy to add first. Two great friendly pairs are:

• Numbers that make 10
• Numbers that make a double, like 4 and 4

If you find an easy pair first, the whole problem becomes easier.

Smart way 2: Make a ten

Making a ten is a great strategy because 10 is very easy to add with another number.

Here are some pairs that make 10:

• \(1 + 9 = 10\)
• \(2 + 8 = 10\)
• \(3 + 7 = 10\)
• \(4 + 6 = 10\)
• \(5 + 5 = 10\)

If you see two numbers that make 10, add those first.

For example, in \(2 + 8 + 3\), the numbers 2 and 8 make 10.

So we can do:

$$2 + 8 + 3 = 10 + 3 = 13$$

Smart way 3: Use doubles

A double is when the same number is added to itself.

• \(1 + 1 = 2\)
• \(2 + 2 = 4\)
• \(3 + 3 = 6\)
• \(4 + 4 = 8\)
• \(5 + 5 = 10\)

If two of the three numbers are the same, you can add the double first.

For example, in \(4 + 4 + 2\), start with the double:

$$4 + 4 + 2 = 8 + 2 = 10$$

You can add in any order

When adding, you can choose which two numbers to add first. This helps you pick the easiest pair.

For example:

$$3 + 5 + 7$$

You could do \(3 + 5 = 8\), then \(8 + 7 = 15\).

But you could also notice that \(3 + 7 = 10\), so that is even easier.

$$3 + 5 + 7 = 10 + 5 = 15$$

Both ways give the same sum.

Worked Examples

Example 1

Solve \(1 + 9 + 4\).

Look for a pair that makes 10. The numbers 1 and 9 make 10.

$$1 + 9 + 4 = 10 + 4 = 14$$

So, the sum is 14.

Example 2

Solve \(3 + 3 + 5\).

Look for a double. The numbers 3 and 3 are a double.

$$3 + 3 + 5 = 6 + 5 = 11$$

So, the sum is 11.

Example 3

Solve \(6 + 4 + 2\).

Look for a pair that makes 10. The numbers 6 and 4 make 10.

$$6 + 4 + 2 = 10 + 2 = 12$$

So, the sum is 12.

Example 4

Solve \(2 + 5 + 2\).

Look for a double. The numbers 2 and 2 are a double.

$$2 + 5 + 2 = 4 + 5 = 9$$

So, the sum is 9.

How to solve adding three numbers

1. Look at all three numbers.
2. Find a friendly pair.
3. Add that pair first.
4. Add the last number.

Ask yourself:

• Do any two numbers make 10?
• Do I see a double?
• Which two numbers are easiest to add first?

Let’s think about one more problem

Solve \(7 + 1 + 3\).

You might first think to do \(7 + 1 = 8\), then \(8 + 3 = 11\).

That works!

But there is also a friendly pair: \(7 + 3 = 10\).

So we can do:

$$7 + 1 + 3 = 10 + 1 = 11$$

The answer is still 11.

Summary

Adding three one-digit numbers is easier when you look for a friendly pair.

Try to find:

• a pair that makes 10, or
• a double

Then add the last number. You can add the numbers in any order to make the problem easier.

With practice, you will get faster at spotting easy pairs and finding the sum!