Your child can quickly solve 5 + 3, but when the problem changes to 8 + 7, the fingers come out. Then numbers get bigger, such as 34 + 28, and suddenly addition feels even more difficult.
This does not always mean a child is weak at math. Often, the child is still relying on counting instead of understanding how numbers can be broken apart and put back together.
Learning addition and subtraction within 20 and 100 is an important step in developing strong number sense. Children gradually move from counting objects to using number bonds, making 10, recognizing doubles, understanding tens and ones, and choosing mental math strategies.
In this guide, we will move through these skills in the same order children can learn them: first understanding numbers, then calculating within 20, and finally applying those ideas to numbers within 100.
What Does Addition and Subtraction Within 20 and 100 Mean?
Adding and subtracting within 20 focuses on calculations involving smaller numbers and helps children develop basic number relationships and mental strategies. Working within 100 extends these ideas to two-digit numbers, where understanding tens and ones becomes especially important.
For example:
8 + 6 = 14
17 − 9 = 8
As children move to larger numbers, they may solve:
34 + 25 = 59
72 − 31 = 41
The important change is not simply that the numbers become bigger. Children must begin thinking about the structure of numbers.
For example:
47 = 4 tens + 7 ones
This understanding prepares children to calculate efficiently rather than counting one number at a time.
| Skill | Within 20 | Within 100 |
| Number understanding | Ones and groups of 10 | Tens and ones |
| Example | 8 + 7 | 38 + 27 |
| Useful thinking | Make 10, doubles, number bonds | Place value and decomposition |
| Helpful models | Ten frames, counters, number bonds | Base-ten blocks, number lines |
| Main goal | Build mental strategies and fluency | Calculate flexibly with two-digit numbers |
Skills Children Need Before Adding and Subtracting Within 20
Before children are expected to calculate quickly, they need to understand how numbers relate to one another. Strong number sense makes later addition and subtraction much easier.
A child should understand that a number can be made in different ways.
For example: 7 = 5 + 2
but also: 7 = 4 + 3
And: 7 = 6 + 1
These relationships are called number bonds. They help children stop seeing numbers as fixed symbols and start seeing how numbers can be composed and decomposed.
Understanding number bonds to 10 is particularly useful:
10 = 1 + 9
10 = 2 + 8
10 = 3 + 7
10 = 4 + 6
10 = 5 + 5
These facts become powerful tools when children start working across 10.
Children should also understand that addition and subtraction are connected.
Consider: 8 + 5 = 13
From this fact, we can also understand:
5 + 8 = 13
13 − 8 = 5
13 − 5 = 8
Instead of memorizing four unrelated calculations, the child recognizes one family of related facts.
Addition Strategies Within 20 That Build Mental Math
Children do not need to solve every addition problem in exactly the same way. Efficient addition means learning several strategies and gradually recognizing which strategy works well for a particular problem.
1.Start by Counting On
When children first move beyond counting objects, counting on is a useful strategy.
For: 8 + 3
instead of starting from 1, begin with the larger number:
8 → 9 → 10 → 11
So: 8 + 3 = 11
This is more efficient than counting all eight objects and then another three. However, as children develop stronger number sense, they should gradually move toward even more efficient strategies.
2.Make 10
Making 10 is one of the most useful strategies for addition within 20.
Consider: 8 + 7
We know that 8 needs 2 to make 10.
Break 7 into 2 + 5: 8 + 7
= 8 + 2 + 5 = 10 + 5 = 15
The child is no longer counting seven individual steps. Instead, the calculation uses a familiar benchmark number: 10.
This strategy becomes especially useful when addition crosses 10.
3.Use Doubles and Near Doubles
Children often learn doubles quickly:
4 + 4 = 8
5 + 5 = 10
6 + 6 = 12
7 + 7 = 14
Known doubles can then help with nearby facts.
Suppose a child needs to solve: 6 + 7
If the child knows: 6 + 6 = 12
then:
6 + 7 = 12 + 1 = 13
This is called a near doubles strategy.
Instead of memorizing every addition fact independently, children use something they already know to find something they do not.
4.Break Numbers Apart
Decomposing numbers can also make calculations easier.
For: 13 + 5
Think: 13 = 10 + 3
Then: 10 + 3 + 5 = 18
This ability to break numbers into useful parts becomes even more important when children start adding within 100.
| Problem | Helpful strategy | Thinking |
| 9 + 2 | Make 10 | 9 + 1 + 1 |
| 7 + 7 | Doubles | Use a known double |
| 6 + 7 | Near doubles | 6 + 6 + 1 |
| 8 + 5 | Make 10 | 8 + 2 + 3 |
| 13 + 5 | Break apart | 10 + 3 + 5 |
Subtraction Strategies Within 20
Subtraction does not always have to mean counting backward one number at a time. Children can use their understanding of 10, number bonds, and addition facts to subtract more efficiently.
1.Count Back for Small Amounts
Counting back can work well when only a small number is being subtracted.
For example: 12 − 3
Start at 12 and count back: 11, 10, 9
Therefore: 12 − 3 = 9
But for larger amounts, other strategies can be more efficient.
2.Break Apart to Reach 10
Consider: 13 − 5
First subtract enough to reach 10.
Break 5 into 3 + 2: 13 − 3 = 10
Then: 10 − 2 = 8
Therefore: 13 − 5 = 8
The child uses 10 as a helpful stopping point rather than counting backward five separate times.
3.Think Addition When Subtracting
Addition can sometimes make a subtraction problem easier.
For: 13 − 8 = ?
Ask: 8 + ? = 13
If the child knows: 8 + 5 = 13
Then: 13 − 8 = 5
This helps children understand that addition and subtraction are inverse operations rather than completely separate topics.
How Children Become Fluent Within 20
Fluency is not simply answering as fast as possible. A fluent child can solve addition and subtraction facts accurately and efficiently while choosing a sensible strategy.
Speed should not come before understanding.
For example, if a child solves 8 + 7 by counting from 1 every time, repeated timed worksheets may encourage faster counting without addressing the underlying problem.
Instead, help the child recognize:
8 needs 2 to make 10.
Then: 7 = 2 + 5
So: 8 + 7 = 10 + 5 = 15
Short daily practice can help these relationships become familiar. Games, oral questions, number talks, ten frames, number bonds, and written practice can all be used together.
Children can also be asked:
“How did you find your answer?”
“Can you solve it another way?”
“Which strategy was easier?”
Questions like these encourage mathematical reasoning rather than answer-only learning.
Moving From Addition and Subtraction Within 20 to Within 100
The bridge between calculations within 20 and calculations within 100 is place value.
A child who understands: 8 + 5
is beginning to develop ideas that can later help with: 38 + 25
But before working confidently with two-digit numbers, the child needs to understand that:
38 = 3 tens + 8 ones
And: 25 = 2 tens + 5 ones
Numbers are not simply collections of separate digits.
For example: 47
does not mean “4 and 7.”
It represents: 40 + 7
Or: 4 tens + 7 ones
Once this idea is clear, addition and subtraction within 100 become much easier to understand.
Addition Strategies Within 100
When adding two-digit numbers, children can use place value to break numbers into manageable parts.
1.Add Tens and Ones
Consider: 32 + 25
Break both numbers apart:
32 = 30 + 2
25 = 20 + 5
Now combine the tens: 30 + 20 = 50
Combine the ones: 2 + 5 = 7
Then: 50 + 7 = 57
Therefore: 32 + 25 = 57
The child can see why the calculation works instead of following a procedure without understanding it.
2.Make Friendly Numbers
Sometimes adjusting a number slightly can make mental addition easier.
Consider: 38 + 24
38 is close to 40.
Move 2 from 24 to 38: 38 + 2 = 40
There are 22 left.
Now: 40 + 22 = 62
Therefore: 38 + 24 = 62
This strategy develops flexible number thinking.
3.Use an Open Number Line
A number line can make addition visible.
For: 34 + 23
start at 34.
Jump forward 20: 34 → 54
Then jump forward 3: 54 → 57
So: 34 + 23 = 57
The child can physically see how tens and ones are being added.
4.Use Base-Ten Blocks
Base-ten blocks are especially helpful when children are first learning two-digit calculations.A number such as 34 can be represented as: 3 tens + 4 ones
A number such as 28 becomes: 2 tens + 8 ones
Children can combine the blocks and physically see when ten ones can be composed into another ten.
This makes regrouping meaningful rather than just a rule about carrying a digit.
Subtraction Strategies Within 100
Place value is just as important for subtraction. Children should understand what is being removed rather than only memorizing a written procedure.
1.Subtract Tens and Ones
Consider: 68 − 24
First subtract 20: 68 − 20 = 48
Then subtract 4: 48 − 4 = 44
Therefore: 68 − 24 = 44
Breaking the subtrahend into tens and ones reduces the amount of information the child has to process at once.
2.Count Up to Find the Difference
Sometimes the difference between two numbers is easier to find by counting up.
For:52 − 48
instead of counting backward 48 times, think: 48 → 50 = 2
50 → 52 = 2
Therefore: 52 − 48 = 4
This also reinforces the relationship between addition and subtraction.
3.Check Subtraction With Addition
If: 63 − 21 = 42
the child can check: 42 + 21 = 63
If the addition returns to the original number, the subtraction is correct.
This encourages children to think about mathematical relationships instead of treating each calculation as an isolated problem.
Best Visual Models for Addition and Subtraction
Visual models help children connect physical quantities to numbers and equations. Different models are useful at different stages.
| Model | Best used for |
| Counters | Beginning addition and subtraction |
| Ten frame | Making 10 and facts within 20 |
| Number bonds | Understanding parts and wholes |
| Number line | Counting on, counting back and finding differences |
| Base-ten blocks | Understanding tens, ones and regrouping |
| Hundred chart | Recognizing number patterns within 100 |
A helpful learning progression is:
Concrete → Pictorial → Abstract
For example, a child learning 8 + 5 might first use counters.
Next, the child can draw dots or use a ten frame.
Finally, the child can work directly with: 8 + 5 = 13
The equation makes more sense because it represents something the child already understands.
Addition and Subtraction Word Problems Within 100
Word problems help children understand when and why addition and subtraction are useful.
Instead of teaching children to search for keywords such as “altogether” or “left,” encourage them to understand what is happening in the situation.
1.Putting Quantities Together
Mia has 24 stickers. Her friend gives her 15 more. How many stickers does Mia have now?
We need to combine the quantities: 24 + 15 = 39
Mia has 39 stickers.
2.Taking Something Away
There are 46 books on a shelf. Students borrow 12 books. How many remain?
46 − 12 = 34
There are 34 books left.
3.Comparing Two Quantities
Ali has 37 points and Sara has 29 points. How many more points does Ali have?
We need to find the difference: 37 − 29 = 8
Ali has 8 more points.
4.Finding an Unknown Part
A box holds 50 pencils. There are already 32 pencils inside. How many more pencils are needed to fill the box?
Think: 32 + ? = 50
The missing amount is: 18
These different situations help children understand that the same operation can appear in many forms.
Common Addition and Subtraction Mistakes and How to Fix Them
Mistakes can show exactly which concept needs more practice. Instead of immediately giving children more questions, first identify why the error is happening.
| If your child struggles with… | Check understanding of… | Try… |
| 8 + 7 | Number bonds to 10 | Ten frame and make-10 strategy |
| 14 − 6 | Decomposition | Break through 10 |
| 36 + 20 | Place value | Base-ten blocks |
| 52 − 48 | Difference | Count up on a number line |
| Word problems | Relationship between quantities | Draw or model the situation first |
1.Counting Everything From 1
If a child repeatedly counts every object from the beginning, encourage counting on from the larger number and gradually introduce number bonds and mental strategies.
2.Getting Stuck When Crossing 10
A problem such as 8 + 7 becomes easier when the child knows which number pairs make 10.
Practice number bonds before expecting fast answers.
3.Confusing Tens and Ones
If a child treats 42 as simply “4 and 2,” return to place-value models.
Show: 42 = 40 + 2
And: 42 = 4 tens + 2 ones
Base-ten blocks can make this relationship visible.
4.Choosing the Wrong Operation in Word Problems
Do not teach children to depend entirely on keywords.
Instead ask:
What is happening?
Are quantities being combined, separated, or compared?
What do we know?
What are we trying to find?
This develops problem-solving skills that continue to be useful as mathematics becomes more complex.
How Parents and Teachers Can Practice at Home or School
Effective practice does not need to mean completing a long worksheet every day. Short, focused activities can help children build stronger mathematical connections.
Try a five-minute mental math routine using questions such as:
What goes with 7 to make 10?
If 6 + 6 = 12, what is 6 + 7?
How could you solve 9 + 8 without counting every number?
What is 10 more than 34?
How do you know that 52 − 48 = 4?
Everyday situations also provide natural practice.
If there are 8 apples and you buy 5 more, ask how many there will be altogether.
If a child has saved $35 toward a $50 goal, ask how much more is needed.
If there are 24 students and 3 are absent, ask how many are present.
These short conversations help children see addition and subtraction as tools for solving real problems.
Worksheets can then reinforce what the child already understands. They are most useful when practice is purposeful rather than simply repetitive.
Check our latest Common Core aligned workbook:
Grade 2 Addition & Subtraction Workbook | Math Practice & Word Problems
Frequently Asked Questions
What does addition and subtraction within 20 mean?
It means working with addition and subtraction in the number range up to 20. At this stage, children develop basic facts and strategies such as counting on, making 10, using doubles, number bonds, and connecting addition with subtraction.
What does addition and subtraction within 100 mean?
It extends addition and subtraction to two-digit numbers up to 100. Children use their understanding of tens and ones, place value, decomposition, number lines, and related addition and subtraction facts to solve calculations.
What strategies help children add and subtract within 20?
Useful strategies include counting on, counting back for small amounts, making 10, using doubles and near doubles, decomposing numbers, using number bonds, and using addition facts to solve related subtraction problems.
How do you teach a child to make 10?
Begin by helping the child learn number pairs that total 10, such as 1 + 9, 2 + 8, 3 + 7, 4 + 6, and 5 + 5. Then show how these facts simplify problems such as 8 + 7 by changing it to 10 + 5.
How can a child become fluent in addition and subtraction?
Build understanding before focusing on speed. Use short daily practice, number talks, games, visual models, mental strategies, and written questions. Encourage children to explain how they reached an answer and compare different strategies.
Should children memorize addition and subtraction facts?
Knowing basic facts is useful, but understanding should come first. Children who understand number relationships can derive an unfamiliar fact from something they already know instead of relying entirely on memorization.
How can I help a child who keeps counting on fingers?
Do not remove fingers before the child has another strategy to replace them. Introduce number bonds, ten frames, make-10 activities, doubles, and short mental math discussions. As number relationships become familiar, reliance on finger counting can gradually decrease.
What is the best way to teach addition and subtraction within 100?
Begin with place value. Make sure the child understands two-digit numbers as tens and ones. Then use base-ten blocks, expanded form, number lines, and decomposition before moving toward more abstract written methods.
When should children learn regrouping?
Regrouping is easier to understand once children know that 10 ones can be composed into 1 ten and 1 ten can be decomposed into 10 ones. Concrete models such as base-ten blocks can help establish this understanding before children rely on written procedures.