Class 1
Class 2
CBSE
UP Board
📘 What's inside:
Concept 1 — What is Addition?
```Addition means putting two or more groups of things together to find the total. When we add, the total is always equal to or greater than the numbers we started with.
Addition in real life:
Riya has 3 pencils. Her mother gives her 2 more. Now she has 5 pencils. There are 4 birds on a tree. 3 more birds land. Now there are 7 birds. A basket has 6 apples. We put in 4 more. Now there are 10 apples.
▶ What Happens in Addition
- We combine two groups into one group.
- The result is called the sum or total.
- The numbers we add are called addends.
- The answer is always found by counting all the objects together.
⚠ Remember
Addition always means joining or putting together. If something is taken away or removed, that is subtraction — not addition.
▶ Solved Example 1
There are 2 cats sitting on a wall. 3 more cats come and sit. How many cats are there in all?
🐱🐱
+
🐱🐱🐱
=
5
- 1First group: 2 cats already sitting.
- 23 more cats join them.
- 3Count all together: 1, 2, 3, 4, 5. Total = 5.
There are 5 cats in all. (2 + 3 = 5)
▶ Solved Example 2
Rohan has 1 balloon. His friend gives him 4 more. How many balloons does he have now?
🎈
+
🎈🎈🎈🎈
=
5
- 1Rohan starts with 1 balloon.
- 2His friend gives him 4 more balloons.
- 3Put them together: 1 + 4 = 5.
Rohan has 5 balloons now. (1 + 4 = 5)
✍ Practice — Concept 1
Q1
There are 4 flowers in a vase. 2 more are added. How many flowers are there in all?
▼
Answer
We are putting two groups together — this is addition.
4 flowers + 2 flowers = 6 flowers.
🌼🌼🌼🌼
+
🌼🌼
=
6
4 flowers + 2 flowers = 6 flowers.
Q2
Sunita eats 3 biscuits. Then she eats 5 more. How many biscuits did she eat in total?
▼
Answer
First she ate 3 biscuits. Then 5 more.
We put these together: 3 + 5 = 8.
Sunita ate 8 biscuits in total.
We put these together: 3 + 5 = 8.
Sunita ate 8 biscuits in total.
Q3
Which of these is an example of addition? (a) Priya has 8 stickers and gives away 3. (b) Amit has 5 sweets and gets 4 more.
▼
Answer
(a) Priya gives away 3 — something is being taken away. This is subtraction, not addition.
(b) Amit gets more — two groups are being joined together. This is addition.
Answer: (b) is addition. 5 + 4 = 9 sweets.
(b) Amit gets more — two groups are being joined together. This is addition.
Answer: (b) is addition. 5 + 4 = 9 sweets.
Q4
A pond has 6 fish. 3 more fish jump in. Write a sentence to describe this as addition.
▼
Answer
Two groups are being joined: 6 fish already in the pond + 3 new fish = total fish.
Addition sentence: 6 + 3 = 9
There are 9 fish in the pond.
Addition sentence: 6 + 3 = 9
There are 9 fish in the pond.
Concept 2 — The + and = Symbols
```We use special symbols to write addition quickly instead of writing words. Let us understand what each symbol means.
+
Plus sign
Means “add” or “and”.
Put the two groups together.
Put the two groups together.
=
Equals sign
Means “is equal to” or “the answer is”.
3+4=7
Together
3 plus 4 equals 7.
▶ Reading the Symbols
- + is read as “plus” or “add”.
- = is read as “equals” or “is equal to” or “makes”.
- 5 + 3 = 8 is read as: Five plus three equals eight.
- The = sign means both sides have the same value.
▶ Solved Example 3
Read this addition statement aloud and write its meaning in words:
6 + 2 = 8
6 + 2 = 8
- 16 is the first addend (first group).
- 2+ means we are adding (putting together).
- 32 is the second addend (second group).
- 4= means the answer comes next.
- 58 is the sum (total).
“Six plus two equals eight.” Meaning: If we put a group of 6 and a group of 2 together, we get 8.
▶ Solved Example 4
Write the correct symbol (+ or =) in each blank:
(a) 3 ___ 4 ___ 7 (b) 5 ___ 0 ___ 5 (c) 2 ___ 6 ___ 8
(a) 3 ___ 4 ___ 7 (b) 5 ___ 0 ___ 5 (c) 2 ___ 6 ___ 8
- a3 and 4 are being added. Their total is 7. Write: 3 + 4 = 7.
- b5 and 0 are being added. Total is still 5. Write: 5 + 0 = 5.
- c2 and 6 are being added. Total is 8. Write: 2 + 6 = 8.
(a) 3 + 4 = 7 (b) 5 + 0 = 5 (c) 2 + 6 = 8
✍ Practice — Concept 2
Q5
Read aloud and write in words: 7 + 1 = 8
▼
Answer
“Seven plus one equals eight.”
It means: putting a group of 7 and a group of 1 together gives a total of 8.
It means: putting a group of 7 and a group of 1 together gives a total of 8.
Q6
Fill in the blanks with + or =: (a) 4 ___ 5 ___ 9 (b) 8 ___ 2 ___ 10
▼
Answer
(a) 4 + 5 = 9
(b) 8 + 2 = 10
(b) 8 + 2 = 10
Q7
What does the = sign mean in 3 + 5 = 8? Explain in your own words.
▼
Answer
The = sign means “is equal to” or “the answer is”.
In 3 + 5 = 8, the = sign tells us that 3 plus 5 and 8 have the same value.
The left side (3 + 5) and the right side (8) are equal.
In 3 + 5 = 8, the = sign tells us that 3 plus 5 and 8 have the same value.
The left side (3 + 5) and the right side (8) are equal.
Concept 3 — The Addition Sentence
```When we write an addition using numbers and symbols, it is called an addition sentence. Every addition sentence has the same structure.
5
+
3
=
8
▲ First Addend
▲ Second Addend
▲ Sum (Total)
▶ Parts of an Addition Sentence
- Addends — the numbers being added together.
- Sum — the answer; the total of all addends.
- Structure: Addend + Addend = Sum
- A number sentence can also have more than two addends: 2 + 3 + 4 = 9.
▶ Solved Example 5
Identify the addends and sum in: 4 + 6 = 10
4
+
6
=
10
▲ Addend 1 = 4
▲ Addend 2 = 6
▲ Sum = 10
- 1The numbers before the = sign are the addends: 4 and 6.
- 2The number after the = sign is the sum: 10.
- 3Read aloud: “Four plus six equals ten.”
Addends = 4 and 6 Sum = 10
▶ Solved Example 6
Write a correct addition sentence for: “Tina had 5 mangoes. She bought 4 more. Now she has 9.”
- 1First group: 5 mangoes she already had.
- 2Second group: 4 mangoes she bought.
- 3Total (sum): 9 mangoes.
- 4Write the addition sentence: 5 + 4 = 9.
5
+
4
=
9
Addition sentence: 5 + 4 = 9
✍ Practice — Concept 3
Q8
In 7 + 2 = 9, name the addends and the sum.
▼
Answer
Addends: 7 and 2 (the numbers being added).
Sum: 9 (the total, written after the = sign).
Sum: 9 (the total, written after the = sign).
Q9
Write an addition sentence: A box has 3 red balls and 5 blue balls. How many balls in total?
▼
Answer
First addend = 3 (red balls). Second addend = 5 (blue balls).
Sum = 3 + 5 = 8.
Addition sentence: 3 + 5 = 8
There are 8 balls in total.
Sum = 3 + 5 = 8.
Addition sentence: 3 + 5 = 8
There are 8 balls in total.
Q10
Find the missing sum: (a) 6 + 3 = ___ (b) 4 + 4 = ___ (c) 1 + 9 = ___
▼
Answer
(a) 6 + 3 = 9 (count on 3 from 6: 7, 8, 9)
(b) 4 + 4 = 8 (count on 4 from 4: 5, 6, 7, 8)
(c) 1 + 9 = 10 (count on 9 from 1: 2, 3, 4, 5, 6, 7, 8, 9, 10)
(b) 4 + 4 = 8 (count on 4 from 4: 5, 6, 7, 8)
(c) 1 + 9 = 10 (count on 9 from 1: 2, 3, 4, 5, 6, 7, 8, 9, 10)
Concept 4 — Adding with Objects and Fingers
```The simplest way to add is by counting real objects or using your fingers. We count both groups together to find the total.
▶ Two Methods for Adding Small Numbers
- Count all: Show both groups of objects. Count every single object from 1.
- Count on: Start with the bigger number. Count forward by the smaller number. This is faster.
▶ Solved Example 7
Add 4 + 3 using the count all method.
⬛⬛⬛⬛
+
⬛⬛⬛
=
?
- 1Show 4 objects (cyan).
- 2Show 3 more objects (gold).
- 3Count all objects from 1: 1, 2, 3, 4, 5, 6, 7.
4 + 3 = 7
▶ Solved Example 8
Add 6 + 2 using the count on method.
- 1Start with the bigger number: 6. Hold it in your head.
- 2Count on 2 more: “6 … 7, 8”.
- 3We counted 2 jumps. We land on 8.
6 + 2 = 8 (Count on from 6: 7, 8)
✍ Practice — Concept 4
Q11
Use count-all: 3 + 5 = ___
▼
Answer
Count all: 1, 2, 3, 4, 5, 6, 7, 8.
3 + 5 = 8
⬛⬛⬛
+
⬛⬛⬛⬛⬛
=
8
3 + 5 = 8
Q12
Use count-on: 7 + 3 = ___
▼
Answer
Start at 7 (bigger number).
Count on 3: 7 → 8, 9, 10.
7 + 3 = 10
Count on 3: 7 → 8, 9, 10.
7 + 3 = 10
Q13
Which method is faster for 8 + 2 — count all or count on? Show the answer using that method.
▼
Answer
Count on is faster.
Start at 8 (bigger number). Count on 2: 8 → 9, 10.
8 + 2 = 10
Count all would mean counting 10 objects from 1 — much slower.
Start at 8 (bigger number). Count on 2: 8 → 9, 10.
8 + 2 = 10
Count all would mean counting 10 objects from 1 — much slower.
Concept 5 — Properties of Addition
```Addition follows some special rules that are always true. Learning these rules helps us add faster and smarter.
Adding Zero
When you add 0 to any number, the number stays the same.
7 + 0 = 7
0 + 5 = 5
Zero is called the additive identity.
7 + 0 = 7
0 + 5 = 5
Zero is called the additive identity.
Adding One
When you add 1 to any number, you get the next number.
6 + 1 = 7
9 + 1 = 10
Adding 1 = counting one step forward.
6 + 1 = 7
9 + 1 = 10
Adding 1 = counting one step forward.
Order Does Not Matter
Swapping the addends gives the same sum.
3 + 5 = 8
5 + 3 = 8
This is called the commutative property.
3 + 5 = 8
5 + 3 = 8
This is called the commutative property.
Adding Same Numbers
Adding a number to itself gives double that number.
4 + 4 = 8
3 + 3 = 6
These are called doubles.
4 + 4 = 8
3 + 3 = 6
These are called doubles.
▶ Solved Example 9
Show that 4 + 6 and 6 + 4 give the same answer. Which property is this?
4
+
6
=
10
6
+
4
=
10
- 14 + 6 = 10. 6 + 4 = 10. Both give 10.
- 2The addends are swapped but the sum stays the same.
- 3This is the commutative property of addition.
4 + 6 = 6 + 4 = 10. This is the commutative property — order does not matter in addition.
▶ Solved Example 10
(a) What is 9 + 0?
(b) What is 0 + 9?
(c) What is 8 + 1?
(d) What is 5 + 5?
- a9 + 0 = 9. Adding zero keeps the number the same.
- b0 + 9 = 9. Same rule — order does not matter.
- c8 + 1 = 9. Adding 1 gives the next number (8 → 9).
- d5 + 5 = 10. This is a double (5 doubled = 10).
(a) 9 (b) 9 (c) 9 (d) 10
✍ Practice — Concept 5
Q14
Fill in: (a) ___ + 0 = 7 (b) 0 + ___ = 4 (c) 3 + 0 = ___
▼
Answer
Adding 0 never changes a number.
(a) 7 + 0 = 7
(b) 0 + 4 = 4
(c) 3 + 0 = 3
(a) 7 + 0 = 7
(b) 0 + 4 = 4
(c) 3 + 0 = 3
Q15
Using the commutative property, write a related addition fact for 8 + 3 = 11.
▼
Answer
Commutative property: swap the addends, sum stays same.
8 + 3 = 11, so the related fact is: 3 + 8 = 11.
8 + 3 = 11, so the related fact is: 3 + 8 = 11.
Q16
Find the doubles: (a) 2 + 2 = ___ (b) 6 + 6 = ___ (c) ___ + ___ = 14 (a double)
▼
Answer
(a) 2 + 2 = 4
(b) 6 + 6 = 12
(c) 14 ÷ 2 = 7. So the double is: 7 + 7 = 14
(b) 6 + 6 = 12
(c) 14 ÷ 2 = 7. So the double is: 7 + 7 = 14
★ Key Points to Remember
- Addition means putting two or more groups together to find the total.
- The + sign means “plus” or “add”. The = sign means “equals”.
- Numbers being added = addends. The answer = sum.
- Adding 0 to any number gives the same number. (7 + 0 = 7)
- Adding 1 gives the next number. (6 + 1 = 7)
- Swapping addends gives the same sum. (3 + 5 = 5 + 3 = 8) — commutative property.
- Horizontal method: Expand each number into place values, add each place, then combine.
- Column method (no carry): Write one number below the other, add Ones first, then Tens, then Hundreds. Each column sum must be less than 10.
Concept 6 — Horizontal Method of Addition
```In the horizontal method, we write both numbers side-by-side and add them in a single line. For larger numbers, we first break each number into its place values (Hundreds, Tens, Ones), add each place separately, and then combine the results.
▶ Steps for Horizontal Method
- Step 1: Expand each number — write it as Hundreds + Tens + Ones.
- Step 2: Group the same place values together.
- Step 3: Add each group separately.
- Step 4: Combine the totals to get the final answer.
▶ Solved Example 11
Find 34 + 25 using the horizontal method.
Step 1 — Expand both numbers
34
= 30 + 4
25
= 20 + 5
Step 2 — Group same places & add
30
+
20
=
50
4
+
5
=
9
Step 3 — Combine
50
+
9
=
59
- 1Expand: 34 = 30 + 4 and 25 = 20 + 5.
- 2Add the Tens: 30 + 20 = 50.
- 3Add the Ones: 4 + 5 = 9.
- 4Combine: 50 + 9 = 59.
34 + 25 = 59
▶ Solved Example 12
Find 246 + 132 using the horizontal method.
246
= 200 + 40 + 6
132
= 100 + 30 + 2
200+100=300
40+30=70
6+2=8
300 + 70 + 8
►
378
- 1Hundreds: 200 + 100 = 300.
- 2Tens: 40 + 30 = 70.
- 3Ones: 6 + 2 = 8.
- 4Combine: 300 + 70 + 8 = 378.
246 + 132 = 378
✍ Practice — Concept 6
Q17
Find 42 + 36 using the horizontal method. Show all steps.
▼
Answer
42 = 40 + 2 36 = 30 + 6
Tens: 40 + 30 = 70 Ones: 2 + 6 = 8
Combine: 70 + 8 = 78
42 + 36 = 78
Tens: 40 + 30 = 70 Ones: 2 + 6 = 8
Combine: 70 + 8 = 78
42 + 36 = 78
Q18
Find 315 + 264 using the horizontal method.
▼
Answer
315 = 300 + 10 + 5
264 = 200 + 60 + 4
Hundreds: 300 + 200 = 500
Tens: 10 + 60 = 70
Ones: 5 + 4 = 9
Combine: 500 + 70 + 9 = 579
264 = 200 + 60 + 4
Hundreds: 300 + 200 = 500
Tens: 10 + 60 = 70
Ones: 5 + 4 = 9
Combine: 500 + 70 + 9 = 579
Q19
A shopkeeper sells 125 apples in the morning and 213 apples in the evening. Find the total using horizontal method.
▼
Answer
125 = 100 + 20 + 5 213 = 200 + 10 + 3
H: 100 + 200 = 300 T: 20 + 10 = 30 O: 5 + 3 = 8
300 + 30 + 8 = 338 apples
H: 100 + 200 = 300 T: 20 + 10 = 30 O: 5 + 3 = 8
300 + 30 + 8 = 338 apples
Concept 7 — Column Method of Addition (Without Carry)
```In the column method, we write numbers one directly below the other and add each column separately — starting from the Ones on the right, moving left to Tens, then Hundreds. In this post we only deal with sums where no column exceeds 9, so no carrying is needed.
▶ How to Set Out Column Addition
- Write the larger number on top.
- Write the second number directly below, aligning digits by place value — Ones under Ones, Tens under Tens, Hundreds under Hundreds.
- Write the + sign to the left of the second number.
- Draw a single line under the second number.
- Add each column from right to left and write the result below the line.
- Draw a second line below the answer.
⚠ Most Common Mistake
Students misalign digits. Always write Ones under Ones and Tens under Tens. Writing 34 + 5 with the 5 under the 3 will give a completely wrong answer.
▶ Solved Example 13 — Single Digit
Find 4 + 5 using the column method.
4
+5
9
O
Ones column: 4 + 5 = 9
Write 9 below the line.
Write 9 below the line.
4 + 5 = 9
▶ Solved Example 14 — Two-Digit Numbers
Find 34 + 25 using the column method.
34
+25
59
O
Ones first: 4 + 5 = 9. Write 9.
T
Tens next: 3 + 2 = 5. Write 5.
- 1Write 34 on top, 25 below it. Tens under Tens, Ones under Ones.
- 2Draw the line. Add Ones: 4 + 5 = 9. Write 9.
- 3Add Tens: 3 + 2 = 5. Write 5.
- 4Read the answer below the line: 59.
34 + 25 = 59
▶ Solved Example 15 — Three-Digit Numbers
Find 243 + 352 using the column method.
243
+352
595
O
Ones: 3 + 2 = 5. Write 5.
T
Tens: 4 + 5 = 9. Write 9.
H
Hundreds: 2 + 3 = 5. Write 5.
- 1Write 243 on top, 352 below. H under H, T under T, O under O.
- 2Ones: 3 + 2 = 5.
- 3Tens: 4 + 5 = 9.
- 4Hundreds: 2 + 3 = 5.
- 5Answer below the line: 595.
243 + 352 = 595
▶ Solved Example 16 — Word Problem
A school library has 312 English books and 465 Hindi books. How many books are there in all? Use the column method.
We need to find 312 + 465.
312
+465
777
O
Ones: 2 + 5 = 7.
T
Tens: 1 + 6 = 7.
H
Hundreds: 3 + 4 = 7.
312 + 465 = 777. The library has 777 books in all.
✍ Practice — Concept 7
Q20
Solve using the column method: 52 + 37
▼
Answer
O: 2 + 7 = 9 T: 5 + 3 = 8 Answer: 89
52
+37
89
Q21
Solve using the column method: 421 + 365
▼
Answer
O: 1+5=6 T: 2+6=8 H: 4+3=7 Answer: 786
421
+365
786
Q22
Ravi saves ₹143 in January and ₹235 in February. Find the total savings using the column method.
▼
Answer
O: 3+5=8 T: 4+3=7 H: 1+2=3
Ravi's total savings = ₹378
143
+235
378
Ravi's total savings = ₹378
Q23
True or False: In the column method for 45 + 32, we add the Tens column first. Correct it if false.
▼
Answer
False. In the column method we always add the Ones column first, then move left to Tens, then Hundreds.
Correct working for 45 + 32:
O: 5+2=7 first, then T: 4+3=7. Answer: 77.
Correct working for 45 + 32:
O: 5+2=7 first, then T: 4+3=7. Answer: 77.
Exam Style — Class 1 & 2
6 Questions on Addition — All Methods
Q1
Name the addends and sum in 5 + 4 = 9. Write the addition sentence in words.
▼
Answer
Addends: 5 and 4. Sum: 9.
In words: “Five plus four equals nine.”
In words: “Five plus four equals nine.”
Q2
Fill in using properties: (a) 6 + ___ = 6 (b) ___ + 1 = 10 (c) 4 + 7 = 7 + ___
▼
Answer
(a) 6 + 0 = 6. (b) 9 + 1 = 10. (c) 4 + 7 = 7 + 4.
Q3
Priya has 3 red pens and 6 blue pens. Write an addition sentence and find how many pens she has in all.
▼
Answer
Addition sentence: 3 + 6 = 9. Priya has 9 pens in all.
Q4
Find 53 + 46 using the horizontal method. Show the expansion step clearly.
▼
Answer
53 = 50 + 3 46 = 40 + 6
Tens: 50 + 40 = 90 Ones: 3 + 6 = 9
Combine: 90 + 9 = 99
Tens: 50 + 40 = 90 Ones: 3 + 6 = 9
Combine: 90 + 9 = 99
Q5
Solve using the column method: 324 + 253. Show the working column-wise.
▼
Answer
O: 4+3=7 T: 2+5=7 H: 3+2=5 Answer: 577
324
+253
577
Q6
A student writes 5 + 3 = 9. Is this correct? Solve it correctly using the column method and write the related commutative fact.
▼
Answer
No, 5 + 3 = 9 is incorrect.
5 + 3 = 8. Commutative fact: 3 + 5 = 8.
5
+3
8
📄 Free Worksheet
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