Mathematics — Numbers

Subtopic: Addition (for age 10 / Grade 4–5)

Addition means putting two or more numbers together to find their total (sum). We use place value (ones, tens, hundreds) to help add accurately.

Key ideas

  • Start from the Ones: When adding in columns, add the digits in the ones column first, then tens, then hundreds.
  • Carry (Regroup) when needed: If a column adds to 10 or more, write down the ones digit and carry the tens to the next column.
  • Commutative property: a + b = b + a. Order does not change the sum. (e.g., 23 + 45 = 45 + 23)
  • Associative property: (a + b) + c = a + (b + c). You can add in any grouping.

Methods of addition

1. Mental (head) addition

Use when numbers are small or easy to combine. Break numbers into tens and ones. Example: 46 + 30 = 40 + 30 + 6 = 70 + 6 = 76.

2. Number line (visual)
0 10 20 30 40 50 60 70
Start 23
+ 30 = 53
Jump by 10 three times (23 → 33 → 43 → 53)
Example: 23 + 30 = jump by 10 three times to reach 53.
3. Column (vertical) addition — step by step

Write numbers one under another, lining up ones, tens and hundreds. Add from the right-hand side (ones).

H T O
Carry
1 7 8
+ 0 6 9
= 1 4 7
Example shown: 178 + 69. Work: Ones 8 + 9 = 17 → write 7, carry 1 to tens. Tens 7 + 6 + 1(carry) = 14 → write 4, carry 1 to hundreds. Hundreds 1 + 0 + 1(carry) = 2. Final sum is 247.

Check your answer

Use subtraction: If 178 + 69 = 247, then 247 − 69 should equal 178. If it does, your addition is likely correct.

Properties with easy examples

  • Commutative: 34 + 12 = 46 and 12 + 34 = 46.
  • Associative: (20 + 30) + 5 = 50 + 5 = 55, and 20 + (30 + 5) = 20 + 35 = 55.

Word problems (Kenyan context)

  1. At the market, Amina bought 15 oranges and then another 27 oranges. How many oranges did she buy in total?
    Solution: 15 + 27 = 42 oranges.

  2. Juma had Ksh 250. His aunt gave him Ksh 380. How much money does Juma have now?
    Solution: 250 + 380 = Ksh 630.

  3. A school collects 120 pens from Form 3 and 95 pens from Form 4. How many pens were collected altogether?
    Solution: 120 + 95 = 215 pens.

Practice exercises

Do these using column method where needed.

  1. 34 + 58 =
  2. 129 + 76 =
  3. 405 + 189 =
  4. 67 + 24 + 9 =
  5. Market example: A vendor sells 46 mangoes in the morning and 57 in the afternoon. How many mangoes sold that day?
  6. Money: Sarah had Ksh 1,250. She sold books and got Ksh 870 more. How much does she have now?

Answers

  1. 34 + 58 = 92
  2. 129 + 76 = 205
  3. 405 + 189 = 594
  4. 67 + 24 + 9 = 100 (you can add 67 + 33 first = 100)
  5. 46 + 57 = 103 mangoes
  6. 1,250 + 870 = Ksh 2,120

Tips for success

  • Write digits in straight columns under Ones, Tens, Hundreds.
  • Always start from the right (ones) and move left.
  • Check your work by subtracting one addend from the total.
  • Use real-life practice: add prices at a market stall or combine scores in games.
Good work! Practice these methods often and try to explain your steps to a friend or parent — teaching helps you remember.

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