Addition & Subtraction • Topic 1 of 5

Addition

Addition is combining quantities to find a total, and it grows in stages a teacher should be able to name. First come the single-digit facts, where the real learning is number bonds (the pairs that make ten: 7 and 3, 6 and 4), doubles like 8 + 8, and near doubles like 8 + 9. A child who knows these by heart is freed from counting on fingers. Next is multi-digit addition, and here the whole game is place value: ones must sit under ones, tens under tens, and you always start from the right. The concept CTET tests most is carry-over, also called regrouping. When a column adds up to ten or more, the digit cannot stay, ten ones become one ten and move next door. Take 28 + 15: the ones give 8 + 5 = 13, so you write 3 and carry 1; the tens give 1 + 2 + 1 = 4, total 43. The carried 1 is not a magic tick mark, it is a bundle of ten, which is why base-ten blocks and a place-value chart matter so much when you teach it. A child who writes 28 + 15 = 313 has simply written each column total down without regrouping, a textbook place-value error, not carelessness.

✅ Solved examples

1. Add 28 + 15 and state which step involves regrouping.
Ones: 8 + 5 = 13, write 3 and carry 1. Tens: 1 (carried) + 2 + 1 = 4. The answer is 43. Regrouping happens in the ones column, where 13 ones become 1 ten and 3 ones.
2. Find 175 + 246.
Ones: 5 + 6 = 11, write 1, carry 1. Tens: 1 + 7 + 4 = 12, write 2, carry 1. Hundreds: 1 + 1 + 2 = 4. The answer is 421.
3. A child writes 23 + 15 = 38 with no carrying. Is this correct, and why was no carry needed?
It is correct. Ones: 3 + 5 = 8, which is below 10, so nothing is carried. Tens: 2 + 1 = 3. The answer is 38. Carrying is only needed when a column reaches 10.
4. Use number bonds of ten to add 7 + 8 mentally.
Split the 8 into 3 + 5. Then 7 + 3 = 10 (a bond of ten), and 10 + 5 = 15. The answer is 15.

✏️ Practice — try these, take hints as needed

1. Add 47 + 36.
Start with the ones column.
7 + 6 = 13, so a carry is needed.
83
2. Find the sum 358 + 167.
Carry from ones and again from tens.
Ones: 8 + 7 = 15.
525
3. A pupil writes 26 + 17 = 313. What place-value mistake has been made?
Look at how each column total was recorded.
The ones column made 13.
The child wrote each column total (13 and 3) side by side instead of carrying the ten; the correct sum is 43.
4. Which two single-digit numbers form a number bond of 10 with a 4?
Pairs that make exactly ten.
4 + ? = 10.
4 and 6

📝 Topic test — 8 questions

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