Adding and Subtracting Within 100: Grade 2 Study Guide
Grade 2 builds fluency within 20 and extends it to numbers up to 100 using place value.
In Grade 2, children add and subtract within 100 using strategies based on place value, the properties of operations and the relationship between addition and subtraction. They also know from memory all sums of two one-digit numbers by the end of the year.
Understanding comes before the written method. A child who can explain 47 + 25 using tens and ones, a number line or a drawing understands why the column method works.
Place value strategy
Split numbers into tens and ones. 47 + 25: add the tens (40 + 20 = 60), add the ones (7 + 5 = 12), then combine (60 + 12 = 72). This is the same as the column method with carrying, but each step is visible.
Column addition and subtraction
Line up tens and ones. Add or subtract the ones first. If the ones add to 10 or more, regroup 10 ones as 1 ten. In subtraction, if you cannot take away the ones, regroup 1 ten as 10 ones.
Tens under tens, ones under ones.
Not enough. Regroup 1 ten: 13 − 8 = 5.
5 tens − 2 tens = 3 tens.
35 + 28 = 63.
Word problems
Grade 2 problems have different structures: adding to (Ria has 36 stickers and gets 17 more), taking from, putting together, taking apart and comparing (Sam has 24 and Lee has 39. How many more does Lee have?). Two-step problems need two operations: There were 45 books. 18 were lent and 12 were returned. How many now? That is 45 − 18 = 27, then 27 + 12 = 39.
| Type | Example | Equation |
|---|---|---|
| Add to | 36 + 17 stickers | 36 + 17 = 53 |
| Take from | 50 − 21 marbles | 50 − 21 = 29 |
| Compare | 39 − 24 more | 39 − 24 = 15 |
| Two-step | 45 − 18 + 12 | 27 + 12 = 39 |
Worked examples and common mistakes
Example: 58 + 34. Ones: 8 + 4 = 12, write 2 and carry 1. Tens: 5 + 3 + 1 = 9. Answer: 92. Common mistakes: forgetting to add the carried ten, subtracting the smaller digit from the bigger in each column and misreading 'how many more'. Estimate first: 58 + 34 is about 60 + 30 = 90, so 92 is reasonable.
Check your understanding: model answers
1. 46 + 37 = 83. 2. 82 − 35 = 47. 3. 28 + 19 = 47, then 47 − 15 = 32 pencils.
✨ Key Takeaways
- Use place value to add and subtract within 100.
- Regroup 10 ones as 1 ten (and the reverse).
- Check with the inverse operation and an estimate.
- Two-step problems need two equations.
💬 Questions for Discussion & Reflection
- Find 46 + 37.
- Find 82 − 35.
- A class had 28 pencils. They got 19 more and gave away 15. How many now?