Subtraction
Subtraction forms the foundation of mathematical reasoning, yet 73% of first-grade students struggle with borrowing concepts by mid-year. Teaching subtraction effectively requires understanding the progression from simple take-away problems with numbers 1-5 to complex three-digit problems requiring regrouping strategies.
Why it matters
Subtraction skills directly impact daily problem-solving situations students encounter throughout their lives. When Emma buys a $12 toy with a $20 bill, she needs subtraction to calculate her $8 change. Construction workers use subtraction to determine remaining materials—if a project needs 847 nails and 259 are already used, they calculate 588 remaining through column subtraction. Financial literacy depends on subtraction for budgeting: subtracting monthly expenses of $3,240 from income of $4,500 reveals $1,260 available for savings. Sports statistics rely heavily on subtraction—calculating point differences between teams scoring 89 and 76 points requires finding 13. Even cooking involves subtraction when recipes call for adjusting ingredient quantities. Research shows students with strong subtraction foundations perform 34% better on standardized math assessments, making this skill crucial for academic success across all grade levels.
How to solve subtraction
Subtraction — how to
- Line up digits by place value, larger number on top.
- Subtract column by column from the right.
- If the top digit is smaller, borrow 10 from the next column.
Example: 52 − 27: 2 < 7, borrow. 12−7=5. 4−2=2. Answer: 25.
Worked examples
There are 2 coins. 1 roll away. How many are left?
Answer: 1
- Look at what we are taking away → 2 - 1 — We start with 2 and need to take away 1. Imagine you have 2 candies and eat 1 of them.
- Count back from the bigger number → 2 - 1 = 1 — Start at 2 and count back 1: 1. We land on 1!
- Check: add back to verify → 1 + 1 = 2 ✓ — To check subtraction, add the answer back: 1 + 1 = 2. It matches what we started with, so we are correct!
Charlotte has 19 balloons. Diego has 6. How many more does Charlotte have?
Answer: 13
- Figure out what 'how many more' means → 19 - 6 — 'How many more' means finding the difference. We subtract the smaller from the larger.
- Subtract → 19 - 6 = 13 — Charlotte has 13 more balloons than Diego.
- Check → 6 + 13 = 19 ✓ — Diego's 6 plus the difference 13 equals Charlotte's 19. Correct!
_______ - 39 = 22
Answer: 61
- Read the problem → ? - 39 = 22 — We need the starting number. If we subtract and get the answer, we can reverse it.
- Add to find the starting number → 22 + 39 = 61 — Subtraction and addition are opposites. 22 + 39 = 61.
- Check → 61 - 39 = 22 ✓ — Plug it in: 61 - 39 = 22. Correct!
Common mistakes
- Students subtract the smaller digit from the larger digit in each column regardless of position, writing 63 - 28 = 45 instead of 35 because they calculate 8 - 3 = 5.
- When borrowing is needed, students forget to reduce the lending digit, solving 52 - 27 as 35 instead of 25 because they subtract 12 - 7 = 5 but keep the 5 in the tens place.
- Students misalign digits when writing problems vertically, placing 147 - 29 as 147 - 290, leading to incorrect answers due to place value errors.
- In word problems asking 'how many more,' students add instead of subtract, calculating 19 + 6 = 25 when comparing Charlotte's 19 balloons to Diego's 6.