Subtraction
Teaching subtraction to elementary students requires scaffolding from concrete take-away problems to abstract multi-digit calculations with borrowing. The CCSS.1.OA and CCSS.2.NBT standards emphasize building number sense through visual models before introducing the standard algorithm. Students master subtraction through systematic practice across 4 difficulty levels, from simple counting back with numbers 1-5 to complex three-digit problems requiring multiple borrowing steps.
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Why it matters
Subtraction skills directly impact daily problem-solving and financial literacy. Students use subtraction to calculate change when buying items worth $3.75 from a $5 bill, determine remaining time when 25 minutes have passed in a 60-minute class period, or find temperature differences when weather drops from 82°F to 67°F. In academic contexts, subtraction supports measurement conversions, data analysis, and algebraic thinking. Research shows students who master multi-digit subtraction by grade 3 demonstrate stronger performance in fractions and decimals by grade 5. The borrowing algorithm specifically builds place value understanding essential for more advanced mathematical concepts including negative numbers and polynomial operations.
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
You have 5 apples. You eat 3. How many are left?
Answer: 2
- Understand the story → 5 - 3 — You started with 5 apples and ate 3. 'How many left' means subtract.
- Take away → 5 - 3 = 2 — Remove 3 from 5 and you have 2 left.
- Answer → 2 apples — You have 2 apples left!
There are 7 people in a queue. 4 leave. How many remain?
Answer: 3
- Look at what we are taking away → 7 - 4 — We start with 7 and need to take away 4. Imagine you have 7 candies and eat 4 of them.
- Count back from the bigger number → 7 - 4 = 3 — Start at 7 and count back 4: 6, 5, 4, 3. We land on 3!
- Check: add back to verify → 3 + 4 = 7 ✓ — To check subtraction, add the answer back: 3 + 4 = 7. It matches what we started with, so we are correct!
The temperature was 90°C and dropped by 12°C. What is it now?
Answer: 78
- Look at what we are subtracting → 90 - 12 — We need to take 12 away from 90. We will do this column by column, starting from the ones (right side), just like you unstack blocks.
- Ones column: we need to borrow! → 0 < 2 → borrow 10 from tens — We cannot take 2 from 0 (that would go below zero). So we borrow 1 ten (which is 10 ones) from the tens column. Now we have 10 ones and 8 tens.
- Subtract the ones → 10 - 2 = 8 — Now 10 - 2 = 8. That is the ones digit of our answer.
- Subtract the tens → 8 - 1 = 7 — Remember we borrowed, so the tens are now 8 - 1 = 7.
- Put the digits together → 90 - 12 = 78 — Tens digit 7 and ones digit 8 give us 78.
- Check: add back to verify → 78 + 12 = 90 ✓ — Adding 78 + 12 gives 90. Our subtraction is correct!
Common mistakes
- ✗Students subtract the smaller digit from the larger digit in each column regardless of position, writing 52 - 27 = 35 instead of 25 because they calculate 7 - 2 = 5 in the ones place.
- ✗When borrowing, students forget to reduce the borrowed-from digit, solving 43 - 18 as 35 instead of 25 because they keep the 4 in the tens place unchanged.
- ✗Students write the borrowing work incorrectly by crossing out numbers without clearly showing the new values, creating confusion in problems like 704 - 156.
- ✗In word problems, students add instead of subtract when key phrases are unclear, calculating 'difference between 15 and 8' as 23 instead of 7.
Practice on your own
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