What is this skill?
Subtracting within 100 means taking one two-digit number away from another, as in 72 − 45 or 60 − 18. Second graders learn several ways to do it: taking away tens and then ones, counting up from the smaller number to the larger one, using a number line, and the written column method that lines up tens above tens and ones above ones.
The tricky problems are the ones where the top ones digit is smaller than the bottom one. In 72 − 45 there are only 2 ones, and you cannot take 5 ones from 2. So one of the 7 tens is broken apart into 10 ones. Now there are 6 tens and 12 ones, and 12 − 5 = 7 ones, 6 − 4 = 2 tens, so the answer is 27. Teachers call this regrouping, decomposing a ten, or borrowing.
Why it matters
Subtraction with regrouping is the mirror image of carrying in addition, and it is where many children find out whether they really understand place value. A child who sees 72 as 6 tens and 12 ones, not only as 7 tens and 2 ones, has a flexible picture of numbers that later makes three-digit subtraction, long division and making change with money much easier.
It also matters for everyday thinking. "How many more pages until I finish the book?" and "How much older is my cousin?" are subtraction questions, and the answer is often easiest to find by counting up rather than taking away. Children who have both tools can choose the one that fits.
Later in the year this leads straight into subtracting three-digit numbers, where a child may need to regroup a hundred into tens as well as a ten into ones. The idea is the same at every size.
Common mistakes
- Subtracting the smaller digit from the larger one in each column, whichever is on top. For 72 − 45 this gives 5 − 2 = 3 in the ones and an answer of 33. The fix is the question "Do I have enough ones on top to take away?"
- Breaking a ten into ones but forgetting to cross out and lower the tens digit, which gives 72 − 45 = 37. Saying out loud "now there are only 6 tens" helps the step stick.
- Trouble with zeros, as in 60 − 18. With no ones on top, children sometimes write 8 or skip the column. Seeing 60 as 5 tens and 10 ones makes the problem 10 − 8 and 5 − 1.
- Not checking. Adding the answer back (27 + 45 = 72) catches most slips and shows that subtraction and addition undo each other.
How to help at home
- Model regrouping with dimes and pennies. To take 45 cents from 72 cents, trade one dime for ten pennies at the "bank" before paying out the 5 pennies.
- Practice counting up: "From 45 to 50 is 5, from 50 to 70 is 20, and 2 more makes 72. That is 27 altogether." This mental method works well for differences.
- Use a hundred chart. Start at 72, jump up a row for each ten you take away, then step left for the ones. Children can see where they land.
- Ask real questions about time and ages: "It is 45 minutes into an hour-long show. How many minutes are left?" or "Grandpa is 72 and Grandma is 68. How much older is he?"
Worked examples
These are real questions from the Tutorsaurus subtracting within 100 practice, with the answers worked out.
Example 1
60 − 1 = ?
Answer: 59. 60 − 1 = 59. You can't take 1 from 0, so borrow a ten: 10 − 1 = 9.
Example 2
72 − 43 = ?
Answer: 29. 72 − 43 = 29. You can't take 3 from 2, so borrow a ten: 12 − 3 = 9.
Example 3
28 − 19 = ?
Answer: 9. 28 − 19 = 9. You can't take 9 from 8, so borrow a ten: 18 − 9 = 9.