Using Objects to Subtract Up to 100

Subtracting using objects means building a number out of real or drawn items, such as counters, cubes, or base-ten blocks, and then physically taking some of them away. Instead of just memorizing a fact, a student can see the group shrink and count what is left. This is one of the first ways subtraction is introduced, and it lays the groundwork for later strategies like using number lines to subtract up to 100 or working directly with the digits.

For smaller amounts, each object can simply stand for one unit. To subtract \( 8 - 3 \), draw 8 counters, then cross out 3 of them. Whatever is left uncrossed is the answer.

This simple crossing-out method works well when the numbers are small. Comparing it side by side with counting to subtract up to 100 helps show that both strategies land on the same answer, just with a different way of tracking the steps.

Once numbers get larger, drawing dozens of single objects becomes slow and easy to miscount. Base-ten blocks solve this by grouping ten ones into a single "tens rod." A number like \( 52 \) is shown as 5 tens rods and 2 ones units. To subtract, remove blocks from the ones first, then from the tens.

Follow the same routine every time an object-based subtraction problem comes up:

1. Build the first number using tens rods and ones units.
2. Look at the ones digit of the number being subtracted. Are there enough ones blocks to remove?
3. If not, trade one tens rod for ten ones, then remove the ones needed.
4. Remove the tens blocks needed for the subtraction.
5. Count what remains: the leftover tens and ones together give the difference.

For \( 52 - 27 \), there were only 2 ones blocks but 7 needed to be removed, so one tens rod was traded for 10 ones, giving 12 ones and 4 tens to work with. Removing 2 tens and 7 ones left 2 tens and 5 ones, or \( 25 \).

Not every problem requires trading a ten for ones. For \( 68 - 15 \), there are 8 ones and only 5 need to be removed, so no regrouping is necessary. Remove 5 ones from the 8 ones, then remove 1 tens rod from the 6 tens rods, leaving 5 tens and 3 ones, or \( 53 \). Comparing problems that need regrouping with ones that do not helps students recognize the pattern before moving on to subtracting with place value models up to 100, where the same ideas are written using numbers instead of pictures.

A quick way to check any object-based subtraction is to add the difference back to the number that was removed. If \( 52 - 27 = 25 \), then \( 25 + 27 \) should rebuild the original 52. Rebuilding the blocks this way confirms the subtraction was done correctly.

Use real counters, buttons, or drawn tens and ones whenever possible rather than jumping straight to written numbers. Always separate ones from tens clearly, and say each step out loud, such as "trade a ten for ten ones" or "remove seven ones," so the reasoning behind the regrouping becomes automatic before moving toward faster methods.

Related lessons

• Math 2