Subtracting with Objects Up to 20

When a number sentence like \( 9 - 4 = 5 \) is still new, it helps to see it happen in real life. Subtracting with objects up to 20 means using counters, blocks, buttons, or drawings of things like apples and stars to act out a subtraction problem. Instead of just remembering a fact, a student starts with a full group of objects, physically takes some of them away, and then counts how many are left.

This "take-away" idea is one of the very first ways children make sense of subtraction. Because the numbers stay at 20 or below, every object in the group can be drawn, counted, and crossed out one at a time, so nothing has to be guessed.

Every subtraction with objects follows the same three steps.

Step 1: Count out or draw the starting number of objects. This is the first number in the subtraction sentence.

Step 2: Remove, cross out, or cover the number of objects being subtracted. This is the second number in the subtraction sentence.

Step 3: Count the objects that are left. This final count is the answer.

For example, to solve \( 8 - 3 \), start with 8 objects, take away 3 of them, and count what remains.

Objects do not always have to be physical counters. Pictures of familiar things like balloons, cookies, or fish work just as well because they can still be counted and marked off one by one. The key idea does not change: draw the full amount, mark off the part being subtracted, then count what is left over.

Try \( 14 - 6 \). Imagine 14 stars drawn in a row. Marking off 6 of them and counting the remaining stars gives 8, so \( 14 - 6 = 8 \).

Subtracting with objects builds the foundation for every other subtraction strategy that follows. Once a student is comfortable taking objects away and counting what is left, it becomes much easier to move to methods that use numbers only, such as counting forward to subtract up to 20 or using a number line to subtract up to 20. Both of these strategies model the exact same take-away idea, just without drawing every single object.

Working through many examples with objects also helps students memorize subtraction facts up to 20, since seeing the same take-away pattern over and over (like always ending with the same leftover amount for \( 10 - 4 \)) helps the fact stick in memory.

When practicing at home, everyday items make great subtraction manipulatives: buttons, coins, cereal pieces, or building blocks all work well. Line up the total amount, physically remove the number being subtracted, and count what is left to check the answer. Writing the matching number sentence, such as \( 16 - 9 = 7 \), right after the hands-on step connects the physical action to the symbols used in later subtraction work.

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• Math 1