Activities Using the Four Models of Subtraction

Teaching all four models of subtraction--take-away, comparison, completion and whole/part/part--can better train elementary school children to think abstractly and relate their math knowledge for the real world. Learning all four models of subtraction can also prepare children for advanced math courses in middle and high school. Unfortunately, many primary school educators only teach the take-away model of subtraction.

The take-away model is the most commonly taught subtraction model. It teaches children the basic concept that taking away some objects from a set results in fewer objects in the set. To teach children the take-away model, set a specific number (e.g. 10) of objects (apples, blocks, etc.) in front of them and ask them to take away a smaller number (e.g. 7) of objects. Then ask them how many objects remain. In doing this exercise, children learn that taking away, or subtracting, objects from a set results in a smaller number (e.g. 10 – 7 = 3).

Learning the completion subtraction model prepares children for algebra lessons later on, since it forces children to manipulate variables in a basic subtraction equation. For example, a completion subtraction is “7 + ? = 10.” Use the same blocks or apples you used in the take-away model to teach children this concept. Have them replace apples or blocks to the original set (e.g. 7) until they reach the desired number (e.g. 10).

The comparison model of subtraction, which involves comparing two different numbers, is a little harder to visualize than the take-away model. An example of comparison subtraction is “If Chrissy is 26 and Bradley is 36, how many years older is Bradley than Chrissy?” Since you can’t physically take away objects and count the remaining objects, students must be more comfortable with subtraction, as opposed to counting, to solve these types of problems. Since students in your class are likely to be the same age, teach them the comparison model by comparing their ages in months: “Jenny was born in April and Jason was born in June. How many months older is Jenny than Jason?”

The whole/part/part model of subtraction involves categories of objects that need to be subcategorized: “I have five apples for sale. Three are green apples. How many aren’t green apples?” Teach children this concept by gathering some objects that share a basic category, like Girl Scout cookies or marbles, but are different in some way, like flavor and color. Ask children subtraction questions about these objects, using the “apple” question as an example.