Is your learner struggling with subtraction? One of the reasons subtraction is so challenging is that there are many different ways to think about it. If kids lack a strong grounding in number sense and subtraction, advanced math and problem solving skills are more difficult.
In this two-part series, we’ll discuss four main ways kids learn subtraction and what you can do when your child is struggling. Part one covers subtraction as takeaway, difference, and counting back from (also known as counting down to). If you’re interested in a deeper dive, see this history of subtraction in the US.
Understanding subtraction as “takeaway” will help learners connect the concept of subtraction to their real life experiences.
Takeaway means removing elements from a larger group. For example, your learner has five cookies. An older sibling may “take away” two for him or herself, leaving your learner with three cookies. This subtraction concept is easy to show visually. However, understanding subtraction only in terms of taking away is challenging, because learners do not have a concrete way to handle negative numbers — you can only take away cookies until you have none left.
Understanding subtraction as the difference between two numbers is also useful. In the previous cookie example, your learner now has three cookies, the difference between the original number of cookies your learner had (five) and the number of cookies his or her sibling “self shared” (two). Difference also helps with understanding negative numbers. For example, the difference between 6 and -1 is 7, the distance between the two on the number line. However, the conceptual understanding of subtraction as difference only allows for the scalar value (the distance or size) between two numbers, not the direction. This approach can be problematic when one must subtract a larger number from a smaller number. For example, it’s unclear why the difference between 8 and 6 is 2, but the difference between 6 and 8 is -2.
Counting back from (Counting down to)
The subtraction strategy of counting back from (counting down to) accounts for both size and direction (vector) of a subtraction problem, enabling students to subtract a larger number from a smaller number (e.g. 5 – 7 = -2). With this approach, you count backwards and track your counting. For example, to determine 8-6, you can count back from 8 or count down to 6. Both give you 2 as the answer.
Fluency in the number line will aid learners who want to use this strategy (which is one reason we made a fun math game about the number line). Come back tomorrow for part two, which explains subtraction as regrouping, borrowing or carrying over and offers tactics you can use to help your child learn subtraction.