Subtraction is always more difficult than addition. Students inevitably struggle with this concept more so than they do with addition. Here’s the good thing – subtraction is directly related to addition. In fact, it is the opposite of addition. Think back to school when you had to do fact families (creating 2 addition and 2 subtraction facts using the same 3 numbers). That concept, in fact, is how teachers have tried to help kids understand the relationship between addition and subtraction. When you subtract, you are “undoing” addition.
Sometimes it’s easier to think about adding and subtracting as parts and a whole. When adding, you know the parts (usually 2 of them) and your task is to determine the whole. For example, my collection contains 4 red marbles and 5 blue marbles so how many is my whole collection? Sometimes you know only one part but you also know the whole. I have 4 red marbles and some blue marbles and my whole collection consists of 9 marbles. You can consider subtracting the exact same way. When subtracting, you typically know the whole, are then given a part to separate from the whole in order to determine the other part.
Success with subtraction depends on 2 key skills – understanding what the action of subtraction is (and the associated symbols in equations) and having effective strategies to solve the problems.
Subtracting is about finding the difference between 2 numbers. Young children frequently think about subtracting as “take away”. In fact, most children will read 4-1 as, “Four take away one.” It is important for kids to gain understanding about the multiple meanings of subtraction. Subtracting is also about splitting or separating a group into parts and determining the size of the parts. For example, you have 10 coins. If they are pennies and nickels and 4 are pennies, how many are nickels? Finding the difference can, perhaps, be the most difficult form of subtracting. We find the difference when measuring. We also find the difference when comparing 2 separate groups. Problems are frequently phrased, “How many more?” or “How many fewer?”
There are many strategies children can use to subtract. Young children may have to represent each problem with some kind of object. Cubes and counters are great tools for this. linking cubes or unifix cubes can be a great tool for subtracting. With these cubes you can link them together into a stick and then physically break it into the appropriate parts. This tool very clearly demonstrates the “parts” and “whole” of adding and subtracting. You can ask your child’s teacher to borrow a few cubes or purchase them online at any teaching resource site. If children understand what the symbols mean when working with equations, and understand the action behind the symbols, cubes or counters can be excellent tools to solve unknown subtraction facts.
If kids have moved beyond the need for concrete representations, they should be using a counting strategy. You’ll find that counting up and back are both effective strategies, depending on the specific fact. For example, given the problem 9 – 2 = ? a child can begin at 9, count backwards 2 counts and “land” on the answer. Counting backwards comes with a few hiccups which you can read about in the counting backwards post. For other problems, counting up makes more sense than counting back. Problems in which the difference between the total and the part is small (i.e. 9 – 8 = ?) do not lend themselves to counting backward. Keeping track of 1, 2 or 3 counts is relatively simple but having to track much more than that requires a tracking device . . . otherwise known as fingers. A more efficient strategy is for a child to start at the smaller number and count up to the larger number. The number of counts is the difference (or answer) between the 2 numbers given. Counting up (or counting forward) is typically easier and more accurate than counting down or counting backward.
A Good Place to Start
Before sitting down to a sheet full of subtraction problems. Gather up some of your child’s little toys (cars, marbles, coins, etc). Play with these items by identifying how many you have in the group, then remove some, say how many you have removed, and ask your child to determine how many are left. You can reinforce the idea of splitting or separating by sorting the group as well. Identify the group size, sort the items into 2 groups, tell how many are in 1 group and ask how many are in the other group.
You can also support your child’s understanding of subtracting in your daily conversations. When running errands, talk about how many errands you will be running throughout the day. After completing a few, ask how many tasks you have left. When setting the table, putting groceries away, folding clothes, talk about how many you have, what you’ve finished and then ask your child to determine how many are left.
By engaging in these activities before completing subtraction equations, you are giving your child a reference. You’ve created a real world situation for him to reference when thinking about subtracting. If your child can associate these kinds of equations with experience, helping your child with subtraction homework will be less about you telling your child the “steps” to completing a problem, and more about him deciding what strategy to use. Working with simple problems in this way will help your child with more difficult, multi-digit problems. It will also increase fluency (speed) and recall.