# How to Teach Subtraction and Borrowing

Updated on October 7, 2013

## Introduction

Subtraction, like many math principles, can be hard to explain to children. Like learning to ride a bike, learning subtraction requires practicing and listening until one day it “clicks”. There are several things that one can do to help a child get the principles and fundamentals a little faster. One of the most important principles of teaching subtraction is to wait to introduce numbers until you have taught the fundamentals of subtraction with pictures and objects. After children understand the basics you can practice subtraction with abstract numbers and introduce borrowing. During the process of learning the principles of subtraction children’s future math competency is increased if they also memorize their math facts.

## Use Different Teaching Methods

Mathematics is often thought of as a bunch of abstract principles. However, much of mathematics, especially basic arithmetic, is very tangible. Before explaining the principles of subtraction with numbers and symbols, start with pictures and physical objects. Children understand having something and then having something taken away. Explain that this is subtraction. Give children a group of ten objects. These can be anything, pennies, buttons, small candies, and unifix cubes work especially well. Let the children practice taking away different amounts from their collection of ten and counting how many they have left.

Many math workbooks use pictures of objects to teach the principles of subtraction. You do not have to have a math workbook to use pictures. You can print out pictures from many places on the Internet and have the children practice crossing out a few of the objects and counting how many objects remain.

Every child, like every adult, learns differently. The more ways, or modalities, used to teach information the deeper the knowledge will penetrate their brains, and the stronger grasp they will have over new skills. This is why using manipulatives, pictures, short videos, written directions, and oral instructions together will help children master mathematical principles like subtraction faster than using only a single teaching method.

## Mental Math

While currently out of fashion in many public schools, memorizing math facts is still vital in promoting lifelong success. It is important that a chid learn the underlying principles of subtraction first, once those are mastered children will be better served in life if they simply memorize the basic math addition and subtraction facts from 1 to 20.

Just remembering that 10 - 4 = 6, instead of having to figure it out every time, improves speed and makes doing math easier and more enjoyable. Memorizing basic math facts before math gets more complicated helps instill greater confidence. Strong mental math ability also helps children perform better on standardized tests.

## Drills and Story Problems

After the basic principles of subtraction have been taught with physical objects and pictures, it is time to apply the principles to numbers. Start out with sets of of problems of no more than ten to twenty at a time. These sets should be math facts subtracting from 10. Math and reading are two skill sets that are essential to succeed in life. Both of these require hours and hours of practice before any type of mastery can be obtained. Sadly, many children never put the hours of practice in because they get bored and quit.

There are several strategies to avoid the "math drop out" problem with young children. First, only do math for 30 minutes at a time. If you feel you must do math for longer in a day, break it up into two or more 30 minute sessions. This will help keep your child fully focused during math time, because they do not have enough time to get bored or distracted. Another strategy is to use a mix of drills, games, and physical activities during math time. Everyone enjoys variety. The more fun something is the more children will want to do it. A third component to successful math instruction is the use of story problems.

Math in the real world is rarely, if ever, a sheet of drills to complete. Math in life is about solving real problems, everything from budgeting to doubling a recipe. Give children word problems early on to solve. After the initial mastery of subtraction, drills should be mostly word problems. Even if a child has difficulty reading, word problems should still be a significant part of math instruction and practice. The word problems can be read to the child, or even recorded and listened to and solved. Like math and reading, problem solving is a skill that needs to be practiced and practiced before it is fully absorbed.

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## Khan Academy Video Explains How Borrowing Works

One of the first places many children begin to dislike math is when they first learn about borrowing. For many the reason that borrowing is so discouraging is because the rationale behind it is not taught, or is not taught clearly. By the time children are ready to learn to borrow they should have already been introduced to the concept of place value and have mastered the skill of carrying in addition.

Borrowing is really carrying in reverse. The idea that you cannot subtract a larger number from a smaller number is again easily demonstrated with physical objects and is usually easy for children to grasp. The problem comes in with where the extra "1" comes from. Some children will simply accept that you are borrowing a one from the neighboring number. But, other children get confused because the neighboring number is really or 100. Where do all the numbers go?

Borrowing is really just a shortcut. To help make sure children understand what they are doing and are not just copying you, you need to explain that you are not just borrowing "1" from the number next door, but are moving a unit of "10" or "100" to the next column. You aren't changing the amount in the problem, you are just redistributing the numbers differently. The video from the Khan Academy is a really short and clear explanation of how borrowing works. Share the video with children learning to borrow and have them rewrite subtraction problems as demonstrated in the video.

## Conclusion

Subtraction and borrowing are fundamental skills that once mastered cannot be forgotten. Like riding a bicycle, it is often almost impossible to describe to the newbie how to do it. The best way to learn both riding a bicycle and almost any math skill, is to just do it over and over again. Lots of mistakes will be made and sometimes frustration will be begin to build in both the student and the instructor, but mistakes and failure are sure signs that learning is taking place. Eventually, given enough time and attempts, everyone gets up on a bicycle, or learns subtraction. But, what you should be aiming for is more than just simply knowing how to subtract, you are looking to have a student who has mastered subtraction. Mastery is simply competence with more practice.

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