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Subtraction means you are taking away something from a number of things or group of things. A subtraction equation looks like this:
The difference is the result of the subtraction.
Subtraction is taught after the student develops a basic understanding of addition. There is a strong link between addition and subtraction. Subtraction can be performed to find out how much should be added to the smaller number to get the larger number. The equation 6 – 4 = 2 can also be written as 4 + 2 = 6. In other words, the subtrahend and the difference in the subtraction equation become the addends; and the minuend becomes the sum in the addition equation.
It is important to note that changing the order of addends do not change their sum. For example, 4 + 2 = 6 and 2 + 4 = 6. This is not true in the case of subtraction, for example, 6 – 4 = 2 but 4 – 6 ≠ 2.
Besides teaching subtraction through textbooks, it can be taught through math games and through manipulatives.
Math games are games in which the structure and the rules of the games are purely based on mathematical concepts, and winnings are totally dependent on mathematical understandings. The three major advantages of understanding the concept of subtraction through math games are:
1. Learning: Mathematics is all about practicing the newly acquired skills and revisiting already introduced skills. Math games have the ability to induce much more practice in kids than the traditional methods of teachings have. While playing subtraction games, the kids don’t mind repeating some procedures or facts over and over. This helps them master subtraction concepts relatively faster.
2. Math skills: The ability to subtract mentally is a skill. Not much focus is put on this while teaching through traditional methods. Math games stress kids to do math in their heads. In classroom teachings, the kids have very few opportunities to check or justify their work. Also, math games entice players to challenge opponents’ unjustifiable moves. This compels kids to prove or convince the opponent their move through their conceptual understanding. Hence, math games help in developing mathematical communication which is the need of the hour.
3. Engagement: One of the most important reasons to introduce subtraction learning games in Mathematical teachings is the excitement and enthusiasm it brings in to the kids. Subtraction games enable kids to experience success and satisfaction and thereby, develop confidence in their newly acquired skills.
1. Counters: Counters are one of the most useful math manipulatives in understanding base math. This method is particularly useful in understanding basic subtraction. It provides the student visual understanding of subtracting smaller numbers. This primitive step can set the foundation for learning subtraction as a simple mathematics process and further enhance their ability to subtract larger numbers as well.
For example, to subtract 3 from 7, the student should place 7 counters on a table, take away 3 from them and then count the remaining number of counters to find the difference.
Counters can be effectively used for performing subtraction within 20. Using counters to solve subtraction problems involving bigger numbers can make it cumbersome and time-consuming. The following methods can help resolve this limitation of the counter method.
2. Base Ten Blocks: The base ten blocks represent the model of base ten number system. The smallest cube is called 1 unit or 1 ones. Each rod consists of 10 such cubes and is called 1 ten or 10 ones. The flat square consists of 10 such rods and is called 1 hundred or 10 tens or 100 ones. The block consists of 10 flat squares and each square has 100 ones, therefore each block is called 1 thousand or 10 hundreds or 100 tens or 1000 ones.
The base 10 blocks make understanding of subtraction with regrouping really easy. It involves trading some of the bigger blocks with blocks of smaller value.
For example: Subtract 29 from 87.
Trade 1 ten from 8 tens with 10 ones. Now, 8 tens 7 ones becomes 7 tens 17 ones.
Subtracting 2 tens 9 ones from 7 tens 17 ones gives 5 tens 8 ones.
So, it gives 87 – 29 = 58.
In Kindergarten, subtraction problems are introduced through pictures wherein the kids are expected to use their counting skills to count the number of objects left after some are taken away. With practice, kids are able to solve subtraction problems without pictures. Kids either count on their fingers to find the difference or they do it mentally. They are also able to convert subtraction sentences to equations. At this level, kids are expected to perform subtraction only within 10.
In Grade 1, the kids are taught to count back on the number line to find the difference between two numbers. At this level, kids are expected to perform subtraction within 10 using their counting skills. The kids are also expected to understand the relationship between addition and subtraction. The knowledge of place value system enables kids to subtract a multiple of 10 from another.
In Grade 2, the kids know from memory the sum of two one-digit numbers which enables them to fluently subtract within 20. The kids are able to subtract 1 digit from 3 digits, 2 digits from 3 digits, 3 digits from 3 digits by using strategies of breaking up tens and hundreds. By the end of this grade, kids are able to perform subtraction with regrouping and without regrouping within 1000.
In Grade 3, building on previous learning the kids are able to perform two digit subtraction with regrouping. The kids are also expected to perform multi-digit subtraction, with and without regrouping using the knowledge of place value system.
With ample practice and application of different strategies, kids are able to develop a deeper understanding to perform subtraction of fractions in Grade 4 and subtraction of decimals in Grade 5.
For example: Write the equation for the given sentence.
3 take away 2 is 1.
Equation: ____ – ___ = 1
For example: Subtract 5 – 3.
Start from 5. Move 3 units to the left. The answer is the number you end up at.
For example: Find the unknown number in the following equations.
5 – ? = 3
3 + ? = 5
The student needs to think of a number that should be subtracted from 5 to get 3 or a number that should be added to 3 to get 5.
For example: Find 15 – 7.
The student knows 8 + 7 = 15, so 15 – 7 = 8.
For example: Find the unknown number in the equation 6 – ? = 2.
A clear understanding of place value system is required for performing subtraction involving bigger numbers. The student needs to understand that hundreds should be subtracted from hundreds, tens from tens and ones from ones.
For example: Find 80 – 60.
80 – 60 is same as subtracting 6 tens from 8 tens which give 2 tens.
For example: Find 700 – 400.
700 – 400 is same as subtracting 7 hundred from 4 hundred which gives 3 hundred.
For example: What is 82 – 31?
8 tens 2 ones – 3 tens 1 ones = 5 tens 1 ones = 51
For example: Subtract:
Since 8 ones cannot be subtracted from 7 ones, so borrowing 1 ten = 10 ones from tens place makes 1 ten 7 ones = 17 ones and 2 tens – 1 ten = 1 ten.
Since 5 tens cannot be subtracted from 1 ten, so borrowing 1 hundred = 10 tens from hundreds place makes 10 tens 1 ten = 11 tens and 5 hundred – 1 hundred = 4 hundred.
So 5 hundred 2 tens and 7 ones become 4 hundreds 11 tens and 17 ones.
The above subtraction problem will look like this:
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