Understanding Elementary Math Concepts

Elementary Math

Especially in elementary school, it helps to think of math problems visually, using groups of objects. As you read through the operations below, you might want to have a group of items, such as pennies or counters, in front of you.

Addition

When you add objects together, you count the total number of objects in two or more groups. For instance, you might have three oranges in one group and two oranges in another group. If you combine these groups and count all of the oranges together, you'll have five (2 + 3 = 5).

You'll also learn that when you're adding together groups of objects, the answer will still be the same no matter what order you add them in. For example, 2 + 3 and 3 + 2 will both give you the same answer. This is called the commutative property.

Subtraction

Subtraction means to take an existing group of objects and make it smaller by removing some of the objects. If you start out with seven pencils, for instance, and you give away five of them, you would have two pencils left over, so 7 - 5 = 2.

Unlike with addition, the commutative property does not apply to subtraction. Since you can't take away seven objects if you only have five to start with, the answer to 5 - 7 is not the same as the answer to 7 - 5.

Multiplication

You'll use multiplication to find the total number of objects that are in a certain number of groups of the same size. For example, if three of your friends are each bringing eight cupcakes for the school bake sale, how many cupcakes will you have altogether? You can find the answer by counting the total number of cupcakes in three groups of eight. You should count 24, so 3 x 8 = 24.

The commutative property applies to multiplication as well, which means that the number of cupcakes in three groups of eight (3 x 8) is the same as the number that would be in eight groups of three (8 x 3). In other words, you could get 24 cupcakes by asking three people to bring eight cupcakes each, or by asking eight people to bring three cupcakes each.

Division

To divide is to separate a group of objects into smaller groups of a certain size. Imagine that you have 15 pieces of candy, and you've promised to give some to five of your friends. If you want to give each friend the same amount, how much should you give each person? To solve this problem, you need to divide your 15 pieces of candy into five portions. In order to make every portion the same size, each one should have three pieces of candy. This means that 15 ÷ 5 = 3.