Following on from the lesson on how to use grouping symbols and the lesson on the rest of the rules for the order of operations work, this lesson will give you the opportunity to write some simple expressions.
By the end of this lesson, your children will be able to use the order of operations rules to write simple expressions, which includes recording numbers, grouping symbols, and operation signs correctly.
They will also be able to understand some basic relationships between numbers and operations in expressions.
The lesson on order of operations rules explains how the location of each number, operation sign, and grouping symbol in an expression can make a big difference in how the expression is evaluated. In this lesson, you will practice writing simple expressions.
Not only are the rules for the order of operations important, but you will also need to remember your basic math vocabulary.
Review these terms:
Sum  The answer to an addition problem.  
Difference  The answer to a subtraction problem.  
Product  The answer to a multiplication problem.  
Quotient  The answer to a division problem. 
Make sure to use grouping symbols in the correct order (parentheses, brackets, then braces) to enclose steps that need to be done first.
Remember that multiplication and division will be done before any addition and subtraction, so you must enclose addition and subtraction with grouping symbols if you need them to be done first.
If you want an expression that accurately shows 7 multiplied by the sum of 4 and 2, you need to think carefully about what you must include, and the order in which you should write it. For the example above, "7 multiplied by the sum of 4 and 2," make a list of the things you know you must include:


Based on the notes listed above, we are ready to write a simple expression for the verbal problem: “seven multiplied by the sum of four and two.” 7 x (4 + 2) 4 + 2 is in parentheses to make sure this addition is done first. Without the parentheses, the operation of multiplication would have to be done first, based on the order of operation rules. Another way you could write it is just: 7(4 + 2) A number right next to a parentheses mark, with no operation sign in between, infers the operation of multiplication. 
Let's try writing a couple more expressions. Write down each of the expressions, then click on the Show/ Hide Answer link to check your work. Remember to think carefully about what to include, and the order you need to write it.
List what you need to include:
Based on all the things I know, I can write the expression: 5 x 2 + 7 or 7 + 5 x 2 It does not matter if I write the 7 at the beginning or the end, because the order of operation rules tell me that the 5x2 will go first either way. 

List what you need to include:
Based on all the things I know, I can write the expression: (12 + 20) ÷ 8 
Besides being able to write simple expressions, you should be able to look at an expression without solving the whole thing and realize some basic things about it. Look at the two examples below.
3 x (4 + 1)  When you see this expression, you should be able to understand that having "3 x" in front of the parentheses means that the value of the expression will be three times as big as 4 +1 would be by itself. 
35  (2 x 4)  When you see this expression, you should be able to understand that having x 4 after the 2 means that you will be subtracting four times as much as you would for 2 by itself. 