Writing Simple Expressions

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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.

Learning Outcomes

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.

Parent Tip: Encourage your children to use a pencil or erasable pen so they can keep their notes and calculations neat without having to start over again every time they want to change the order of part of the expression.

Warm Up

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.

Pre-assessment worksheet

Have your children take the Pre-Test that follows to make sure you are able to identify which operation comes first in each expression, and why it is first. If they get 7 or less correct, review the introduction with them or go back to the lessons on grouping symbols and order of operations before continuing on to the lesson.

Main Lesson: Writing Simple Expressions

Writing Simple Expressions

Parent Tip:

Writing expressions can be extremely hard for students since there are so many things to consider at the same time. Remind your children to slow down and think about each step, one at a time, to prevent them from becoming frustrated.

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:

  • The numbers 7, 4, and 2.
  • "multiplied" tells me I will need the operation of multiplication.
  • "sum" tells me that I will need the operation of addition.
  • "Multiplied by the sum" tells me that I will need to get the sum of 4 and 2 before multiplying. Since addition usually comes after multiplication, I will need to put 4 + 2 inside parentheses.

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.

The product of five and two, added to seven.

Click to Show/ Hide Answer

The sum of twelve and twenty, divided by eight.

Click to Show/ Hide Answer

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.


  • Using the correct numbers and operation symbols is important when writing simple expressions.
  • You must consider the rules for the order of operations to help you decide whether or not you need to include any grouping symbols.
  • You can get some basic understandings about an expression, without having to evaluate it, by looking at the relationship between the numbers and the operations being used.

Test Questions

Review the above recap points with your children and then print out the Post Test that follows.

At least 7 out of 10 correct will show that your children are ready to go on to move on.

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