Help with Solving 3rd Grade-Level Equations

Equations for 3rd Graders

An equation uses the '=' sign to tell you that two expressions have the same value. Equations can take many different forms. Here are some examples:

3 = 3

5 - 2 = 3

3 ÷ 1 = 3

5 - 2 = 3 ÷ 1

Solving Equations

In the 3rd grade, you'll practice solving equations. This means that you'll be given equations that have a number missing, and you'll have to figure out what that number is. The missing number is called a variable, and you can represent it with any symbol. We often use letters like x or n for this purpose, but you can use any symbol you'd like. Here are a few equations with variables:

4 + x = 7

n ÷ 2 = 4

4 x 5 = ?

The first two examples might be new to you, but the last one should be more familiar. That's because, even though you might not realize it, you 'solve' an equation every time you complete a math problem. When you answer the problem 4 x 5 by writing 4 x 5 = 20, you've just found a missing variable!

Now, let's practice solving equations that have the variable on the other side. To identify x in the problem 4 + x = 7, ask yourself, 'Four plus what number equals seven?' You'll recall that 4 + 3 = 7, so you can say that x = 3.

It works the same way for multiplication and division. To solve for n in the problem n ÷ 2 = 4, you'll have to figure out what number divided by two equals four. Since 8 ÷ 2 = 4, n = 8. Now, let's try the problem 5 x ? = 20. You already know from earlier that 5 x 4 = 20, so four is the missing variable.

Equations for Word Problems

Another pre-algebra skill you'll learn in 3rd grade is writing equations to represent word problems. Here's an example:

Danika, Caleb and Tammy went out for ice cream. Danika ordered two scoops of ice cream, Caleb ordered three scoops and Tammy also ordered some ice cream. If they ordered six scoops of ice cream altogether, how much ice cream did Tammy order?

Since the total number of scoops ordered was six, that number goes on one side of the '=' sign. We want to know how many scoops of ice cream Tammy ordered, so we'll represent that with the letter T. We know that the number of scoops ordered by Danika and Caleb plus the number ordered by Tammy equals six, so we can write the equation 2 + 3 + T = 6. Since 2 + 3 + 1 = 6, we can say that Tammy ordered one scoop of ice cream.