3rd Grade Algebra Concepts and Problems

Algebra Concepts for 3rd Graders

Unknown Numbers

Algebra revolves around the concept of 'unknown numbers' or 'variables.' You'll spend lots of time identifying these in 3rd grade, especially when you study multiplication and division. Of course, when you solve any math problem, you're finding a missing number (the answer); however, you'll also solve problems with missing numbers in other places. For instance, you might see a problem like this: 3 x ? = 18.

To solve missing number problems, you'll need to have a good grasp of your multiplication and division facts. One way to approach this problem is to recall that 3 x 6 = 18, so six is the missing number. Another approach is to divide 18 by three to get six (18 ÷ 3 = 6).

Number Properties

Another algebraic concept you'll learn about in 3rd grade is the idea that there are 'properties,' or rules, that apply to all whole number operations. One of these properties is the relationship between multiplication and division. If two numbers can be multiplied to get a third number, then that third number can be divided by either of those numbers to get the other number. For example, 4 x 5 = 20, so 20 ÷ 4 = 5 and 20 ÷ 5 = 4.

Commutative Property

The commutative property tells us that it doesn't matter what order you add or multiply two numbers in because the answer will always be the same. For instance, 2 x 3 = 6 and 3 x 2 = 6 as well. The same is not true for division. For example, 8 ÷ 2 = 4, but 2 ÷ 8 doesn't have a whole number answer (the answer would be a fraction, but you won't learn about this type of problem until later in school).

Associative Property

The associative property states that when you're multiplying several numbers together, you can group them in any way and still get the correct answer. Imagine that you're multiplying 2 x 3 x 4. In this case, you could multiply 2 x 3 first to get six, and then multiply 6 x 4, or you could multiply 3 x 4 to get 12, and then multiply 2 x 12. Both 6 x 4 and 2 x 12 equal 24, so you would get the same answer either way.