# Algebra for 4th Grade: Introduction to 4th Grade Algebra

Fourth graders usually study a variety of math topics, including arithmetic, geometry and algebra. When 4th graders learn algebra, they learn very basic topics, which may include expressing and solving simple equations or, in some cases, using the order of operations.

## What Do Students Learn in 4th Grade Algebra?

### Simple Multiplication Equations

In 4th grade, your child will look at word statements that indicate a comparison that can be expressed as a multiplication equation. For example, when he sees an equation such as 42 = 6 x 7, he will understand that 42 is six groups of seven.

In early algebraic equations, your 4th grade child will be solving problems where one of the numbers in the equation is missing. For example, a problem might be written as 4 x _ = 20. These kinds of problems help students prepare for more complex linear equations and variables.

When reading a word problem, your child might encounter something like, 'You removed x dandelions for your mom. Your cousin removed 50 fewer dandelions for her. How would you express how many dandelions your cousin planted?' The answer is x - 50 because your cousin removed 50 fewer than you, who removed an unknown amount, x.

To practice this concept outside of school, look for real-world examples that require algebraic thinking. For instance, at the grocery store, you might present a problem like this:

You have \$15 to spend on cereal. If each box is on sale for \$3, how many boxes can I spend?

To solve this, your child will have to come up with an equation, like 15 = 3x. To solve, he or she will have to figure out what number times three equals five. The answer is five cereal boxes because 3 x 5 = 15.

### More Complex Equations

More difficult equations may use any of the four math operations (addition, subtraction, multiplication and division). In a multi-step problem students need to know the order of these operations.

The order of operations has three rules, to be followed in order:

1. Perform any operations inside parentheses first.
2. Going from left to right, do the multiplication and division operations.
3. Again going from left to right, do the addition and subtraction operations.

Following these rules, if the problem were 4 + 5 x 2 = _ , your child will first multiply 5 x 2 and then add four. Before doing the math, he might rewrite the problem as 4 + (5 x 2). Either way, the answer is 14.

However, if the original problem were (4 + 5) x 2, he must first add 4 + 5 and multiply the sum times two. This would give an answer of 18.

There could be a problem such as 4 + 6 + 8 x 2. He would first solve 8 x 2; the problem would then become 4 + 6 + 16, with the answer being 26. The problem 15 - 4 x 2 + 3 = x could be written 15 - (4 x 2) + 3 = x; the solution would be 15 - 8 + 3 = 10. He must now work from left to right: (15 - 8) +3 = 10. If he were to work it as 15 - (8 + 3), his answer (= 4) would be wrong.

A complex word problem might read:
Chris has been collecting U.S. state quarters for some time. She placed them in 12 baggies with 4 coins in each bag. Which equation would you use to show how many state quarters Chris has collected?
a) 4 - c = 12
b) 4 ÷ c = 12
c) 48 ÷ 12 = c
d) c ÷ 12 = 4.

The correct answer is d. Model the reasoning aloud for your child for each possible answer:
a) Since 12 is larger than four, you can't subtract anything concrete from four to equal 12.
b) This uses the same logic as a.
c) The problem does not give the number 48 anywhere, so 48 cannot be part of the equation.
d) This is the only remaining choice, and it is logical that the number of quarters divided by 12 would be four.

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