When students try to turn word problems into algebraic expressions, they often make some common mistakes. Here are some things to watch out for:

1. Forgetting About Keywords

The first thing to do when changing words into math is to pay attention to important keywords. Words like “sum,” “difference,” “product,” and “quotient” tell you what math operation to use.

• Example: If you see "the sum of a number $x$ and 5," you should write it as $x + 5$, not $x - 5$!

2. Getting Mixed Up with Order of Operations

Sometimes, students forget the order to do math operations or get confused with parentheses. Remember this order: do everything in parentheses first, then look for exponents, then multiplication and division from left to right, and finally, do addition and subtraction from left to right.

• Example: If you read "three times the sum of a number and 4," you should write it as $3(x + 4)$, not $3x + 4$.

3. Missing Unit Conversions

In word problems that use different units, it’s important to change all amounts to the same unit before making an expression.

• Example: If a problem says "John drives 60 km and Jane drives 1500 m," remember to change 1500 meters to kilometers (1.5 km) first.

4. Using the Wrong Variables

Sometimes, students pick variables that do not match what the problem is about. It’s important to clearly define what each variable means.

• Example: If $x$ stands for the number of apples and the problem wants to know "the total cost when each apple costs 3 dollars," the right expression is Total Cost = $3x$, not just $x$.

5. Not Checking Their Work

Lastly, a big mistake is rushing through the problem and not going back to check the expression they made. Reading the problem again can help make sure the expression really fits what was asked.

By watching out for these common mistakes, students can get better at finding and making algebraic expressions. This will make the whole process much easier and more effective!