In my time with Year 7 students learning about algebra, I've noticed some common mistakes they often make. Here’s a simple list of those errors:

1. Mixing Up Adding and Subtracting Variables

Students sometimes forget that they can only add or subtract “like” terms. For example, if they see $3x + 2x$, they can add those up to make $5x$ easily. But when they look at $3x + 2y$, they get confused. It’s important to remind them that they can’t mix these because $x$ and $y$ are different.

2. Ignoring Parentheses

When students multiply, they sometimes forget about parentheses. For instance, if they have $2(x + 3)$, some might just multiply $2$ by $x$ and not think about $3$. The right way is to do $2x + 6$. It’s very important to pay attention to what’s inside the parentheses!

3. Mistakes with Division

Division can be tricky, particularly with algebraic fractions. Students often don't simplify properly. For example, if they need to simplify $\frac{2x^2}{2x}$, they might just say it equals $x$, missing that $2x$ cancels out. The final answer is just $x$.

4. Skipping the Order of Operations

Some students jump into solving problems without following the order of operations (which is sometimes called PEMDAS or BODMAS). This can lead to errors in more complicated problems like $2 + 3(4 + x)$, where they may completely forget the parentheses.

5. Confusion with Negative Signs

Lastly, negative signs can confuse them, too. They might mix up subtracting a variable and multiplying by a negative number. For example, looking at $-x + 3$ can lead to mistakes if they don’t pay attention to the signs.

To help students improve, encouraging them to practice these areas can make a big difference!