Using wrong circle type on number line
"The Circle Confusion"
The Mistake in Action
Represent $x \leq 3$ on a number line.
Wrong: Open circle at 3, arrow pointing left.
Why It Happens
Students mix up when to use open vs closed circles, or may not have learned the distinction clearly.
The Fix
Open circle ○: Value NOT included ($<$ or $>$) Closed circle ●: Value IS included ($\leq$ or $\geq$)
For $x \leq 3$:
- The symbol is $\leq$ (less than or equal to)
- 3 IS included
- Use a closed (filled) circle ●
Memory aid: "Equal means fill-ed" (the line under the symbol means fill in the circle)
Spot the Mistake
Can you identify where this student went wrong?
Represent $x \leq 3$
Open circle at 3
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: