The child uses a filled (closed) circle for x > 5 or x < 5, and an open circle for x ≥ 5 or x ≤ 5. They mix up which sign gets a filled dot and which gets an open one.
The child does not link the dot to whether the number itself is part of the answer. A closed dot means "include this number" (≥ or ≤). An open dot means "do not include it" (> or <). They treat the dot as just a starting mark.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
Shades the wrong direction
What you might hear
It says greater than 5, so I colored back toward the small numbers.
The child shades toward the smaller numbers for x > 5 (shading left), or toward the bigger numbers for x < 5 (shading right). The arrow points the wrong way from the endpoint.
The child reads the symbol by its shape, not its meaning. They may think the open side of > "points" one way, or just shade toward zero out of habit. They do not test a sample number.
This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.
Marks only the point, not the whole ray
What you might hear
The answer is 5, so I just marked 5.
The child marks a single dot on 5 for x > 5 and stops. They do not shade the line or draw the arrow showing all the numbers in the solution.
The child thinks the inequality has one answer, like an equation x = 5. They do not yet see that an inequality has many answers — a whole ray of numbers, not a single value.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
What to say when you see it
For each mistake above, Algo School gives you the words to say next — the specific response that corrects the thinking instead of just marking the answer wrong, plus practice aimed at that exact error.
Distinguish strict from non-strict for Alexei's number line.
Ax ≥ 9
Bx > 9
Cx < 9
Dx ≤ 9
AnswerA — x ≥ 9
Generated by equations-inequalities-6, a deterministic question engine — not written by an AI, and verified before any child sees it.
FAQ
Questions parents ask about this
How do I know which of these mistakes my child is making?
Look at what they SAY, not just what they wrote. Each mistake above includes the phrasing a parent typically hears — that sentence is usually the giveaway. In Algo School, the tutor recognises these patterns while your child is working and adapts the session around the one it sees.
Is "Represent inequality solutions on number lines" something children normally struggle with?
Yes. We track 3 distinct approved mistake patterns for this concept, each one written up because it recurs — not because it is unusual. A child making one of them is doing something systematic, which is far easier to fix than random errors.
What should I do once I know which mistake it is?
Respond to the thinking, not the answer. Algo School gives parents the specific wording for each mistake, then generates practice targeted at that error and shows you whether it actually cleared.
Where do these mistakes come from?
They are part of the same content library that drives practice: each one is reviewed and approved before it is used, and the Expressions and Equations questions on this site are checked by an automated verification pass before a child is ever served them.
Related
Other places children go wrong
Where this sits
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