Finds how far apart the x values and y values are, then just adds those two gaps together. For (1,2) to (4,6) the gaps are 3 and 4, so the child writes 7 instead of 5.
The distance looks like it should be the across gap plus the up gap, the way you walk along streets. Squaring and a square root feel like extra steps, so they get dropped.
Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.
Forgets to square before adding, or forgets the root
What you might hear
I did 3 plus 4 under the root, so it is square root of 7.
Sets up the formula but skips the squares inside the root, or finds the right inside number and forgets to take the square root. For (1,2) to (4,6) they write √(3+4)=√7 instead of √(3²+4²)=√25=5.
The distance formula has several parts: subtract, square, add, then root. Under time pressure one part gets left out, usually the squaring or the final root.
This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.
Subtracts negative coordinates the wrong way
What you might hear
From −2 to 1 the gap is 1, because 1 minus 2 is negative 1.
When a point has a negative coordinate, the child subtracts without flipping the sign, so the gap comes out too small. For (−2,1) to (1,5) they do 1−2=−1 for the x gap instead of 1−(−2)=3, getting √17 instead of 5.
Subtracting a negative number means adding, but children often just drop the minus sign or treat −2 like 2. The wrong gap then feeds a wrong distance.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
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.
Compute the distance between (0, 0) and (9, 12) exactly for Tatiana.
Answer15
Generated by pythagorean-8, 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 "Find the distance between two points on the coordinate plane" 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 Geometry 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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