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The Number System

Find distances between points using coordinates and absolute value: why children get it wrong

There are 5 recognisable ways a child goes wrong here — distinct patterns, not carelessness.

Each one below is a mistake our question bank was built to expose, written out the way you would actually hear it said out loud at home.

Knowing which one you are looking at is the whole job. "Check your answer" does not help a child who is confidently applying the wrong rule.

The mistakes, one at a time

  1. Subtracts across zero instead of adding
  2. Uses both coordinates to find distance
  3. Gives a negative distance
  4. Plots x and y in the wrong order
  5. Adds the coordinates instead of subtracting

Subtracts across zero instead of adding

What you might hear

Five minus three is two, so they are two apart.

For points on opposite sides of zero, the child subtracts the coordinates (treating both as positive) instead of adding the two distances. For (-3, 2) and (5, 2), they compute 5 - 3 = 2 instead of 3 + 5 = 8.

The child always subtracts the smaller number from the bigger one. They ignore the signs and don't see that one point is left of zero and one is right.

Words rarely shift this one. It needs something to look at — a picture, a fold, an object on the table — before the explanation lands.

Uses both coordinates to find distance

What you might hear

I have to use both numbers from each point, right?

When points share an x- or y-coordinate, the child still changes both coordinates or applies a two-step formula. For (2, 1) and (2, 6) they subtract the x's too, or combine 0 and 5 wrongly, instead of just |6 - 1| = 5.

The child thinks every distance problem needs both numbers. They don't notice the shared coordinate means only one coordinate changes.

This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.

Gives a negative distance

What you might hear

Three minus seven is negative four, so the distance is negative four.

The child subtracts in an order that gives a negative number and reports it as the distance. For (1, 7) and (1, 3) they write 3 - 7 = -4 and call the distance -4, forgetting absolute value.

The child subtracts left point minus right point and keeps the sign. They forget distance is always positive and skip taking absolute value.

This one responds to correction in the moment — the idea is there, the rule being applied is not.

Plots x and y in the wrong order

What you might hear

Wait, which number goes sideways again?

Reads (x, y) but moves up first then across, swapping the two coordinates when plotting. The mis-plotted point then makes the distance answer wrong.

The child has not locked in that the first number is always horizontal. They treat the pair as two numbers without a fixed order, so they sometimes go vertical first.

This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.

Adds the coordinates instead of subtracting

What you might hear

I added them, so the distance is the total.

For two points on the same line, the child adds the two changing coordinates instead of finding the difference, giving a distance that is too big.

Distance feels like 'combine the numbers,' so the child reaches for addition. They have not connected distance to the gap between values.

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.

See your child's own results — start free
A real question from the bank

What this looks like in practice

(abs-only) Help Leo find the distance between A(4, 5) and B(4, 8) using absolute value.

  • A 13
  • B 3
  • C 2
  • D 4

Answer B — 3

Generated by coordinate-plane-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 "Find distances between points using coordinates and absolute value" something children normally struggle with?

Yes. We track 5 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 The Number System 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

The year this concept belongs to

See the full curriculum map — every Common Core concept we cover, the verified question count, and what a child at this level should know.

Find out which one it actually is

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