It said 25 heads but I got 23, so the coin model is wrong.
The student sees that the observed count does not exactly equal the predicted count and concludes the model must be broken. A fair coin model predicts 25 heads in 50 flips. They observe 23 heads and say the model is wrong, instead of seeing 23 as a normal, expected wobble around 25.
Kids treat probability like a guarantee. They think a 'good' model should nail the count every time. They have not yet learned that real data wiggles around the prediction, especially with small sample sizes.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Expects observed to match the model exactly
What you might hear
It should be exactly 10 sixes in 60 rolls, but I got 8, so something is off.
The student believes the data must land on the predicted number exactly. A die model says P(6)=1/6, so over 60 rolls it predicts 10 sixes. They expect to see precisely 10 and are confused or call the data 'fake' when they see 8 or 12.
They confuse the long-run prediction with a short-run promise. They think the model 'tells' each batch what to do, so a result like 8 instead of 10 feels like a contradiction rather than ordinary variation.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Cannot compute the model's expected count
What you might hear
The model is one fourth and I got 9, so I cannot tell if it matches.
To compare, the student must turn the model probability into an expected count by multiplying probability by trials. They skip this. With P=1/4 over 40 draws, the model predicts 10, but they compare the observed 9 to the raw '1/4' or '4' instead of to 10, so the comparison is meaningless.
They do not connect probability to a count. Multiplying P by the number of trials feels like a separate, forgotten step. So they line up an observed count against a fraction, comparing apples to oranges.
This one is not a slip to correct — the underlying idea needs re-teaching before more practice will help.
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.
For Sophia's experiment of spinning a fair four-color spinner, a model predicts "Green" will occur 30 times over 120 times, but it was actually observed 24 times. What is the difference between the predicted and observed counts?
Answer6
Generated by probability-7, 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 "Compare model probabilities to observed frequencies" 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 Statistics and Probability 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
Free for 15 days — a card is kept on file, but $0 is charged until
the trial ends. Cancel in one click before then and pay nothing.