The constant is 5, because that is the number being added.
In an equation like y = 3x + 5, the child names 5 as the constant of proportionality. They grab the number that is added on, not the number that multiplies x. For a true proportional equation y = 4x, they may even invent a +0 and call k zero.
The child hears the word 'constant' and matches it to the lone number sitting by itself. A multiplier feels like part of x, while an added number looks like the real 'constant'. They do not yet see that k is the rate that scales x, not a fixed amount tacked on.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Thinks k changes point to point
What you might hear
k is 4 here, but it is a different number over there, so it keeps changing.
Given a word problem or pairs like 3 apples cost $12 and 5 apples cost $20, the child computes a different k at each point and reports several values. They divide 12 by 3 to get 4, then divide 20 by 4 instead of by 5, and think the constant keeps changing.
The child does not yet trust that a proportional relationship has ONE fixed rate. They treat each pair as its own little problem and may even cross numbers from different rows. They miss that y divided by x gives the same k every time.
This one responds to correction in the moment — the idea is there, the rule being applied is not.
Names one data value as k
What you might hear
k is 24, that is the number of miles right there in the problem.
For 'a car goes 6 miles every minute', the child says k is 6 because they saw the number 6. But if a problem says '4 minutes for 24 miles', they answer k = 24 (a single value) instead of dividing 24 by 4 to get 6. They report a quantity from the problem, not the y-to-x ratio.
The child grabs a number straight from the text instead of building a rate. They confuse the constant with the largest or most obvious value and skip the division step. They do not see k as y divided by x.
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.
The graph shows a proportional relationship between two quantities x and y. What is the constant of proportionality (y per x)?
Answer10.0
Generated by ratios-rates-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 "Identify the constant of proportionality" 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 Ratios and Proportional Relationships questions on this site are checked by an automated verification pass before a child is ever served them.
Related
Other places children go wrong
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