See how a wrong answer becomes the next better practice

Student attempt

The student finds the total flour needed for 8 batches but submits that value as the final answer.

Likely misconception

The proportional reasoning is mostly intact. The miss is the final comparison: the baker already has 5 cups, so the question asks for the shortage.

Adaptive scaffold

Ask for two labels before calculation: total needed and already available. Then subtract only after the scaled total is known.

Next practice

Another ratio problem with an already-have amount, followed by one with irrelevant information to test transfer.

Student attempt

The student writes 2.75 + 4m = 31.50 because 2.75 appears first as the per-mile number.

Likely misconception

This is a setup error, not a calculation error. The repeated quantity is miles, so the per-mile cost must multiply the variable.

Adaptive scaffold

Have the student mark fixed fee once and repeated fee per mile before writing the equation.

Next practice

One more fixed-plus-rate problem, then a plan-comparison problem where two linear expressions must be compared.

Student attempt

The student tries to solve using only the money total and guesses the number of adult tickets.

Likely misconception

The student is missing the second constraint. This problem needs both total tickets and total money.

Adaptive scaffold

Reduce depth for one attempt: define a and s, write the count equation, then write the revenue equation.

Next practice

A similar two-constraint story with a different surface context, such as animals and legs or items and revenue.