Choose a learning goal small enough to test
“Learn fractions” can cover several unrelated skills. A tighter goal is “explain why 3/4, 0.75 and 75% represent the same share.” That goal gives the lesson a start, a set of connected representations and a finish you can test. Provide the class level and any representation your teacher requires.
Use Lesson Studio when the relationship needs more than one answer line. A tutor follow-up can settle one question; a lesson can connect the meaning, the model and an application. Keep those parts aimed at the same concept so the visual does not become a separate topic.
Keep the whole fixed when comparing fractions
Half of a small cake and half of a large cake are the same proportion but different amounts. A picture cannot establish equal quantities unless the wholes are equal in the relevant measure. Name whether you are comparing a share or an amount.
For a shared whole, thirds and sixths can be compared by subdivision: one third becomes two sixths, so 1/3 = 2/6. Additive changes do not preserve that relationship: 1/3 is not equal to 2/4. Explain why multiplying numerator and denominator by the same nonzero factor changes the number of pieces while preserving the share.
Check the lesson before practicing it
Inspect labels and conditions. Do the pieces have equal areas? Does the decimal refer to the whole, rather than to the count of selected pieces? Does “75%” describe 75 out of 100 equivalent parts? Correct a mislabeled model before turning it into a study set.
A second check is to work backward. Starting from 0.75, write 75/100 and simplify to 3/4 by dividing numerator and denominator by 25. Reversing the route tests the same relationship from another starting point. Compare notation with your class materials.
Turn the central idea into recall
Make one question for the conversion and another for the condition. The conversion card can ask “Write 2/5 as a decimal and a percentage.” The condition card can ask “Why must the pieces of the whole be equal when counting selected parts?” Keep each answer hidden during the first attempt.
The checked conversion is 0.4 and 40%. The condition matters because counting unequal pieces would not measure their share of the whole. Use the explanation to correct the miss rather than memorizing three values without their meaning.
Return to the lesson with a specific gap
After closing the lesson, try an exit task: “Three of ten equal parts are selected. Express the share as a fraction, decimal and percentage.” The result is 3/10, 0.3 and 30%. If you get the numbers right but cannot explain the equal-part condition, revisit that condition instead of replaying every conversion.
A useful second task changes the representation first: “A diagram labels the selected share as 60%. What fraction of equal fifths is selected?” Since 60% = 0.6 = 3/5, three of five equal parts fit. Returning from a percentage to a visual checks whether the representations remain connected.
