19 of 26 During Guided Practice, 8 of 26 Alone
Mr. Reyes teaches sixth-grade math to 26 students. In a lesson on unit rates, he models two problems at the board, works three more with the class, then assigns six. Nineteen of 26 students get the guided problems right. Only 8 get the independent set right, and 11 of the 15 who miss write the ratio upside-down - for example, 3 dollars per 12 pencils written as 12:3. During the guided phase, three students answer most of his questions and the rest copy what those three say. He has 20 minutes left in the period and a quiz scheduled for tomorrow that he cannot move because the team gives it.
1. Diagnose what the guided-practice data actually show, then decide how to use the remaining 20 minutes.
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Diagnosis: the gap between 19 of 26 and 8 of 26 is not a practice-volume problem, it is a signal that the guided phase measured imitation rather than understanding. Three students supplied the answers, so the class chorus was the three students' thinking, and 19 correct responses probably reflect following a demonstrated procedure. The error pattern confirms it: 11 students inverted the ratio, which means they never attached units to positions. They learned that a ratio has two numbers, not which number goes with which quantity. That is a conceptual gap, not a careless slip, and re-explaining the same procedure will reproduce it.
Use of the 20 minutes - do not start the independent set over.
- (5 min) Return to a single problem with the units labeled in the problem stem and have students physically label each quantity before writing anything. Model once with a table: quantity, number, unit.
- (8 min) Students redo two of the missed problems in pairs, required to say the units aloud ('dollars per pencil') before writing the ratio. Mr. Reyes circulates and listens for unit language, not for the right number.
- (5 min) Whole-class share of one pair's reasoning, deliberately choosing a pair that made the inversion error and corrected it.
- (2 min) Exit ticket: one new problem, plus the sentence 'The ratio compares ___ to ___.'
Why not just do more guided problems: it would raise today's accuracy and fail tomorrow's quiz for the same 11 students. What would change the call: if the errors had been scattered across many patterns rather than concentrated in inversion, the problem would be attention or pacing, and drill would be the right response.
2. What should change in tomorrow's re-engagement before the quiz, and how will he know within the period that the change worked?
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Structural change: replace the model-we-do-you-do sequence with a label-first routine. Every problem begins with a two-column table - quantity and unit - completed before any ratio is written. The procedure is unchanged; the entry point into it is.|Participation change: stop taking whole-class choral answers. Use cold call on labeled wait time, and have students write before anyone speaks, so the three dominant students cannot pre-empt the thinking. If he keeps asking 'what do we do next?' he will keep getting the same three voices and the same false positive.
Productive failure instead of demonstration: give one problem with the units deliberately mismatched and ask students to find what is wrong and fix it. Naming the error in someone else's work is easier than avoiding it in your own, and it directly targets the inversion pattern he observed.
In-period evidence: the exit ticket from today and the warm-up tomorrow should be scored for unit labels, not just answers. Decision rule: if 18 or more of 26 label both quantities correctly on the warm-up, proceed to the quiz with a short review. If fewer than 14, the quiz will generate scores that reflect a concept he has not yet taught successfully - he should give the quiz as required but record it as formative and plan a re-teach, telling the team why the score is not usable as summative evidence.
What he should not do: re-teach the same procedure more slowly. The data point to a missing conceptual step, and pace is not the variable.