# Repair a ratio lesson before release

Published 2026-10-13 · Version 1.0

Find an answer-key mismatch, a weak exit check, and an over-helpful scaffold, then release only a coherent packet.

Proposed estimate: 25 minutes. Proposed practice estimate, including an independent attempt and comparison with the worked answer.

## Existing workflows
- [Author a lesson from a teaching goal](/educators/author-lesson-from-goal/)
- [Verify sources and answer keys](/educators/verify-sources-answers/)
- [Adapt a task without changing its learning goal](/educators/adapt-language-access/)
- [Build a coherent lesson-material packet](/educators/build-coherent-lesson-packet/)
- [Check a lesson before teaching](/educators/verify-lesson/)

## Synthetic brief and materials

Everything here is invented. An educator has 25 lesson minutes, paper, and two differently labeled tile symbols. The goal is to scale a 2-light-to-3-dark tile ratio to a specified total and explain why the ratio is preserved. Prerequisites are multiplication and recognizing equal groups. There is no required standard in this exercise.

The draft packet contains: P1, a plan with 5 minutes of explanation, 10 of practice, and 10 of discussion; H1, “Make a 20-tile pattern using 2 light tiles for every 3 dark tiles”; K1, “10 light and 15 dark”; E1, “What does the word ratio mean?” The proposed support sheet already shows four complete groups of two light and three dark tiles. The plan includes no allowance for distributing materials.


## Try before opening the worked answer

Identify each mismatch. Produce a repaired 25-minute sequence, separate learner directions and teacher answers, and a support that does not solve H1. Give every task a stable label. Finish with a ready, revise, or hold decision and one reason. Do not send real learner work to an AI tool; this brief is sufficient.


## Worked answer: repair the dependencies

K1 totals 25, whereas H1 requires 20. Matching the ratio alone does not satisfy the total. E1 checks vocabulary rather than scaling. The completed support sheet gives away H1’s multiplication factor. The schedule consumes all 25 minutes before materials and transitions.

A repaired sequence is: 3 minutes recall a single five-tile group; 5 minutes model M1 for 10 tiles; 6 minutes work together on G1 for 15 tiles; 6 minutes attempt H1 for 20 tiles; 3 minutes complete E1 for 35 tiles; 2 minutes for materials and transitions. Total: 25. This is a proposed sequence, not a prediction of classroom pacing.

Learner directions for H1: “A pattern uses 2 light tiles for every 3 dark tiles. Make 20 tiles altogether. How many of each kind do you need? Show how your answer preserves the ratio.” For E1, replace 20 with 35 and request a fresh explanation. Keep both answers in the teacher key.

Teacher key: one group contains 2 + 3 = 5 tiles. M1 requires 10 ÷ 5 = 2 groups, giving 4 light and 6 dark. G1 gives 6 and 9. H1 needs 20 ÷ 5 = 4 groups, giving 8 and 12; 8 + 12 = 20 and both original quantities were multiplied by 4. E1 needs 7 groups, giving 14 and 21; the total is 35. Check the total and the common factor separately.


## Adaptation and release decision

Replace the completed scaffold with blank space for drawing and labeling groups, leaving the number of groups for the learner to determine. A labeled drawing with a spoken or written explanation can show the same mathematics when prose composition is not the goal. Use labels or patterns as well as color; color alone should not carry the quantities.

Keep P1, H1, K1, and E1 at packet version 1.0, but do not treat matching version labels as proof of consistency. Open the learner copy and ensure K1 is absent. If H1 later changes to 30 tiles, its key must change to 12 light and 18 dark, and every reference to H1 must be reviewed. Changing the number only on the handout invalidates the release.

Decision: ready for teacher consideration after subject, format, and practical checks. Hold any required translation pending qualified review. If time is short, shorten the discussion while keeping a fresh scaling check; do not replace the check with a definition question.

## Self-check
- Did your repair catch the total, goal, support, and timing problems?
- Can you verify every answer without consulting the draft key?
- Does the learner still choose the multiplication factor?
- Can you identify all dependencies affected by changing H1?

## Evidence and limits
Original mathematical exercise. Calculations and dependency checks are worked explicitly; no classroom trial or outcome is reported.

Published October 13, 2026. All time budgets are proposed planning estimates, not measured results. Public sources inform stated principles but do not evaluate or endorse these paths, prompts, worked answers, or exercises. No learning gains, workload savings, or historical classroom outcomes are claimed.