A No-Prep Sub Plan for Ratio and Proportion (Arizona)

The sub plan you write at six in the morning with a fever is the one that fails. Ratio and proportion is a topic where a substitute without math background cannot rescue a vague instruction, since the whole lesson turns on one relationship. What follows is a lesson for an Arizona upper elementary class that runs on a printed script, needs no login, and leaves you work worth reading when you get back.

The folder, and why it is paper

Keep it in a labeled folder in your desk, not in a cloud drive a substitute cannot reach. Inside: a one-page script written for an adult with no subject knowledge, a seating plan naming the students who need version B, thirty-two copies of each task sheet, and a sealed envelope marked "only if they finish early". A plan that depends on a projector or a password becomes forty minutes of coloring.

Write the script in the words the substitute should say: timings on the left, exact phrasing in the middle, what to do if it goes wrong on the right.

The lesson, phase by phase

1. Eight minutes: the recipe warm-up. A recipe for four is printed on the sheet; students rewrite it for eight, then for six. The six is where the thinking starts. Purpose: brings prior knowledge to the surface and gives an early success.
2. Twelve minutes: the mixing task. Three paint mixtures given as ratios, and the question of which two would look the same. Purpose: separates students who reason about the relationship from those who compare the left-hand numbers only, which is the central misconception of the topic.
3. Fifteen minutes: the scaling problem. One realistic problem with three parts of increasing difficulty, worked alone and then checked with a partner in a different colored pencil. Purpose: the color makes the change of mind visible without you being in the room.
4. Ten minutes: explain it in words. Students write two sentences saying how they knew, on the printed recording sheet. Purpose: the piece of work you will actually read, and the only part that shows reasoning rather than answers.
5. Five minutes: collect and note. The substitute collects everything in the folder and writes down the names of anyone who could not start. Purpose: a controlled ending, which stops the last stretch of the period unraveling.

The whole thing depends on the tasks being right, and building them from nothing while unwell is not realistic. Algebra Basics – Ratio, Proportion and Percentage | Math Foundations Workbook | GRADE 5–9 has the graded problems and full answer keys already assembled, so version A and version B can be pulled and copied in ten minutes on a day when you are fine, and left in the drawer for a day when you are not.

Making it substitute-proof

Three rules keep it working. Every phase must function in silence. No phase may depend on the one before it, so a student who did nothing in the warm-up can still attempt the scaling problem. And nothing is graded in the room, because a substitute making judgment calls about partial credit will do that instead of supervising.

For students who cannot access the ratio work at all, the folder needs a parallel task that is still math rather than a word search. Independent Math Practice for Grade 3 – Place Value, Operations & Shapes is designed for exactly this: printable pages a student works through alone with no explanation, which keeps them on number sense while the class scales recipes.

What to put in the sealed envelope

Early finishers wreck sub plans. The envelope solves it, provided the substitute is told not to open it before the last fifteen minutes. Put something in it that a child can read and complete alone, and that has nothing to do with tomorrow's teaching. Birds Through the Year: Nests, Migration & Winter | Science Unit (Grades 3-4) works well as that reserve, not because it teaches ratio but because it is self-contained printable science reading with questions attached, which is precisely what a five-minute-notice extension needs to be.

What you do with the work on Monday

Read the two-sentence explanations first and sort them into three piles: reasoned correctly, right answer with no reasoning, and additive thinking. The third pile is your next lesson, since a student who adds two to both sides of a ratio has a coherent idea that happens to be wrong. The Arizona Academic Standards treat proportional reasoning as a gateway, and it returns in the measurement and percentage questions on the AASA. Done properly, you come back to a class that had a real lesson and a folder that tells you exactly where to start.

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