Substitute Guide: Proportional Reasoning and Percents
Learning goal (plain language)
Students practice unit rates (a price or amount "per one"), proportional relationships (a steady rate shown as a table, a graph, and an equation y = k · x), and percents (tax, tip, and discounts). You do not need a math background to run this. Every formula and a worked example are printed in the student packet. Students show their work; you do not need to teach the method — the packet does the teaching. Your job is to hand it out, read the start script, keep the room on task, and collect the packets.
Standards alignment
Framework: 19 TAC §111.27 (Grade 7 Mathematics). Knowledge & skills 7.4 — proportional relationships and percents.
- Primary — 7.4A: represent constant rates of change / the constant of proportionality (k = y/x) in tables, graphs, equations, and situations.
- Primary — 7.4D: solve problems involving ratios, rates, and percents, including tax, tip, and discount.
- Supporting — 7.4E: convert between measurement/rate representations to compare proportional situations.
Provisional — pending educator verification against the current official TAC source.
(Standards are paraphrased here, not quoted. Please confirm codes and wording against your official source.)
Setup Before class (5 min)
- Count and hand out one student packet per student.
- Confirm each student has a pencil. A basic calculator is allowed but not required; students who have one may use it.
- Write the date on the board and remind students to fill in the name line.
- Keep the answer key with you — it is a separate file and is not in the student packet.
Materials What's needed
- Printed student packet (4–6 pages) per student.
- Pencil per student; a basic four-function calculator is optional.
- This guide and the separate answer key (teacher only).
- No technology, no internet, no special supplies.
Timing Suggested pacing (~45–60 min)
| Segment | Time | What students do |
|---|---|---|
| Start — Retrieval warm-up | 5 min | Q1–Q2 (unit rate, simple percent) |
| Build — Study the math | 5–10 min | Read reference box, worked example, graph; Q3 |
| Apply — Use what you know | 20–25 min | Q4–Q7 (four forms, tax/tip, error analysis, recipe) |
| Explain — Justify (CER) | 5–10 min | Q8 claim/evidence/reasoning |
| Close — ACE | 5 min | Articulate / Connect / Extend |
| Continue — early finishers | optional ~15 min | Two-discounts challenge |
Script Read aloud to start
"Today's assignment is a paper math packet called Proportional Reasoning and Percents. You will work by yourself with a pencil. A basic calculator is allowed if you have one, but you do not need one. The most important rule: show your work — write down the numbers you use, not just a final answer. Everything you need is printed in the packet, including a worked example and all the formulas. Start with the warm-up, then read the Build section before the Apply questions. If a question is tricky, skip it and come back. Put your name, class period, and date at the top now. You have about 45 minutes; raise your hand if you need help reading a question."
Support When students ask for help
- Students show their work; you do not need to teach the method. Point them back to the printed reference box and the worked example — the method is right there.
- You may read any part aloud to a student or the class.
- If a student is stuck, prompt with "What does the worked example do?" or "What's the unit rate — the amount for one?" rather than giving the answer.
- For percents, remind them the packet shows: multiply for "percent of," and subtract for a discount ("percent off").
- It is fine if a student cannot finish the optional early-finisher challenge.
Access Accommodations & language support
- Read-aloud of any question is allowed for all students.
- Point students to the worked example, the formulas in the reference box, and the sentence stems for Q8 and ACE.
- A calculator is allowed for any student who wants one — this removes the arithmetic barrier so students can focus on the reasoning.
- Extended time is fine; the core can stop after Q8 if time runs short.
- Students may show work with numbers and short phrases if writing full sentences is a barrier, as long as the reasoning is clear.
- The packet is grayscale-safe — it prints and reads clearly in black and white.
Tools Allowed & not allowed
Allowed: pencil, the printed packet, a basic (four-function) calculator, quiet self-read-aloud. Not needed / not allowed: phones, internet, graphing/AI calculators, or getting answers from another student.
Teacher follow-up (for the returning teacher)
The highest-value items to review next class are the error analysis (Q6) and the justification (Q8), which reveal the "percent of" vs. "percent off" confusion and whether students subtract a discount. Watch for additive instead of multiplicative reasoning on the recipe scaling (Q7). The four-forms item (Q4) shows who can move between a table, an equation, and a graph point using k = y ÷ x. The separate answer key lists worked steps, alternate strategies, and a 3-point rubric for Q8.