Substitute Guide: Ratios, Rates, and Percents
Learning goal (plain language)
Students practice ratios (comparing two amounts, in simplest form), equivalent ratios and ratio tables, unit rates and unit prices (an amount "per one," used to find the better buy), and percents (a ratio out of 100, used for tax and for a percent of a quantity). 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 §111.26 (Grade 6 Mathematics). Knowledge & skills 6.4 and 6.5 — ratios, rates, and percents.
- Primary — 6.4B (provisional): apply qualitative and quantitative reasoning to solve prediction and comparison problems involving ratios and rates.
- Primary — 6.5B (provisional): solve real-world problems to find the whole given a part and a percent, to find the part given the whole and a percent, and to find the percent given the part and the whole.
- Supporting — 6.4C (provisional): give examples of ratios as multiplicative comparisons of two quantities describing the same situation.
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 (ratio, unit rate) |
| Build — Study the math | 5–10 min | Read reference box, worked example, ratio-table figure; Q3 |
| Apply — Use what you know | 20–25 min | Q4–Q7 (match forms, best buy, error analysis, percent of a quantity) |
| Explain — Justify (CER) | 5–10 min | Q8 claim/evidence/reasoning |
| Close — ACE | 5 min | Articulate / Connect / Extend |
| Continue — early finishers | optional ~15 min | Write-your-own best-buy challenge |
Script Read aloud to start
"Today's assignment is a paper math packet called Ratios, Rates, 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 says a percent means "per 100," so a percent becomes a decimal by putting it over 100 (6% = 6/100 = 0.06).
- For a best buy, remind them the lower price for one (unit price) is the better deal.
- 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 (the ratio-table figure uses a pattern, not color).
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 whether students understand "percent means per 100" and why unit price is the fair comparison for a best buy. Watch for additive instead of multiplicative reasoning on the ratio-scaling items (Q3, Q4b), and part-part vs. part-whole confusion on Q4c. The percent-of-a-quantity item (Q7) shows who can find a part from a whole and a percent. The separate answer key lists worked steps, alternate strategies, misconceptions, and a 3-point rubric for Q8.