Substitute Guide: Fractions and Decimals: Compare and Combine
Learning goal (plain language)
Students practice equivalent fractions, comparing fractions, adding and subtracting fractions that have the same bottom number, and writing tenths and hundredths as fractions and decimals. You do not need a math background to run this. Every method 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. This whole guide takes about 5 minutes to read.
Standards alignment
Framework: 19 TAC §111.6 (Grade 4 Mathematics). Number and operations — fractions and decimals.
- Equivalence & comparison: find equivalent fractions and compare two fractions with the same denominator using a model.
- Fractions: add and subtract fractions with like (equal) denominators.
- Connections: relate a fraction with a denominator of 10 or 100 to its decimal (tenths and hundredths).
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. This is not a claim of TEKS alignment.)
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, no physical manipulatives.
Timing Suggested pacing (~45–60 min)
| Segment | Time | What students do |
|---|---|---|
| Start — Warm-up | 5 min | Q1–Q2 (name a fraction, which is bigger) |
| Build — Study the math | 5–10 min | Read reference box, worked example, area model; Q3–Q4 |
| Apply — Use what you know | 20–25 min | Q5–Q8 (compare, ribbon story, fraction–decimal match, error analysis) |
| Explain — Justify (Answer/Model/Why) | 5–10 min | Q9 short explanation |
| Close — ACE | 5 min | Articulate / Connect / Extend |
| Continue — early finishers | optional ~15 min | Draw a model for 4/6 |
Script Read aloud to start
"Today's assignment is a paper math packet called Fractions and Decimals: Compare and Combine. 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 steps you use, not just a final answer. Everything you need is printed in the packet, including a worked example and a picture that shows how to add fractions. 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, the worked example, and the picture (Figure 2) — the method is right there.
- You may read any part aloud to a student or the class.
- If a student is stuck adding fractions, prompt with "Are the bottom numbers the same?" and "If they match, you add just the tops and keep the bottom" — rather than giving the answer.
- For comparing, remind them that when the bottoms match, the fraction with the bigger top is bigger.
- For the decimal match, have them read the fraction aloud: "three tenths" is 0.3; "three hundredths" is 0.03.
- 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 short numbered steps in the reference box, the area model, and the sentence starters for Q9 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 Q9 if time runs short.
- Students may show work with numbers, simple pictures, and short phrases if writing full sentences is a barrier, as long as the reasoning is clear.
- The packet is grayscale-safe — pictures use patterns, not color, so 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 (Q8) and the justification (Q9), which reveal the "add the denominators" misconception and whether students understand why the bottom stays the same when denominators are alike. Watch for "bigger bottom = bigger fraction" in Q2 and Q5, and the 0.3 vs 0.03 place-value slip in Q7. The separate answer key lists worked steps, alternate strategies, common misconceptions, and a 3-point rubric for Q9.