Substitute Guide: Fractions and Decimals in Everyday Problems
Learning goal (plain language)
Students practice comparing decimals, adding and subtracting fractions that have different bottom numbers, and connecting a fraction to its decimal. 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 §111.7 (Grade 5 Mathematics). Number and operations — decimals and fractions.
- Decimals: compare and order decimals to the thousandths using place value.
- Fractions: add and subtract fractions with unlike denominators using equivalent fractions (a common denominator).
- Connections: relate a fraction to its decimal form.
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, no physical manipulatives.
Timing Suggested pacing (~45–60 min)
| Segment | Time | What students do |
|---|---|---|
| Start — Warm-up | 5 min | Q1–Q2 (compare decimals, name a fraction) |
| Build — Study the math | 5–10 min | Read reference box, worked example, area model; Q3 |
| Apply — Use what you know | 20–25 min | Q4–Q7 (recipe, money, error analysis, choose the operation) |
| Explain — Justify (Answer/Numbers/Why) | 5–10 min | Q8 short explanation |
| Close — ACE | 5 min | Articulate / Connect / Extend |
| Continue — early finishers | optional ~15 min | Draw a model for 1/3 + 1/6 |
Script Read aloud to start
"Today's assignment is a paper math packet called Fractions and Decimals in Everyday Problems. 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, prompt with "What does the worked example do first?" or "Can you make the bottom numbers match?" rather than giving the answer.
- For decimals, remind them to line up by place value and add zeros so both numbers have the same number of decimal places.
- 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 steps in the reference box, the area model, and the sentence starters 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, 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 (Q6) and the justification (Q8), which reveal the "add the denominators" misconception and whether students understand why a common denominator is needed. Watch for lining up decimals by digits instead of place value in Q1 and Q5, and the 1/2 = 0.2 slip. The choose-the-operation item (Q7) shows who reads for key words like "in all." The separate answer key lists worked steps, alternate strategies, common misconceptions, and a 3-point rubric for Q8.