Substitute Guide: Multiplication and Fair Shares
Learning goal (plain language)
Students practice multiplication as equal groups and arrays and division as fair sharing, with small numbers within 100. You do not need a math background to run this. Every method and a picture example are printed in the student packet. Students show their work (they may draw dots or arrays); 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 §111.5 (Grade 3 Mathematics). Number and operations — multiplication and division.
- Multiplication: represent multiplication as equal groups and as arrays (rows × columns).
- Division: represent division as sharing a total into equal groups (fair shares).
- Connections: multiplication and division are related (3 × 4 = 12, so 12 ÷ 3 = 4).
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 calculator is not required; a basic calculator is allowed for any student who has one.
- 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 (about 4 pages) per student.
- Pencil per student; a basic four-function calculator is optional (not required).
- This guide and the separate answer key (teacher only).
- No technology, no internet, no special supplies, no physical manipulatives — students draw to model.
Timing Suggested pacing (~45–60 min)
| Segment | Time | What students do |
|---|---|---|
| Start — Warm-up | 5 min | Q1–Q2 (skip-count by 5; count 3 groups of 4) |
| Build — Study the math | 5–10 min | Read reference box, worked example, array picture; Q3 |
| Apply — Use what you know | 20–25 min | Q4–Q7 (equal-groups story, array match, fair share, find the mistake) |
| Explain — Tell how you know (Answer/Picture/Why) | 5–10 min | Q8 short explanation |
| Close — ACE | 5 min | Articulate / Connect / Extend |
| Continue — early finishers | optional ~15 min | Draw 6 × 2 as groups and as an array |
Script Read aloud to start
"Today's work is a paper math packet called Multiplication and Fair Shares. You will work by yourself with a pencil. You do not need a calculator, but you may use a basic one if you have it. The most important rule: show your work — you may draw dots or groups to help you. Everything you need is printed in the packet, including a picture that shows how it works. Start with the warm-up, then read the Build part before the Apply questions. If a problem is tricky, skip it and come back. Put your name and the date at the top now. You have about 45 minutes. Raise your hand if you need help reading a question — I can read any part out loud."
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 array picture (Figure 2) — the method is right there.
- You may read any part aloud to a student or the whole class.
- If a student is stuck, prompt with "Can you draw the groups?" or "How many are in each group?" rather than giving the answer.
- For a fair-share problem, suggest they draw the groups and "deal out" one at a time, like dealing cards.
- 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 — this packet is written to be read aloud.
- Point students to the worked example, the array picture, and the sentence starters for Q8 and ACE.
- A calculator is allowed (not required) for any student who wants one, so the focus stays on the groups-and-sharing idea, not the arithmetic.
- Extended time is fine; the core can stop after Q8 if time runs short.
- Students may answer with drawings and numbers instead of full sentences if writing is a barrier, as long as the thinking is clear.
- The packet is grayscale-safe — pictures are plain black-and-white dots and arrays, so they print and read clearly in black and white.
Tools Allowed & not allowed
Allowed: pencil, the printed packet, drawing dots/arrays, 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 find-the-mistake item (Q7) and the fair-share explanation (Q8), which reveal the "unequal groups" and "×/÷ mix-up" misconceptions. Watch for adding instead of multiplying in Q4 and skip-counting by 1 in Q1. The separate answer key lists worked steps, alternate strategies, common misconceptions, and a 3-point rubric for Q8.