Use this sample to make one short-cycle team decision. Record comparison accuracy and explanation quality separately. The illustrative aggregate later in this sample is synthetic and does not claim learner impact.
1 · 20-minute teacher-team kickoff
Before the kickoff: administer the starting check to pupils and bring only pre-collected anonymous response totals or work samples to the meeting. Do not teach during the check.
0–2 min · Name the focus
Compare a fraction to 0, 1/2, or 1. Require a representation or stated relationship.
2–7 min · Review pre-collected evidence
Review anonymous starting-check responses; do not administer a pupil check during this staff meeting.
7–13 min · Read the evidence
Which anchor caused uncertainty? Which explanation gives a rule without a reason?
13–18 min · Choose one action
Use the 1/2 anchor on a number line before asking for common denominators.
18–20 min · Commit
Assign sessions, materials, and a Friday review.
2 · Starting check · teacher copy
For pupils, print student-checks.html. It contains the starting and follow-up checks without keys and asks only for an anonymous class code.
Write <, >, or =. Then explain using an anchor, equivalent fraction, or number line.
S1. 3/8 ___ 1/2
Key: < · 1/2 = 4/8; 3/8 is one eighth less.
S2. 7/6 ___ 1
Key: > · 1 = 6/6; 7/6 has one extra sixth.
S3. 5/8 ___ 1/2
Key: > · 1/2 = 4/8; 5/8 is one eighth more.
S4. 3/4 ___ 1
Key: < · 1 = 4/4; 3/4 is missing one fourth.
3 · Three 15-minute teaching routines
Routine 1 · Build the anchors · 3 min model / 7 min work / 3 min talk / 2 min exit
Mark 0, 1/2, and 1 before comparing
Teacher language: “Before I compare two fractions, I ask which side of a landmark each fraction lives on.”
Student task: Place 3/8, 5/8, 3/4, and 7/6 on a shared line; write one reason each.
Likely misconception → response: “A bigger denominator means a bigger fraction.” Keep the whole fixed; partition the same whole into more equal pieces.
Answer reasoning: 3/8 is before 4/8 (=1/2); 5/8 is after; 3/4 is before 1; 7/6 is after 1.
Pacing: 3 min model the landmarks; 7 min pairs place and justify; 3 min compare two placements aloud; 2 min exit: “Is 5/8 before or after 1/2? Because…”
Routine 2 · Just under / just over · 3 min model / 7 min work / 3 min talk / 2 min exit
Locate the anchor first
Teacher language: “I do not need to convert every fraction to a decimal. I can compare it to a useful anchor.” Model 3/10 by locating 5/10 first.
Student task: Sort 3/10, 7/4, 5/6, and 5/8 as under or over 1/2 or 1, then justify one sort.
Likely misconception → response: “5/8 is below 1/2 because 5 is less than 8.” Locate 4/8 (= 1/2) first.
Answer reasoning: 3/10 is below 1/2; 7/4 is above 1; 5/6 is above 1/2 and below 1; 5/8 is above 1/2.
Pacing: 3 min model 3/10; 7 min independent sort and one written reason; 3 min partner talk; 2 min exit: circle one fraction just over 1/2 and explain.
Routine 3 · Claim swap · 3 min model / 7 min work / 3 min talk / 2 min exit
Check the reason, not only the sign
Model: Claim A: “5/8 is less than 1/2 because 5 is less than 8.” Claim B: “5/8 is greater than 1/2 because 1/2 = 4/8.”
Teacher language: “We are checking the reason, not just the sign.”
Student task: Label each claim valid/not yet; revise one sentence using because.
Likely misconception → response: Any explanation containing numbers is accepted. Require a link to the same whole, an anchor, or a representation.
Answer reasoning: Only Claim B establishes valid equivalence.
Pacing: 3 min model the two claims; 7 min pairs label and revise; 3 min share one revision; 2 min exit: write a valid “because” sentence for 5/8 and 1/2.
4 · Follow-up check
F1. 5/12 ___ 1/2
Key: < · 1/2 = 6/12; one twelfth less.
F2. 9/8 ___ 1
Key: > · 1 = 8/8; one extra eighth.
F3. 7/12 ___ 1/2
Key: > · 1/2 = 6/12; one twelfth more.
F4. 7/8 ___ 1
Key: < · 1 = 8/8; one eighth short.
Item-by-item rubric
| Score | What counts | What does not count |
|---|
| Comparison correct · 1/0 | Correct <, >, or = sign. | Correct explanation with an incorrect sign. |
| Explanation valid · 1/0 | Mathematically valid reason, anchor, equivalent fraction, or number-line relationship. | Blank, circular statement, unrelated numbers, or invalid rule—even with a correct sign. |
5 · Filled synthetic aggregate example
Illustrative planning data only. It is invented for this worked sample and does not claim real learner results or efficacy.
| Evidence | Starting check | Follow-up | Teacher reading |
|---|
| Comparison correct | 68 / 96 item opportunities | 80 / 96 | More signs are correct; inspect item patterns. |
| Explanation valid | 40 / 96 | 52 / 96 | Reasons still trail comparison signs. |
| Sessions delivered | 3 / 3 planned sessions | Delivery is recorded separately from learner response. |
| Mixed item | F3: 18 / 24 comparison correct; 11 / 24 explanation valid | Review work before concluding why. |
One next teaching action: retain the visible 1/2 anchor and add one spoken/written “because” sentence before the next comparison check.
6 · Reusable weekly action record
Team / week:Focus:Compare fractions with 0, 1/2 and 1
Starting check totalsComparison correct: ____ / ____ · Explanation valid: ____ / ____
Sessions delivered:____ / ____
Follow-up totalsComparison correct: ____ / ____ · Explanation valid: ____ / ____
Mixed evidence to inspect:Next teaching action / owner:Next check date: 20-minute review agenda
- Review comparison and explanation columns separately.
- Inspect one mixed item or work sample without naming students.
- Decide: keep, change, or stop the action.
- Assign the next teaching action and owner.
- Set the next check and review date.
Original instructional sample. No learner identities, inputs, external services, pricing, or curriculum-standard claim are included.