Ratio: from data to intervention
One class sits an 8-question ratio quiz. This page shows how I read the results, decide what to fix first, give feedback to the teacher, and check a week later whether it worked.
Illustrative data. The class, the scores and the spot-check are simulated to show the method. They are not real pupils or teachers. The quiz questions, answers and misconceptions are real P6 content.
1. The quiz
| # | Question | Answer | Skill |
|---|---|---|---|
| 1 | Write the ratio of 8 apples to 12 oranges in its simplest form. | 2 : 3 | Simplest form |
| 2 | The ratio of boys to girls is 3 : 5. What fraction of the class are boys? | 3⁄8 | Ratio ↔ fraction |
| 3 | Share $72 between Amy and Bala in the ratio 4 : 5. How much does Bala get? | $40 | Dividing in a ratio |
| 4 | A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C. | 8 : 12 : 15 | Combining ratios |
| 5 | The ratio of P to Q is 3 : 7. Q has 28 more than P. How many does P have? | 21 | Difference → unit |
| 6 | Ali and Ben had marbles in the ratio 5 : 3. After Ali gave Ben 12 marbles, they had the same number. How many did Ali have at first? | 60 | Before–after, total unchanged |
| 7 | 6 : 9 = ? : 15 | 10 | Equivalent ratios |
| 8 | The ratio of John's money to Mary's is 3 : 5. Mary spends 1⁄5 of her money. What is the new ratio? | 3 : 4 | One quantity changes |
2. Which questions went wrong?
The first view is the percentage correct for each question. Anything under the 75% target needs action.
Q1, Q3 and Q7 (the routine skills) are fine. Q2, Q4, Q6 and Q8 are the problem, and Q5 is borderline. Hover over or tap a bar to see the most common wrong answer.
3. Who got what wrong, and how
A score alone hides why. Every wrong answer was coded by the misconception behind it (see the key). Rows are pupils, sorted by total score.
| Code | Misconception | Typical wrong answer |
|---|---|---|
| R1 | Treats a part-to-part ratio as a part-to-whole fraction | Q2: 3⁄5 · Q8: answers as a fraction |
| R2 | Joins two ratios without making the shared term the same | Q4: 2 : 3 : 5 |
| R3 | Doesn't notice what stays the same in a before–after problem | Q6: 30. Takes the 12 marbles as the whole gap (2 units = 12), missing that giving 12 away closes the gap by 24 |
| R4 | Changes the quantity that didn't change | Q8: 2 : 4 or 3 : 1 |
| U | Finds units but uses the wrong one at the end | Q5: 49 (gave Q instead of P) |
| s | Slip: arithmetic or copying error | any |
4. What I fix first
I rank fixes by how many pupils it reaches × how many questions it unlocks. A single misconception behind several wrong questions comes before a question that's simply hard.
- R1: part-to-part vs part-to-whole, for the whole class (10 min).
R1 shows up in Q2 and Q8 and hits about half the class, so it gets a whole-class fix. The next lesson starts with a routine: draw the bar for each part, then circle the whole and count all its units before writing any fraction. Then a hinge question: "Red : blue = 2 : 7. What fraction is blue?" (Options: 7⁄9 ✓, 7⁄2 R1-flip, 2⁄7 R1, 5⁄9 subtracted)
- R3: before–after, for a small group of 12 pupils (20 min, in a breakout room).
A mini-lesson for the 12 pupils with an R3 error. The rule they learn: first ask what stays the same. In Q6 the total stays the same (Ali gives to Ben, so nothing leaves the pair). Before: 5u + 3u = 8u. After: equal, so 4u each. Ali dropped from 5u to 4u, so 1u = 12 and Ali had 5 × 12 = 60 at first. Two similar problems follow, then one where the difference stays the same, so they don't just learn "always the total".
- R2: combining ratios, through homework + a worked example (self-paced).
Most pupils with R2 got the other skills right, so they only need one procedure. A 3-minute worked-example video ("make B the same in both: 2:3 → 8:12, 4:5 → 12:15") and a 6-question set. No live class time is spent on this unless the re-check fails.
- Q5 slips (U): no new teaching.
These pupils found the unit correctly and then answered for the wrong person. Add "underline what the question asks" to the class checklist, and recheck in the warm-up.
5. Feedback to the teacher
The same quiz was given to three parallel classes. On Q2, this class is clearly behind:
Spot-check note to Teacher A (from 10 minutes of the week-1 recording):
"When you introduced 3 : 5 you drew a lovely bar for boys and girls. The class I compared with went one step further: the teacher drew a brace round both bars and wrote '8 units = whole class' before asking any fraction question. Can you add that brace and ask 'how many units is the whole class?' every time a ratio question asks for a fraction this week? I'll look at Q2-type warm-up results on Friday and share them with you."
Feedback is specific (one move), shows what to do instead of what was wrong, and comes with a date to check it.
6. Did it work? The re-check
One week later, a 4-question re-check uses parallel questions: same skill, new numbers and context, so pupils can't just remember the answers.
| Fix | Re-check question | Success means | If not met |
|---|---|---|---|
| R1, whole class | Cats : dogs = 4 : 7. What fraction are dogs? | ≥ 75% of the class correct, and no more than 3 pupils still making an R1 error | Teach again with fraction strips, and check Teacher A's next recording |
| R3, group | A before–after problem with a constant difference (both receive the same amount) | ≥ 8 of the 12 group pupils correct | A second group session, plus the game's before–after levels as homework |
| R2, homework | X : Y = 3 : 4, Y : Z = 6 : 5. Find X : Y : Z (9 : 12 : 10) | ≥ 75% correct | Move it into a live-class warm-up |
| Q5 slips | A difference question that asks for the larger quantity | ≥ 80% correct | Nothing new. Keep the checklist |
Closing the loop: each fix has a named owner (me, or Teacher A), a date, a measure and a decision for both outcomes. Nothing is "done" until the re-check says so. Results then feed the PSLE-style revision plan: any skill below target for two re-checks gets a slot in the term's revision lessons.