Fraction of a set
A 60-minute live online lesson. Pupils learn to find a fraction of a set of objects, and to explain why "divide by the bottom number, then multiply by the top number" works.
1. What pupils will be able to do
- Find a fraction of a set, for example 3⁄4 of 12, by sharing the set into equal groups.
- Draw a bar model for it: 4 units = 12, so 1 unit = 3, so 3 units = 9.
- Write the same idea as 3⁄4 × 12 = 9, and say in words why it works.
- Solve 1- and 2-step word problems, including ones that ask for "the rest".
Success check: at least 4 out of 5 pupils get 2 or more of the 3 exit-ticket questions right. Pupils who don't are flagged for the follow-up described in section 7.
Prior knowledge (checked in the first 5 minutes)
- Division facts within the multiplication tables (P3).
- A fraction as equal parts of one whole, e.g. shading 3⁄4 of a rectangle (P2–P3).
- Equivalent fractions (P3). Not needed today, but useful for the stretch question.
2. Misconceptions this lesson targets
Every activity below is built to bring one of these out where the teacher can see it. Each wrong option in the hinge question in section 4 is tied to one of them.
| Code | What the pupil does | Example for 3⁄4 of 12 | What is really going on |
|---|---|---|---|
| M1 | Multiplies by the top number only | 3 × 12 = 36 | Has learnt "of means times" as a rule, with no sense that the answer must be smaller than 12 |
| M2 | Divides only, and stops | 12 ÷ 4 = 3 | Has found one group (1⁄4), not three groups |
| M3 | Divides by the top number | 12 ÷ 3 = 4 | Mixes up which number tells you how many equal groups to make |
| M4 | Answers with the fraction's parts | "3 out of 4", so 3 | Reads the fraction as a count, not as a share of the set |
| M5 | Answers the wrong question | "How many are not red?" answered with the red amount | Did not re-read the question after calculating |
3. Lesson flow
- 0–5
Hook: the sticker share Concrete
On screen: 12 cartoon stickers. Mei has 12 stickers. She gives 3⁄4 of them to her brother. Before we work anything out, will her brother get more than 12 stickers or fewer? Vote now.
A quick poll brings out M1 straight away. A pupil who votes "more" is told nothing yet. The teacher notes the name and comes back to it at 25 min.
- 5–15
Share it out Concrete
Each pupil drags the 12 virtual counters into 4 equal groups on the shared whiteboard.
The bottom number, 4, told us how many equal groups to make. How many stickers are in one group? So what is 1⁄4 of 12? Then: Her brother gets 3⁄4, so how many groups does he take? Pupils circle 3 groups and count: 9.
Repeat once with 2⁄3 of 15. The pupils lead and the teacher only asks questions.
- 15–25
Draw it as a bar Pictorial
Turn the groups into a bar model, the diagram pupils will use all the way to PSLE:
12 stickers4 units = 12
1 unit = 12 ÷ 4 = 3
3 units = 3 × 3 = 9We wrote this in three lines. Every line says something true about the picture. Point to the "1 unit" in the bar.
- 25–35
Say it in numbers Abstract
Write 3⁄4 × 12 = 9 and link each step back to the bar. Come back to the pupils who voted "more" in the hook: We took 3 of the 4 equal parts. Can that ever be bigger than the whole 12?
Name the rule only now, once it makes sense: divide by the bottom (make the groups), multiply by the top (take that many groups).
- 35–45
Hinge question + guided practice
Everyone answers the hinge question (below) at the same time. The teacher reads the spread of answers and decides on the spot:
- 8 or more pupils correct: move on to the worksheet.
- Mostly B (M2): go back to the bar and ask "how many units did we need?"
- Any C or D: pair those pupils in a breakout room with the counters again.
- 45–55
Worksheet + game
Pupils work through worksheet Q1–Q6. Early finishers try Q7–Q8. Anyone who gets Q1–Q4 right plays the in-class game round (fraction-of-a-set levels) for practice, while the teacher works with the rest.
- 55–60
Exit ticket
Three questions, done alone and marked automatically. The results go to the weekly mastery tracker (section 7).
4. Hinge question
Each wrong option points to a different misconception, so the spread of answers tells the teacher what to fix, not just how many pupils got it wrong.
5. Worksheet
The questions get harder as they go: fluency, then word problems, then PSLE-style multi-step. Answers and working are hidden under each question.
Answer
Answer
Answer
Answer
Answer and marking
Girls = 36 − 16 = 20 A1
Another way that gets full marks: girls are 5⁄9 of the class, so 5 × 4 = 20. Watch for M5: writing 16 and stopping.
Answer
Answer and marking
Left: 30 − 10 − 12 = 8 A1
Both fractions are of the original 30. A common slip is taking 2⁄5 of the 20 that are left, which is a P5 "fraction of a remainder" idea that does not apply here.
Answer
The same bar works backwards. This sets up "finding the whole" for P5 and P6.
6. Exit ticket
7. After the lesson: how I know it worked
Same day. Exit-ticket scores go into the mastery tracker, one row per pupil, with misconception codes on each wrong answer. A pupil with 0–1 correct, or any M1 or M3 error, gets a 5-question follow-up set in their homework.
Next lesson. The warm-up includes two fraction-of-a-set questions without warning. If the class drops below 75% correct, the lesson did not stick, and I go back over the bar model before starting new content.
Across classes. If one teacher's class has many more M2 errors than the others, I spot-check that class's recording at minutes 15–25. Usually the bar was drawn but "how many units do we take?" was never asked.