The idea, step by step
A list keeps the original answers
A response list records what people said. For example: apple, pear, apple, banana, pear, apple. A list is useful, but finding every total can take time.
Choose one group at a time. Mark each response as you count it. Apples occur three times, pears twice and bananas once. Each response belongs in one group.
A table organises the count
A frequency table has a row for each choice and a number showing how often it occurred. Give the columns clear headings so readers know what the numbers mean.
Check the total: 3 + 2 + 1 = 6. This matches the six responses in the list. The total check helps reveal a missing or repeated response.
| Fruit | Responses |
|---|---|
| Apple | 3 |
| Pear | 2 |
| Banana | 1 |
A common trap
Writing the number of different choices as the number of children.
Instead: Count every response. Three choices can represent six children.
See the thinking
Organise a colour list
Make a table for: blue, red, blue, green, red, blue.
| Colour | Responses |
|---|---|
| Blue | 3 |
| Red | 2 |
| Green | 1 |
- Use blue, red and green as the groups.
- Count blue three times, red twice and green once.
- Check 3 + 2 + 1 = 6, the number of entries.
Find a recording error
A child counts the fruit choices as Apple 3, Pear 2, Banana 2. Does that match the original table?
| Child | Choice |
|---|---|
| Ari | Apple |
| Bo | Pear |
| Cleo | Apple |
| Dara | Banana |
| Eli | Pear |
| Finn | Apple |
- Add the recorded counts: 3 + 2 + 2 = 7.
- Only six children are listed, so seven responses cannot be correct.
- Recount banana: only Dara chose it.
Check your understanding
A list says cat, dog, cat, fish, dog, cat. How many cat responses are there?
Show answer
3.
Cat occurs as the first, third and sixth entry.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Count the apple choices in the fruit table.
Six children choose one fruit each. Child Choice Ari Apple Bo Pear Cleo Apple Dara Banana Eli Pear Finn Apple - Make a frequency table for: bus, walk, walk, car, walk, bus.
- How many vehicles are recorded altogether?
Vehicles observed in five minutes. Vehicle Number Car 6 Bus 2 Bicycle 3 - Write the book types from the fewest choices to the most.
Books chosen by a group. Type Number Animals 4 Space 2 Stories 5 - Seven children each give one answer to a survey. A table shows 2, 3 and 3 responses. Explain why it needs checking.
- Use the weather record to make a frequency table for Sunny, Cloudy and Rainy.
Weather observed over five school days. Day Weather Monday Sunny Tuesday Cloudy Wednesday Sunny Thursday Rainy Friday Sunny
Read the worked solutions
- Count the apple choices in the fruit table.
Six children choose one fruit each. Child Choice Ari Apple Bo Pear Cleo Apple Dara Banana Eli Pear Finn Apple Ari, Cleo and Finn chose apple.
3. - Make a frequency table for: bus, walk, walk, car, walk, bus.
Count each choice once.
Check 2 + 3 + 1 = 6.
Bus: 2; walk: 3; car: 1. - How many vehicles are recorded altogether?
Vehicles observed in five minutes. Vehicle Number Car 6 Bus 2 Bicycle 3 6 + 2 + 3 = 11.
11 vehicles. - Write the book types from the fewest choices to the most.
Books chosen by a group. Type Number Animals 4 Space 2 Stories 5 Their counts are 2, 4 and 5.
Space, Animals, Stories. - Seven children each give one answer to a survey. A table shows 2, 3 and 3 responses. Explain why it needs checking.
2 + 3 + 3 = 8.
Check for a repeated response in the original records.
The counts total 8, but only 7 children answered. - Use the weather record to make a frequency table for Sunny, Cloudy and Rainy.
Weather observed over five school days. Day Weather Monday Sunny Tuesday Cloudy Wednesday Sunny Thursday Rainy Friday Sunny Monday, Wednesday and Friday are sunny.
Tuesday is cloudy and Thursday is rainy.
The total is 5 days.
Sunny: 3; Cloudy: 1; Rainy: 1.
Curriculum reference & lesson scope
Australian Curriculum v9; SA Curriculum Mathematics 2026
Surveys/observations; lists/tables; creating displays; comparing representations and conclusions.
Official curriculum source ↗