The students examine properties of functions (injective, surjective, and bijective) in small groups. Then, they practice these properties by assigning specific functions to them.
| Parameters: | |
|---|---|
| Duration: | 20–30 minutes |
| Participants: | 3–X students |
| Instructors: | 1 teacher |
| Class: | tables |
| Resources: | cards |
| Prerequisites: | read the notation of relations |
- Understand the difference among injective, surjective, and bijective functions.
- Determining whether a given function is injective, surjective, or bijective.
- Print the cards with functions and their properties for each student group.
- The students will work in groups of 3 or 4 people.
- Each printed page can accommodate 4 groups (that is, at least 12 students).
- Use one-sided printing.
- Cut the cards and divide them into equal groups.
- The whole preparation takes at most 60 minutes.
The steps below are separated so that you can explain them one by one. The students need not know the whole process from the beginning: first, they do the step 1, then you explain step 2, and so on.
- Divide the students into groups of 3 or 4 people so that each group has one table.
- Give the printed property cards to each group. Make sure they can read and understand the definitions.
- Give the printed function cards to each group. Their goal is to assign the function cards to the property cards.
- Move around the tables and regularly check on each group and ask if they need help.
- When everyone is finished, check the results with the whole class. For example, you can ask each group one by one how they assigned a specific function and why.
- Leave time for the students' questions.
- Ask questions to the group. For example, you can ask which function was the most difficult to determine and why.
- You can split the function cards into two sets: simpler and more difficult, and hand them out in two rounds.
- You can prepare simple variations to the functions and ask the students how would the function property change.
- This is a good warm-up activity after a lecture on functions.
- There are more good examples on Wikipedia.
Radka Cieslarová, 2017