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Necessary and Sufficient

Necessary and Sufficient


Assumptions can sometimes be discovered in gaps in arguments about whether conditions exist to draw a specific conclusion. Identifying whether support exists in the argument for either necessary or sufficient conditions can be a useful skill for students to learn.

The activity

This activity is simple, and consists of giving students a premise and a conclusion and asking whether the premise by itself contains:

(a) a necessary condition for the conclusion

(b) a sufficient condition for the conclusion

(c) both necessary and sufficient conditions for the conclusion

(d) neither necessary sufficient conditions for the conclusion


Premise: John was driving 55mph in a 30mph zone

Conclusion: Therefore, John got a speeding ticket

Answer: This is a necessary but not sufficient condition, as there must also have been a police officer there to observe and give the ticket.


This is most effective when the premises and conclusions are generated from your course content.


Combine this with a Think-Pair-Share or make the scenario very detailed and combine it with a Four-S activity to increase the level of social engagement.

Adapted from: Van Den Brinkbudgen, R. (2000). Critical thinking for students: Learn the skills of critical assessment and effective argument (3rd Edition). London: How to Books.

Framing this activity for success

We all want students to carry our teachings into their lives. Often, however, we must make our intentions very plain for students to understand that an assignment will equip them with skills and empower them, and is not an arbitrary hoop through which they must jump.

For this reason, frame each activity using these four steps:

  1. Introduce the activity by making clear the specific critical thinking skill the assignment will give them practice using. They may not understand the precise definition of the term, so provide it in writing on the board or overhead. (As a reminder, definitions are here.)
  2. Share examples of how this skill can serve them in their daily lives (e.g., guiding them to buy better products, improving their performance in other classes, advancing their career, communicating better with people they care about, better understanding their own experiences, etc.).
  3. Conduct the activity as described above, making it as active and interactive as possible. When students can talk about their thinking, that thinking moves forward. Teaching for critical thinking is teaching for active learning.
  4. Conclude the activity by reflecting back to students examples that you saw of them using the critical thinking skill effectively, and reminding them to consider the relevance of that skill in other aspects of their. Repeating the examples given in Step 2 may be appropriate, as students will have a different understanding of the skill once they have experienced the assignment.

Important: Wait Five Seconds!

Among the most useful things we as teachers can do during class discussion is shut our mouths. In an oft-cited meta-analysis of wait-time research, Tobin (1987) described findings of greater engagement and achievement when teachers waited at least three to five seconds after asking a discussion question before speaking again. Above this threshold, higher level thinking was observed and student academic performance improved. However, teachers behaving "normally" only tend to wait about one second. Students need a few moments to digest what they have recently heard, formulate their responses, and work up the courage to speak. Slow down, and more of your students will keep up with you.

Reference: Tobin, K. (1987). The role of wait time in higher cognitive level learning. Review of Educational Research, 57, 1: 69-95.