Conditional Statements

Conditional statements are “if-then” statements.

  • If A=B, and B=C,then A=C.
  • If you complete all your homework and study for the tests, you will pass the class.
  • If a shape is a square, then it is also a rectangle.

We use them all the time, and they can be phrased in both English and math terms. They can therefore spark grammar, math, and critical thinking lessons. Yet, even though we use them so often in daily life, they can give the class headaches when it comes time to formalize and calculate with them.

Here are some snazzy links for working with this challenging topic:

  • The Worry Reducer is a great and funny starting point for a lesson on conditional statements. To use it, you pick an event that you are worried about. Ask your students for a suggestion. Let’s suppose that someone worries that they will end up in an orphanage. Using the Worry Reducer worksheet, you must then work backwards to identify the events that would have to take place to get from the current state to that state, and then calculate their probability. I particularly like this, because when actually worrying we tend to use “what if” statements and work out further and further into worry, as in “What if my parents got sick? And then what if they died? And what if my Nana wouldn’t take me in and I had to go to an orphanage?” The Worry Reducer goes in the other direction: “Unless my Nana refused to take me in, I wouldn’t have to go to an orphanage.” “Unless both my parents died while I was still a child, my Nana wouldn’t have to take me in.” And so forth. For each link, you then do the research involved in calculating the probability of the event. The Worry Reducer includes a chart for these calculations.
  • A lesson plan on colds and flu is designed to provide ESL students with practice on if-then statements. We think you could also use this lesson, which includes reading practice and useful reminders about avoiding contagious disease, to clarify the concept of conditional statements for native-speaker students who need something concrete. “If you have these symptoms, it’s probably a cold,” is the kind of example sentence involved.
  • NTTI once published an intriguing lesson called “The Syllogism Blues.”  One of the activities was having students watch part of a documentary on the Blues and call out “IF-THEN” every time they heard a conditional statement. You could do this with any carefully-chosen video clip that you have access to.
  •  Crossing the River is one of our favorite conditional thinking problems. Click on its name and you will find a clear statement of the problem, complete with conditional statements, as well as a number of different phrasings of the answer. I would have the class work out the puzzle, using manipulatives if necessary, and then analyze the various answers at that site for clarity.

If anyone is still confused, we have a little trick for you. One of our favorite publishers of critical thinking materials is The Critical Thinking Company. In their book Building Thinking Skills, they present if-then statements by saying that the ”if” part means “only look at this group.” That is, saying “If Socrates is a man…” means to think only about men. Forget women, dogs, angels, helicopters, rocks…. Now look at all those men. The second part of the sentence is “… then Socrates is mortal.” Sure enough, all those men we are looking at are mortal. But if we do it the other way around, and start with “If Socrates is mortal…” then we are thinking just about mortals. Forget angels and rocks, but we still have women and dogs in mind. “… then Socrates is a man.” Nope. What a nice, clear way to distinguish conditional statements from statements of equivalence! This also allows you to introduce the idea of the inverse of the proposition, but we would wait until everyone is very clear on conditional statements.

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