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Computer Science in Math

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Booleans

Getting your program to ask the right questions

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Vocab

Boolean - a type of data with two values: true and false
Return - used as a synonym for output of a function.

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Types of Data

What types of data have we used in our programs?

What are some examples of Number values?

25, ⅓, -42, 90.3

What are some examples of String values?

“Hello”, “25”, “outline”, “purple”

What are some examples of Image values?

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What type of data do these return?

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A New Data Type!

(3 < 4) states “3 is less than 4”
The block returns true
What if we swapped the arguments?
“4 is less than 3” would return false
true and false are called boolean values
What other math functions might return booleans?
< (less than), > (greater than), = (equal to)

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20 Questions!

On a 3x5 card, answer the following questions

What is your hair color?
Do you wear glasses/contacts?
What is your favorite number?
What is your favorite color?
What month were you born?
How many siblings do you have?
What is the last digit of your phone number?
What is something that your classmates don’t know about you and could tell just by looking at you?

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20 Questions!

Everyone stand up
I’m going to read the answer to #8 but if it is you, don’t say anything.
Using only questions that return a boolean (yes/no) value, we’re going to try and figure out whose card was picked
If your answer to a question is false, sit down

Select a card
Say: I’m going to read the answer to #8 but if it is you, don’t say anything.
Say: Now everyone stand up and we are going to ask some questions with Boolean answers to help determine who this person is.
Begin the following true/false questions. Preface each one with “If you answer false to the following question, please sit down.” The person whose card you are reading should always answer true so you will need to change the example questions below. For this example, the answers were brown, yes, 13, blue, December, Yes, and 9

My hair color is brown.
I wear contacts or glasses. (you only have to answer true to One of these to remain standing)
My favorite number is greater than 10 and less than 20. (you have answer true to both these.)
My favorite color is blue or green.
I was born in a month containing an m.
I have at least one sibling.
The last digit of my phone number is a prime number.

Because of how numbers 3,4, 5, and 7 were asked it is likely that some people will still be standing. You will need to revisit these and ask them again in a more narrow fashion such as “My favorite color is blue”.

Play this several times. Be creative with using or’s and and’s. Remind students that the OR means that either part of the statement being true will result in the entire statement being true. (See next two slides for more information about and/or’s and future rounds of this game.)

In English, an “or” is often an “exclusive or” such as “You can have chicken or fish.” In English, you only get to pick one, but with Boolean logic you could have chicken, fish, or both!! For the example person above, “I was born in December OR my favorite number is 13” is true. Note that “I was born in December AND my favorite number is 13” is also true.

Having a student try to act as the quizmaster after several rounds. If a mistake is made by you, a student quizmaster, or the person whose card you are reading, see if you can analyze where the mistake was made or why the question being asked might not have been clear.

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Combining Boolean Questions

You can combine or modify boolean functions using and, or, and not
And returns true if both of its parameters are true

(10 > 6) and ( 6 > 2) - True!

Or returns true if either of its parameters are true

(10 > 6) or ( 2 > 6) - True!

Not returns true if its parameter is false

not (6 > 10) - True!

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20 (more) Questions!

Now play the boolean 20 questions game again, but this time use and, or, and not in your questions!