All right, your brain may still be hurting from working on these discussion questions,

but let's review them and talk about how you can help your students work through them.

So, our first question was about a weather probe,

and you'll notice the spelling out of things in English is

over 100 degrees and we choose not to use the greater than signs,

so that students would have to convert.

Then also with the below 10 degrees, below zero.

That's negative 10, right?

So, what's the correct answer here?

There's two, there is C and D. People say "But Dr. Simon: C or D wasn't an option."

Yeah, this is a really great trick to use,

because students like to get queasy.

You'll find the first one is that correct thoughts good,

but then you'll get really engaged discussion

in the classroom and students start to be like,

"What, they're talking about a different one, how is that?"

It's just a fun thing to do to keep people

on their toes and make life a little different.

All right, let's talk about how you'll help

students figure out that these are the correct answers.

We did this previously with

regular conditionals and that is you want to have students draw things out,

even more important for compound conditionals.

So, we've got a number line here that spans more or less the appropriate place,

would be nice if it went over a 100,

but we'll just draw on that.

So, we're going to start off by drawing

our original conditions and then we'll look at our possible answers.

So, we said the temperature needs to be over a 100 degrees.

So, that's the orange box on the right.

So, that represents all of that part over 100 degrees,

and then the box on the left,

that's below 10 degrees below zero or below negative 10 degrees.

So, we've got those there.

So, now what we're basically looking at the difference between

options A and B and option C and D,

is that the first to use AND and the second two use OR.

So, lets figure out AND versus OR. Is it AND?

Well, is it possible to have a value that is both

greater than a 100 and less than negative 10?

No. We've got a box over here, we've got a box over here,

you can't be a number that's in both of those places at the same time.

We can tell that because we drew it out on the number line.

OR says, "Okay, you can either be

in the box on the right or you can be a number in the box on the left,

you don't have to be in both places at the same time."

So, hopefully this drawing is a little

easier for students to visualize and see it's like,

"Oh, you could be in one of the two places."

Now, the last thing we want to get down to is

why are both C and D are the correct answer?

Well, really A and B are exactly the same thing and C and D are exactly the same thing,

all I did was switch the order in which we asked,

is temp greater than 100 or temp less than negative 10?

It's important to know that,

are these Boolean conditions both AND and OR have what we call the mathematical

symmetric property and that the order in

which you check the condition doesn't matter, right?

It doesn't matter if you ask if temp is

greater than 100 and temp is less than negative 10,

or if you ask it in the reverse order,

if temp is less than negative 10 or temp is

greater than 100 and temp is greater than 100.

Onto the next question,

which of these expressions can possibly evaluate to true?

Let's start off just by looking at that question,

this is a spooky question, right?

Can possibly evaluate to true, why would you say that?

Well, this is really just a way to say,

"Is there any numerical value at

all for which these critical expressions could be true? "

So, just note first off,

let's look at the bottom one,

it is correct and that is,

if X is less than seven and X is greater than negative two.

But let's go through, again,

using our drawing approach and evaluate each one and draw it out.

So, let's start with A, this one we're going to use

two different colored boxes so that we can see the differences.

So, X greater than five,

that's going to be the orange box,

and X less than five is going to be the blue box.

Let's draw it on the number line, there we are.

So, this isn't beautifully perfectly

accurate because we're really only dealing with whole numbers here.

But what you see is that the X greater than five,

that's just a little bit to the right of the five on the number line,

and the X is less than five is just a little bit to the left of the five.

So, now we're asking about AND not OR,

is it possible to have a value that is both in the orange box and in the blue box?

No, we don't see any overlap.

So this is the key thing to help students learn about AND.

AND, if we express it on a number line, requires overlap.

There needs to be some value for which it's true for both things.

All right, let's look at the next one.

Draw it on the number line.

X greater than five,

that orange box stays in the same place.

X less than negative seven.

Now, we've just moved that blue box down even further.

So, these are, maybe it's even more obvious here, it's hard to say.

Yeah, there's no overlap here.

AND requires overlap.

There's no way you can possibly have a value that is

both greater than five and less than negative seven at the same time.

All right, so finally we'll get down to how would you draw out our correct solution?

What does overlap look like?

Well, here's a way to make overlap look like on the number line.

So, we have the orange is X less than seven,

and then the blue is the X greater than negative two.

I think it's pretty clear that you can say,

"Hey look, there's some overlap here,

there are some values on our number line for

which both the orange condition and the blue condition can be true at the same time."

So, this is a great way to help students visualize AND. Going along.

Yeah, Boolean expression evaluation definitely exercising the brain here.

This question was about the American grading system,

about earning a C grade.

It used a mathematical nomenclature which probably you will need

to spell out for your students if you likely don't remember.

But a C grade in US is a value in the 70's.

So, we give it the close bracket 70 that means it can be equal

to 70 percent but less than 80 percent.

So, any number in the 70's but not 80.

So, up to 79.999999 whatever.

So, the grade would need to be greater than or equal to 70 and less than 80.

The trick here is,

we need to make our own greater than or equal to sign,

because Snap doesn't have that neither does scratch either by the way.

But that's kind of actually cool in this case because it

has helped us having students do

something that we need to learn to do in computer science a lot,

and that is to break complex things down into smaller pieces.

So, in this case, we're going to break the complex greater than AND or equal to,

greater than, equal to,

into a Boolean expression.

So, on the right hand side of B here,

we've got X greater than 70 or X equal to 70,

and then that whole expression is,

AND X is less than 80.

All right, I think we can go on.