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Volusia County Schools: Calibration Event - 2026-2027 — Transcript

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0:05[music]
0:10>> Okay everyone, what I need you to do
0:11today is take out your Chromebooks.
0:14There's directions on the board up here.
0:15You're going to go to a website called
0:18student.desmos.com.
0:21If you use Desmos before, you may have
0:23used this website as well.
0:25It's going to ask you for a class code.
0:29This is your class code. Make sure it's
0:31all capitals.
0:33No lower case.
0:34And then it's also going to instruct you
0:37to sign in with Google. So make sure
0:39that your UDSD Gmail is up there and you
0:42can sign in that way.
0:44And once you do that, your screen should
0:45look like this.
0:50Yeah, Connor. Uh I left my Chromebook in
0:52gym class. Okay,
0:54here. Write a pass and you can go grab
0:55it. All right.
1:00If you're in, your screen should look
1:01like this. You all good?
1:03Yeah, almost. Not if you're in.
1:08>> [snorts]
1:09>> If we're looking at this picture, what
1:10do we look What do we think this picture
1:12is of? A street. A street. It's a map of
1:15streets, right? Does anyone know what
1:17this map is of? This is Philly. It is.
1:19So this is Center City, Philadelphia. So
1:22if you look there, City Hall Station,
1:24you have um
1:26Jefferson Hospital down here, the Union
1:28League, and Elvez, which is one of the
1:30best restaurants ever.
1:31So if you could get a chance to check
1:33that out, you should. Now, what we're
1:34going to do today is look at parallel
1:36and perpendicular lines.
1:38With your hands, show me what parallel
1:40lines look like.
1:43What about perpendicular?
1:46What's important about perpendicular
1:47lines? So some people are going like
1:48this, some people are like this, some
1:50people are like this. What do we know
1:52about perpendicular lines, Rafe? They
1:54make right angles. They make right
1:55angles. So that's something that's super
1:57important to remember when you're
1:59talking about perpendicular lines are
2:00supposed to be intersecting but at a
2:02right angle, not just at any angle.
2:05So, if we look at this picture, do we
2:07see pairs of parallel lines, pairs of
2:10perpendicular lines?
2:13Yes. Do we have any examples of those?
2:16Rafe, again? Uh towards the top, Arch
2:18Street and Race Street. So, if you look,
2:20Arch Street and Race Street, are they
2:22parallel or perpendicular? Parallel.
2:25Parallel. What do we know about parallel
2:27lines?
2:28They never intersect.
2:29>> They never intersect. Do we see a pair
2:31of perpendicular lines?
2:33Back. Um South 12th Street and Clover
2:36Street. So, we have South 12th right
2:39here and Clover Street. So, if we look,
2:41Clover intersects 12th Street at a
2:44perpendicular
2:45angle, which is an angle of how many
2:47degrees? 90.
2:48>> 90 degrees.
2:49Emma. Uh another one is at South 12th
2:52Street and Chestnut Street.
2:54Awesome. So, if we look at 12th again,
2:56we follow that down, we see an
2:57intersection at Walnut, also a
3:00perpendicular intersection.
3:03It's good so far on perpendicular and
3:05parallel? Okay, so we're going to go to
3:06the next slide.
3:09And your slide should look something
3:11like this.
3:13So, we want to drag these points to
3:16create parallel lines. So, our red line
3:19we're going to drag in order to make it
3:22parallel to the black line.
3:34And if you guys are finished, uh can I
3:35have a volunteer?
3:36>> I already did one
3:38right there.
3:40Thank you.
3:41Volunteer to come up on the board and
3:43drag the points. I will. Sammy.
3:52I'm going
3:54>> Oh, make sure you have that point
3:56highlighted. Yeah, there you go.
4:02So, what could Sammy do in order to make
4:04these lines parallel?
4:06Drag the point. He So, he's dragging the
4:08the top point, right?
4:10So, you can get Yeah, there you go.
4:12Perfect.
4:14So, we know parallel lines never
4:15intersect, right? All right, next slide
4:18we're going to go to.
4:21So, we have a true or false here.
4:23So, Lisa is a student in an algebra
4:26class and she made the following
4:27statement regarding parallel lines. Can
4:29someone read um Lisa's statement?
4:32Volunteer. Rafe. Uh two lines which are
4:34parallel must both have positive slopes.
4:38Okay, so what I want you to do right now
4:40is think about this to yourself about
4:43what slope means.
4:45And think about what positive slope
4:48means.
4:49And then enter a um submission into the
4:53box that explains what you think about
4:56Lisa's statement.
4:58And once you're finished that, I want
5:00you to discuss with a partner.
5:02So, either someone in front of you or
5:04next to you.
5:23Okay, so
5:25Can we still see our answer once we
5:26submit it?
5:27Should you be able to? Yeah, should I
5:29discuss it with someone?
5:30Yes.
5:32So, your some other of your um peers'
5:35answers should be popping up underneath
5:36of yours. So, once you submit in here,
5:39it should say these answers up here.
5:46So, I'm actually going to call on before
5:48you guys get into this this discussion.
5:51So, Dominic wrote as his submission that
5:54it is true because if they had a
5:55negative slope they were would
5:57intersect. So, what do you think about
5:59that? Negative slope, does that mean
6:01it's
6:02going up from left to right, down to
6:04left to right? What do you think? Down
6:06to left from what down from left to
6:07right.
6:08>> Down from left to right. And what about
6:09a positive slope? Up from left to right.
6:11>> Up from left to right. So, we're going
6:13up and down
6:15those lines are going to intersect,
6:16right?
6:18Does anyone want to add anything to
6:19that?
6:21Emma? Parallel lines can have the same
6:24slope but just different Y intercepts.
6:27Okay, so parallel lines can have the
6:28same slope but different Y intercept.
6:30What's a Y intercept?
6:32Reese? Uh where it crosses the Y axis.
6:35Where it crosses the Y axis, good job.
6:37So, can we have negative slopes at all
6:40for parallel lines?
6:42When can that happen?
6:46When they both have the same
6:49slope.
6:50So, they both have to have the same
6:51slope. So, if one of them's negative,
6:52what does the other one have to be?
6:54Negative. Negative as well. So, we can
6:55either have both positive or both
6:57negative but never one or the other. So,
7:00we can't have a positive and a negative
7:02or a negative and a positive.
7:03Okay?
7:05Now, we're going on to the next one.
7:08So, on this screen what I want you to do
7:10is drag these lines. So, you have the
7:12two points again. You're going to drag
7:14the two points to make two parallel
7:16lines.
7:18And as you're doing this I want you to
7:19watch these values over here. So, we
7:21have M of the purple line, Y of the
7:24purple line, M of the red line, Y of the
7:26red line. What does M stand for? Slope.
7:30Slope, right?
7:31And what does Y stand for?
7:34The Y intercept, okay? So, as you're
7:36dragging these lines try to um
7:39see the relationships between the M's
7:42and the Y's of each different line.
7:47And then I'm going to need another
7:48volunteer to come up here.
7:55Do you want to volunteer?
7:59You want to?
8:05Good job.
8:09Okay, are you ready for a
8:09[clears throat] volunteer?
8:12Emma, you want to go up on the board and
8:13show your parallel lines?
8:16Good job. Good job.
8:20I'll pass the pen.
8:23Yes.
8:39Now look.
8:40Okay, perfect. Thank you. Now if we look
8:43at the M and the Y values, what do we
8:45notice?
8:50Easily? The M values are the same.
8:53The M values are the same. So if we look
8:55at M of the purple line, we have that
8:58it's equal to 0.5. M of the red line is
9:01equal to 0.5 as well. What about the
9:03Y's?
9:06They're different. Mhm.
9:08Okay, so let's go to the next slide.
9:14Don't look. Don't look.
9:15Okay. So what we want to do for this
9:17line is submit a an answer to the
9:19question of what you observe about the
9:22slopes and the Y intercepts.
9:26Once you do that submission, take a
9:28second to talk to a partner
9:30or
9:32a group of people.
10:00>> You don't have to whisper. Okay.
10:03>> [laughter]
10:04>> Talk, talk, talk. It's Friday.
10:31Are they the same sign?
10:33Is it the same sign?
10:37So, you're going to follow those
10:38directions, okay?
10:42So, what did we come up with from
10:43talking with our partners?
10:47Emma. The slopes are the same, but the Y
10:49intercepts are different. So, we have
10:51the slopes are the same, but the Y
10:53intercepts are different. Does anyone
10:54agree? Does anyone disagree?
10:56Gabe gives a thumbs up. I hear some I
10:59agrees. Do they have to have the same
11:02sign? Yeah. What happens if they are
11:04different signs?
11:07Then they will be perpendicular.
11:10Hmm, let's keep that in the back of our
11:11heads for a second.
11:13Okay?
11:15So, let's go to
11:17a little secret. So, the secret behind
11:20parallel lines is that the slopes are
11:21going to be identical. They're going to
11:22be exactly the same. Exactly the same
11:24number, exactly the same line.
11:27Questions about that?
11:30Now, what about the Y intercepts? Do
11:31they have to be the same as well?
11:33What happens if they are the same?
11:36They're the same
11:37line. Say that louder. They're the same
11:39line.
11:40>> Did everyone hear what Max said? Yeah.
11:42So, if we have the same Y intercept and
11:44the same slope, say something like
11:48Y = 2X + 3,
11:51we know the slope is what here?
11:53Two. Two. And our Y intercept is? Three.
11:57So, if I have another line with the same
11:59slope and the same Y intercept, it's
12:02going to be the same exact line.
12:04Okay?
12:06So, we're going to move on to
12:07perpendicular now. Sort of the same kind
12:10of flow of things. So, we're going to be
12:12given this these two lines. We want to
12:15create a line that is perpendicular to
12:17the black line.
12:19So, you're going to drag those points
12:20again.
12:24>> [snorts]
12:31>> Do I have a volunteer to come up on the
12:32board and show their perpendicular line?
12:43Emma, you want to?
12:44Sure. Thank you.
12:46So, Emma's going to drag points and show
12:48her line.
12:50If you look at the screen on the left
12:52side, there is an equation there. So,
12:55that is the equation of the black line.
13:00Here you go.
13:04Okay. Is that it? Yeah, that's good.
13:06So, what do we notice about Emma's
13:08perpendicular lines?
13:13Say that again. 90°. So, Nia just said
13:16that Emma's lines intersected at a 90°
13:18angle.
13:20Do we have anything to add to that?
13:23Are we all okay? What if I moved this
13:25dot
13:27like that. Are those perpendicular? No.
13:30Why not? Because it's an acute angle.
13:32Because it's an acute angle. I like
13:34that. So, we have these two angles here
13:36that are smaller than 90°. They're acute
13:39angles. They are not right angles, which
13:42shows us that they're just intersecting
13:43lines, not perpendicular.
13:46Okay, so next we have
13:50another um scenario kind of thing. So,
13:52we have this kid named Brandon in our
13:54class, and he made a statement about
13:56perpendicular lines saying, "In order
13:58for two lines to be perpendicular, one
14:01must have a positive slope and one must
14:03have a negative slope."
14:05What do we think? So, make your
14:06responses, and then we're going to have
14:08a little conversation about it.
14:11Okay.
14:58So, what do we think? Anyone want to
14:59share their response?
15:02Mac?
15:02Um I said false because if
15:05like if you have two lines that are like
15:08this, Mhm.
15:09neither of them have like a slope as a
15:12positive
15:13so, it doesn't have to be So, Mac is
15:15talking about the scenario if we had
15:19a vertical line.
15:22So, if we have a vertical going this way
15:24and a horizontal going this way. And if
15:26they created a a right angle like that.
15:29So, what kind of slopes do we have for
15:33vertical and horizontal lines?
15:35Do you remember those?
15:38Positive One of them is no slope. One of
15:40them is no slope and one of them is has
15:42an undefined slope. So, this is going to
15:44be the exception to the rule here. So,
15:47this is the only only time ever that we
15:50will have a scenario where there's
15:53either no slope or a zero slope. But,
15:55they have to be uh I'm sorry, an
15:57undefined slope or no slope.
15:59So, this is the case when that would be
16:01different. Now, Connor, I saw that you
16:04were writing that you don't need to have
16:06So, Connor's response says false. You
16:09don't need to have a positive slope, but
16:10you can have one as long as it makes
16:12four right angles and it is
16:14perpendicular.
16:16So, you don't need to have a positive
16:17slope.
16:18Why do you think that?
16:21Uh
16:22I just don't think you need one. Like
16:24that you can have one. Okay, so you
16:26don't think it's necessary to have a
16:28positive. Okay, so if we have Let's say
16:31if we don't have a positive, we'll have
16:33two negative slopes, right?
16:36So, if I draw a little sketch here,
16:38we'll have two
16:41negative slopes.
16:43Something like that. Do you think if we
16:45keep rotating those lines that they'll
16:47ever intersect at a 90° angle?
16:51This is actually So, I If we rotated the
16:55lines, kept rotating the lines, and
16:56changing the slopes, they'll never
16:57intersect at a 90° angle. It's either
16:59going to be an acute angle or an obtuse
17:02angle. Yeah, man. Unless one of them
17:04becomes positive. Exactly. So, unless
17:07one of them is positive. So, in this
17:09case, we would have a negative slope
17:12and a positive slope. That gives us that
17:15T. So, we have our 90° angles or
17:18perpendicular lines. So, we actually do
17:21need to have a positive and a negative.
17:24How is this different from the parallel
17:25lines?
17:27You can only have a positive and a
17:28positive or a negative and a negative.
17:30Awesome. Okay, so now we are going to do
17:34this example here.
17:37So, instead of just having two lines, we
17:39have one purple line and we have a bunch
17:42of these orange lines.
17:43So, we're going to drag the orange lines
17:46in order to see We're going to drag
17:48right here
17:49this little
17:51slidy thing
17:52to see how you can make these
17:55orange lines perpendicular to the
17:57purple.
18:11Okay.
18:14I have a volunteer
18:17to do the slidy?
18:33Awesome. Thanks, Mac. You're welcome.
18:34So, you chose to have M equal to -2. Why
18:38did you choose that number?
18:40Um because it's the
18:42reciprocal.
18:44What kind of reciprocal? Opposite
18:45reciprocal.
18:46>> Opposite reciprocal. So, if we look,
18:47what's our slope of the purple line?
18:491/2. 1/2. What do we know is the
18:52opposite reciprocal to 1/2? -2. -2. So,
18:55we just went backwards from the same
18:58exact slope that we used before.
19:00Now, if we look at these orange lines,
19:03how are they different from each other?
19:06>> [snorts]
19:07>> Right? They have different Y intercepts.
19:08They have different Y intercepts.
19:10Awesome. So, if we look, they all have
19:12the same exact slope because these
19:13orange lines are what kind of lines?
19:16Parallel lines. They all have the same
19:18exact slope.
19:19But, they all have different Y
19:22intercepts.
19:23Are they all still perpendicular to this
19:25purple line?
19:27Why?
19:29Because they're on the same slope.
19:31Because they all have the same slope,
19:34which is what kind of slope in
19:36relationship to the purple line?
19:38They're all perpendicular.
19:40The opposite reciprocal. Awesome. So,
19:42the only thing that matters here is your
19:44slope. Your Y intercept can be anything
19:47at all, as long as you have that
19:49opposite reciprocal slope, you will be
19:52able to have a perpendicular line.
19:55Questions on that?
19:58Okay, so now we are going to move on to
20:01the next slide.
20:02Next slide. Where it's the same thing we
20:05did for parallel lines, we're going to
20:07write two equations that give us two
20:10perpendicular lines.
20:16Now, what what kind of equation are we
20:18writing here?
20:20What's that form called?
20:22Slope intercept. Good job.
20:34Can I have a volunteer in a second?
20:43Anyone that I haven't heard from today?
20:47Want to go up and type their lines in?
20:54Let me see what you got.
20:58Can you change the slope?
21:01Yeah. So, these are right, but that's
21:03the same slope we've been working with.
21:05Oh, okay.
21:06>> So, let's do a try a new one.
21:09Perfect. Okay. Okay. So, Dominic is
21:12going to come up and type in his two
21:15equations
21:20for perpendicular lines.
21:46Dominic, got to be careful.
21:49See if Yeah, there you go.
21:52Good job. Thank you.
21:56What do we think? We agree, disagree?
22:00Did anyone have the same slopes as Dom
22:02did?
22:04Nia, you have 5 and -1 bit.
22:07Very cool. Does anyone else want to give
22:08an example of their slopes that they
22:10used?
22:11Reese. I did 2 2x and -1/2x.
22:15Perfect. Now, Reese said 2x and -1/2x.
22:21Are those the slopes?
22:22No.
22:23That's the piece of the equation. So,
22:25that our equation is y = mx + b, the
22:29slope is that m. So, just the number
22:32value. The x does come next to it, but
22:34that's just the form of the equation.
22:36Okay?
22:37So, what I want you to do now is take 2
22:40to 3 minutes and work with a partner and
22:42come up with your own slope equations.
22:46And we're going to enter
22:49them into the next
22:52um slide. So, this asks for a pair of
22:56numbers, so let's just enter an actual
22:58equation instead of a pair of numbers.
23:00So, we're going to enter
23:02two equations per group, Um two sets of
23:05equations per group that show parallel
23:07perpendicular lines.
23:12You can push your desks together, too,
23:13if you like.
23:20You want me to get it?
23:51So each person is doing their own work.
23:56No,
24:05Teamwork makes the dream work.
24:11So you have five and one fifth. So we
24:13have the reciprocal part. What part are
24:15you missing?
24:17Here you go. They're good.
24:18The negative part. Remember it's
24:20opposite reciprocal.
24:22One of them
24:23is positive and one of them has to be
24:25negative.
24:29Yeah.
24:33There you go. Good job.
24:38Yeah, that's fine.
24:40Perfect.
24:45Okay, so I'm going to ask for
24:49three groups
24:51to volunteer. Emma, Naya, Aisling, and
24:54Mac.
24:56Any one more group.
25:01Dom and Ray.
25:02Thanks for volunteering, guys.
25:05So, you are going to pick let's do
25:08one there and two up here of your
25:12examples for your perpendicular lines.
25:24You just put this right.
25:28If you want to push your desk back, you
25:29can.
25:47Uh yeah, you can write both.
25:51Yes. Do we write like mine is really
25:53small? Yes. Please.
25:57So, you're going to write both sets per
26:00pair.
26:05What numbers did you guys pick?
26:11Very good.
26:13Good job.
26:23Board, awesome.
26:27Perfect.
26:28Good job, guys.
26:31Thanks, guys.
26:36Ooh, we got some decimals up here.
26:39I like.
26:43Thank you. You're welcome.
26:47All right, so we are going to go to each
26:49of these
26:50partner share outs and discuss what's
26:53going on.
26:54So, Aisling and Mack were first.
26:57We have two different sets of
27:00two parallel or perpendicular lines. So,
27:03let's talk about the first one. What's
27:04our slope in the first line of the first
27:07set?
27:091/8 x 1/8. Just 1/8, remember? No x.
27:12Sorry. No, that's okay. So, what do we
27:15think the slope is in the next one?
27:17-8 -8. Are they opposite reciprocals?
27:20Yes. Good job. Now, I like this decimal
27:23here getting a little funky with the
27:24y-intercept.
27:26And then here in our second set, we have
27:28the same slopes, but what's different?
27:33The y-intercept The y-intercept. Now,
27:35Rafe, what did you ask about for the
27:37y-intercept? Do you remember? I said
27:38does it really ever matter what the
27:40y-intercepts are? So, Rafe asked does it
27:42really ever matter what the y-intercepts
27:44are? What do we think? No. So, your
27:46y-intercept can be anything that you
27:48want it to be as long as the slopes are
27:50opposite reciprocals.
27:53Emma and Nya, you want to explain?
27:56Um
27:57-9 and 1/9 are the slopes
28:01for the set one and then -4 and 1/4 are
28:04the slopes for set two. Perfect. And
28:07then last but not least, we have Dom and
28:10Rafe. Our opposite reciprocals for the
28:13first set are 5 and -1/5.
28:16And then for set two it's 3 and -1/3.
28:19Perfect. So, we all chose our first
28:22slope to be a whole number, correct? So,
28:26we have 8, 8, 9, 4, 5, and 3. What if I
28:30had an equation say
28:32y = 2/3 x + 1?
28:38How's that different?
28:43Yeah, Max? It would be a whole number
28:45the opposite reciprocal. Perfect. So,
28:47Mac just said the opposite reciprocal is
28:49not going to be a whole number. How did
28:51you know that? Because
28:533/2
28:55isn't a whole number, and that's not the
28:57solution.
28:58So,
28:59instead of having 2/3 in our next line,
29:02we're going to flip this to get that
29:04reciprocal, which is 3
29:07over 2. What else do we need there?
29:10Thanks. The negative
29:11>> The negative sign. Awesome.
29:13So, we have -3/2
29:15x + Does it have to be one here?
29:19Nope, I can pick anything, right? So,
29:20we'll say +4. So, we can also have these
29:23opposite reciprocal slopes without whole
29:26numbers. As long as it is the fraction
29:29flipped around with a different sign,
29:31we're good to go.
29:33Okay? Do you have any other questions?
29:36All right. So, I think we are good with
29:39parallel and perpendicular lines.
29:42No more questions?
29:44Okay. So, how can we think about this?
29:47We talked about reciprocals, right?
29:49So, what were we learning before we got
29:50into parallel and perpendicular lines?
29:52Do you remember?
29:53Radicals Not radicals.
29:56Sounds like it. Rational Rational
29:58expressions. So, we know that rational
29:59expressions are Give me an example of a
30:02rational expression. The y
30:05+ 2
30:07over
30:104y
30:124y, perfect. So, we can also think about
30:15reciprocals in terms of rational
30:17expressions. So, this word reciprocal is
30:19going to come up a lot. It's always just
30:21the flipped fraction.
30:23Okay?
30:24All good?
30:25Well, thank you. Thank you very much.

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