8th Grade MathSeptember 28 – October 2

(Mon/Tues) What are we doing today?

• Unit 1 Lesson 5 – Coordinate Moves

• Trying to take over the world.

• Assignment #1 & #2 will close on Tuesday at 3pm.

• On Friday, expect a short quiz.

Learning Targets

• I can apply transformations to points on a grid if I know their coordinates.

Coordinates (Review)

• When working in a coordinate plane, we will be always be given coordinate pairs in (x, y) form.

• The first number is the x-coordinate. It lets us know how far to travel left or right on the x-axis.

• The second number is the y-coordinate. It lets us know how far to travel up or down on the y-axis.

• In the example, our point is (6, 4). So we go right 6 and up 4 to find the point.

Translation Using Coordinates

• In the triangle on the right, Point Q is located at (–3, 1).

• If we translate this triangle by moving it right 3 units and down 1 unit, where would Point Q’ be located?

• How would this translation affect Point P and Point R?

Translation Using Coordinates

• Point Q was at (–3, 1). After moving right 3 and down 1, Point Q’ is at (0, 0).

• Point P was at (–5, –1). After moving right 3 and down 1, Point P’ is at (–2, –2).

• Point R was at (–1, –4). After moving right 3 and down 1, Point R’ is at (2, –5).

• Do you see how, in general, translation affects the coordinates?

Translation General Rule

• If we are translating a point (x, y) by moving it left/right by a units or moving it up/down by b units, we can follow the rules shown on the right.

Note: Moving left or right always involves the x-coordinate as that is the direction of the x-axis. Moving up or down always involves the y-coordinate as that is the direction of the y-axis.

Reflection (X-Axis) Using Coordinates

• In the triangle on the right, Point K is located at (1, –3).

• If we reflect this triangle across the x-axis, where would Point Q’ be located?

• How would this reflection affect Point L and Point J?

Reflection (X-Axis) Using Coordinates

• Point K was at (1, –3). After reflection across the x-axis, Point K’ is at (1, 3).

• Point J was at (4, –3). After reflection across the x-axis, Point J’ is at (4, 3).

• Point L was at (0, –5). After reflection across the x-axis, Point L’ is at (0, 5).

• Do you see how, in general, reflection across the x-axis affects the coordinates?

Reflection (X-Axis) General Rule

• If we are reflecting a point (x, y) across the x-axis, we can follow the rule on the right.

Note: Reflection across the x-axis affects the y-coordinate only. This is because it flips the point up or down (which is the direction of y).

Reflection (Y-Axis) Using Coordinates

• In the triangle on the right, Point T is located at (–3, –1).

• If we reflect this triangle across the y-axis, where would Point T’ be located?

• How would this reflection affect Point V and Point U?

Reflection (Y-Axis) Using Coordinates

• Point T was at (–3, –1). After reflection across the x-axis, Point T’ is at (3, –1).

• Point V was at (0, 1). After reflection across the x-axis, Point V’ is at (0, 1).

• Point U was at (–4, 4). After reflection across the x-axis, Point U’ is at (4, 4).

• Do you see how, in general, reflection across the y-axis affects the coordinates?

Reflection (Y-Axis) General Rule

• If we are reflecting a point (x, y) across the y-axis, we can follow the rule on the right.

Note: Reflection across the y-axis affects the x-coordinate only. This is because it flips the point left or right (which is the direction of x). The point with 0 as the x-coordinate did not change as the negative of 0 is still 0.

Classwork

• https://forms.office.com/Pages/ResponsePage.aspx?id=fSGa33NnF021d4XclgeCIslaDQMWMuNBpzeNhT_XGjpUNVI1Vlk0TlRHNkxOSU4zTkQwRTBBUUxGRS4u

(Wed/Thurs) What are we doing today?

• Unit 1 Lesson 5 – Coordinate Moves (FINISH) & Learn to be Guinea Pigs ☺

• Trying to take over the world.

• Assignment #3 will close early next week.

• On Friday, expect a short quiz.

Classwork (9/29) Discussion

• Some things I noticed involved formatting errors. For example, when writing a coordinate pair you need to have parentheses. A point would be written (5, 3) and not just 5, 3 or 5 3.

• When one of the coordinates is 0, you need to include it. For example, (7, 0) is a point on the x-axis. It is different from (0, 7) which is on the y-axis. If you just put “7” that does not refer to a point at all.

Rotation (Origin) Using Coordinate

• Rotation, using the origin (0, 0) as the center, affects both the x- and y-coordinates.

• Notice in the examples here how the coordinates are change are reversed if the rotation is 90º or 270º.

• If the rotation is 180º then the coordinates stay the same values but both change signs.

• Note: While I do want you to see how this works, assessment questions from this lesson will focus on translations and reflections as this will be covered in more detail in geometry.

Rotation (Origin) General Rules

Time to be a Guinea Pig

• If you are logged into Clever, you should see an application called “Carnegie Learning – MATHia”. If it does not appear immediately, it can be found in the applications that I have shared or by searching for it.

Time to be a Guinea Pig

• When you connect to MATHia, you will either see a module called “Pre-Launch Protocol” or “Grade 8 Illustrative Unit 0” depending on if you have connected to MATHiabefore.

• If you select the module, you can begin working on it. The program does offer hints if you get stuck on a problem though I suggest that you should always try 2 things before asking for a hint.

MATHia

• How are we going to use MATHia?

I am going to expect everyone to spend at least 60 minutes per week working on MATHia. Since we do not have class sessions on Monday or Wednesday, you could spend 30 minutes each day fulfilling this requirement or could spent 20 minutes per day 3 times per week during any of your independent learning times after lunch. MATHia can help you practice what we do in class or get ahead.

• Will MATHia be graded?

Yes, it will be part of a classwork/participation grade. To get full credit for a week, you will be required to do one of two things. First, you can put in the 60 required minutes for the week. Alternatively, if you work ahead and are currently in a module ahead of where we are in class then I will give you credit. For example, we are currently in Unit 1. If you worked ahead and got to Unit 2, then I would not be concerned with the time that you spent on MATHia as you are ahead of where we are in class. This grade will start being recorded next week (and not this week).

MATHia

• Could I just login, take a nap, and then logout after 60 minutes?

No, it does not record time in that way. If you are not actively working, the timer stops counting your time after about a minute or so. Thus, if you are in another window or otherwise not actually working then your time will not increase.

• Will we have time to do MATHia during class?

Generally, no. However, I may ask that you work on MATHia if I have a substitute and am unable to be in class. In that instance, I will expect additional time for that week. If you finish your work, you could connect to MATHia as well. If we have finished the material for a week and do not have a quiz, I may occasionally give you time on Fridays to work in MATHia.

(Fri) What are we doing today? QUIZ!!

• The link to the quiz will be posted in the chat and e-mailed to you. Make sure when you open it that it reads “Quiz #1 – Transformations (8th)”.

• During the quiz, I expect silence sothat others can work in peace. If youintentionally disrupt class, I will giveyou a 0.

• If you have questions during the quiz, you may post them in the chat or e-mail me. I will not answer any question that asks how to do a problem as that is the point of a quiz.

• If you do not do well on the quiz, I will give you opportunities in the future to redo it. However, if you are found to be cheating on any assessment in my class then you will receive a 0 with no opportunity to make it up.

• If you finish and turn it in, I will askyou to stay in the “room” at least untilI have taken attendance.

• Quizzes take me time to grade. Donot expect this to be in PowerSchool quickly.

• The quiz will close today at 4:00pmand no longer be available to complete.