R-54 Transversals

R-54 Transversals





















Things we notice:

-appear the same degree
-could make angles-which are sturdy.
-maybe ,'s a + b arent equal to b + c
-a + b+ c+ d= 360
-looks like a previous strategy when we broke off the corners and made a circle of 360

Supplementary<'s=180
1. a and b
2. c and d
3. a and d
4. c and b

Are a and c equal? Are d and b equal?

-Some think a and c equal each other, but they are not supplemental.

Can you prove a=c and b=d?

Math sentence
a+b=180
c+d=180
a+d=180
c+b=180

How can you use these mathematical sentences to prove that a=c and d=b? 

 Idea:
a+b=c+d

 Idea:
c+d=180
a+d=180
so 
c+d=a+d
c=a 
How does this idea make sense? 

Big Idea: 
These are your supplementary angles
a=c
b=d
we can prove it! 

 R-55

What do you think a,b, and c is? How can you justify it?
180-150=30 degrees
a and c are both equal to 30.
4 angles equals 360 degrees. If you add them all together and subtract them it equals 180
150+30+30=210+150=360

The shape in the middle is a parallelogram.

How is that helpful to us?
I know its a quadrilateral, 2 sets of parallel lines, 2 angles the same and opposite of each other.

60/2=30+30 (there were 2 equal angles left)

How do I now know that m is 30?
l=150
n=150
210+150=360


L-55
What observations can you make about the relationships between angles with a transversal?

-With a transversal through parallel lines, the opposite angles and are always going to be equal.
- All angles in a circle=360
-adjacent (<'s next to each other) <'s=180)
-Exact same number of 150's as there are 30's
-You can make the exterior angles in there to represent 180.

Projects due tomorrow. Justifications are due on Friday.

Quadrilaterals

R-53 What do we know about triangles?

-Exterior + interior
-Angle sum =180 degrees
*at least 3 pieces of info needed for duplicating a triangle
-They can tile and tessellate 
*2 small sides greater>biggest side

Quadrilaterals -How many pieces of information do we think we would need to give? 
-4 pieces of information needed (3 angles, 1 side or 4 sides)
-2 for some where2 sides are the same (if equilateral)
-3 (side, side, angle)
*Class still is not sure how many pieces of info. would be needed

Side Lengths            Did we create a unique quad?                    Sketch
6,10,15,15                yes-unique-only one can be made
3,5,10,20                  no-not unique-multiple quads can be made
8,8,10,10                  Impossible-can't make a quad
12,20,6,9

Make up your own

L-53 Make 5 observations about your chart
-No unique quads
-were repeated #'s in side lengths
-may need < to make unique(conjecture)
-both angles and side lengths are relevant for unique shapes
-these smallest +2 >largest to make quadrilateral (because of extra bend in the shape)
-All could shift around to make lots of quads

Students were given a challenge. They needed to make a quadrilateral. Then, needed to make a structure so that it would be stable and not move because there are no unique triangles.

Chris discovered that if you put a poly strip in the middle it creates two triangles. Triangles are unique.

Creating triangles creates stability.

Many builders create triangles. There are many structures that have triangles throughout.

L-53 2 Big Ideas:
 1st Big Ideas
You can't make a unique quadrilateral because it is flexible.
To make a quad stable, create 2 triangles with a diagonal


2nd Big Idea:
Their side lengths have to be bigger than the biggest one.
Their smallest +2 >largest to make quad

Debate! 3 sides vs. 2 sides

The class had a debate!

They needed to prove whether or not 3 sides works or 2 sides works. 

3 side idea
-If you just had 2 angles, there are so many different ways to make it. 
-multiple angles from 4 cm and 74 degrees

2 sides

-Angle BCA=60 degrees
Side CA =3.6 cm
Side CB=4cm

Draw angle first

L-52 Notes of text Presentations

L-52 Notes of text Presentations

What do you think is the least amount of information you could use in a text?

Class came up with different ideas:

3 pieces of info- side, side, side (Noah) or side, side, angle (Bella) or angle, angle, side (Gabby)
2 pieces of info-side, angle (Mac)

Text triangle

What information would you text to someone in 7A so that they could build this triangle? 

1. angle A is 74 degrees, angle B is 60 degrees, angle C is 46 degrees.

-The length is between A and B is 3 cm and B and C is 4 cm and C and A is 3.6 cm.  Draw this triangle.

2. Angle ACB is 46 degrees, angle CBA is 60 degrees, Angle BAC is 74 degrees and side A-C is 3.6 cm. Side C-B is 4 cm and side B-A is 3 cm. This is a triangle. Draw it.

3. Angle A is on top. B is to the left and lower. C is to the right and lower

4. AB is 3 cm.

5. It's a scalene triangle.

Lars thinks there is a more efficient way to write this.

R-52 Is there a shorter way to write this? Is it possible for me to give a little bit less information and get the exact triangle? What is the shortest possible text I could send?

1. Abby2

AC=3.6 cm

BC=4cm

BA=3cm

2. Abby 1

Angle ACB= 46 degrees

Angle CBA=60 degrees

Angle BAC=74 degrees

2. Abby1/Bella

Top C=74 degrees

Bottom Left=60 degrees

Bottom Right= 46 degrees

3. Ursula and Lauren's' Text

Angle ACB=46 degrees

CBA= 60 degrees

BAC=74 degrees

AC=3.6cm

BC=4 cm

BA=3cm

4. Advik

Angles= 46, 60, 74 degrees

Sides= 3.6cm, 4 cm, 3cm

5. Lars

Side AB=3cm

Side BC=4cm

Angle BCA=46 degrees 

6. Noah

Angle ABC=60 degrees

Angle BCA=46 degrees

BC=4cm 

Make a triangle

Make 5 triangles.

Class Observations:

Yes

*equilateral triangles

*#'s close together

*Larger

No

*Smaller

*#'s farther apart

Aiden's idea: *two smaller #'s if they don't add up to the biggest # or higher they don't make a triangle.

(ex. 4,6, 3   4+3)


There was some disequilibrium in the room.

How do we know for sure its a no? How do we know for sure its a yes?

Word Problems from Class: Reflection and Edit

L-47


Name of the problem (Hindu Dilemma, Minted Coins, Newspaper Ads)
1. Type your response (Shared Google Doc or word doc printed out)
2. Three parts to your response
       a. Answer the prompt or question (Draw visually and show work)
          -attach any paper w/drawings or math as needed
      b. Explain your strategy. What was your thinking? Think about your process of solving the       
      problem. (We want to know the messy stuff. Tell us everything you tried, your thought process)
         -Needs to be thorough
      c. How could you challenge yourself with this problem?
         -Is there another question I could ask? Is there another part of the problem I could solve?








L-46


Edit Problem Paper
1-Read Rubric on your Google Doc
2-Reread your problem
3-Assess your work by highlighting in yellow the correct space in the rubric. Please use yellow.
4-Edit your work.


**Ms. O'Toole is only assessing the edited work.
**Push yourself the problem so that you can make generalizations and look for patterns and regularity.
**This is a finished project. Would be published in a math journal.



Due Thursday 10/23

The Classroom: What does it look like and sound like?

-Direct instruction
      -Quiet
      -Eyes on instructor, board, Elmo
      -follow instructions
      -Giving information like an answer
      -Copy/write notes
      -Check work
      -Listen to understand
      -Ask questions

-private think/ write time

       -giving ppl space, quiet, focused on the problem, write alone and not with partner, develop individual ideas. If I have a question I can write it down (instead of raise my hand)

-partner work

-plenary-whole class discussion 

        -listen to your peers, share your ideas, don't interrupt, ask questions. Raise hands: so we take turns and are repsectful. 

        -should be quiet, except for one voice. 

        -we need to stay relevant to the math 

        -collaborating 

        -teacher: selects speakers to record ideas. Connect speakers to connect ideas. 

        -students ideas only 

        -teachers push on your thinking 

-homework
      -Complete: Best of your ability (Ask family for help, use your notebook, online notebook, phone a friend, ask Mrs. O'Toole or in class, take a break and come back later)
      -If none of the above work: Show your evidence of an attempt or ask questions in notebook
      -Finish your HW on time
      -Quiet work space
      -FADAF (Frustration and difficulty as feedback) Write about the feedback in your notebook.
      -Answer all the questions and explain
      -Email Mrs. O'Toole
      -Lots of Room

 -Small group work

         -not commenting about partners

         -equity among partners (equal or fair amount of time to share/speak) 

         -need to make decisions together, equal share work
         -Volume should be in the middle: people can hear you, but you aren't yelling 
         -If no one is in your group, you can do pieces of the group work
         -Include everyone by asking for their opinion and making the work equitable.

-Debate


        -Listen to each other
        -Prove/explain your idea and how it is correct
        -Share with equity--choose from multiple ideas
        -Write questions down
        -Debating ideas, NOT people
        -Prove why other idea doesn't work--explain with steps


       
   

Exterior and Interior Angles

Exterior Angles: are measured by extending a side of a convex polygon and measuring the angles that lie outside the line.


























R-49 Draw 4 different polygons. Measure the exterior angle and compute the sum.