Transversal 2

R-57 Transversals

Find all the angles and label them. You need to justify how you came up with every single angle.
Should have 15 math sentences to go with your idea.

One idea:
The middle shape is a parallelogram.
h=150
o=g

L-57 Transversal Definition

*A line that intersects two other lines

a,b,c
a=30
b=150
c=30

d,e,f
d=150
e=30
f=150

h,i,j
h=150
i=30
j=150

l,m,n
l=150
m=30
n=150

Justify
150+150=300
360-300=60/2=30

360 is the sum of all angles measured for a quadrilateral.

Justify
150+a=180
150+c=180
150+30+30+6=360

R-56 Transversals

R-56 Transversals

What do we notice?



















*Supplementary <'s-2 ,<'s add to 180

1. b and c make up line 1
2. a and d make up other sides of line 1
3. a and b make up line 2
4. d and c male up line 2

-all ,'s together=360 degrees
-Does A=C??
-Does B=D??
The class thinks they look the same. Someone thinks because the lines intercept
-If I moved one of the lines, they would still be the same.
-Line 1 is splitting like a circle in half, 180+180=360
-They look like interior <'s
-They make 4 different triangles or 2 different triangles. 

Class is wondering: Why does a=c and b=d? How can we prove/justify?

Line 1=180
Line 2=180

If b+c=180 and a +d=180
a+b=180 and c+d=180

a+b=180
a+d=180 so b=d

a+d=180
80+100=180

c+d=180
80+100=180

Quadrilaterals

Triangles Recap

-Sum of all angles= 180
-3 vertices
-3 sides
-regular angle =60 degees
-2 short sides have to be bigger than the longest side
-exterior sum of the angle is 360 degrees


Exploring Quadrilaterals



Side Lengths             Does it make a unique Quad.                  Sketch
1. 6, 10, 15, 15
2. 3,5,10,20
3. 8,8,10,10
4. 12,20,6,9

*Can't make a unique quad. because too flexible. 
*We decided to add a piece in the middle for stability (diagonal) 
*Creates triangles which are more stable shapes

Where do we see triangles in our everyday lives?
-Construction (saw: 2 ends are triangles, stable enough to hold pieces of wood)
-Buildings, roofs
-Tips of a saw, ridges

2 Big ideas about Quadrilaterals:

1) Can't make a unique quad. because too flexible. We decided to add a piece in the middle for stability (diagonal). It creates triangles which are more stable shapes

2)  3 smaller sides need to be greater then the biggest side

Text triangle posters

The class is determining how many pieces of information to give to the other 7th grade class. They tested the text messages by trying them out on their own.


L-55 Notes of text Presentations

Some ideas:
Amount of info given
4 pieces=3 sides, 1 angle
3 pieces=2 angles, 1 side or 3 sides or 2 sides, 1 angle
2 pieces= 1angle, 1 side

 Students are trying to prove how 2 angles and one side can work.

If the angles are different it will go up by a different amount

Math Problem Assignment

 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?


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 so that you can make generalizations and look for patterns and regularity.
**This is a finished project. Would be published in a math journal.

Triangles

We are going to make several polygons and record data.


In a table:


Make 5 triangles.


1. Side lengths (Between 2 and 20)
2. If a triangle could be created

3. Space to sketch the triangle

L-52

Rules for Knowing if 3 Side Lengths Will make a Triangle

**Two short sides added together must be longer than the longest side

Text Messages to send to 7A

-3 corners A, B, and C. A is at the top

-B is at the bottom left, C is at the bottom right.

-A's measure is 74 degrees

-B's angle measure is 60 degrees and C's angle measure us 46 degrees.

-Side AB is 3 cm. Side BC is 4 cm and side AC is 3.6 cm.

-Build this triangle: angle A(top)=74 degrees

-Angle B (bottom left)=60 degrees

-Angle C (Bottom right)= 64 degrees

-Line segment AB=3 cm, BC=4 cm, CA=3,6 cm

Could I minimize this data and still produce the triangle?

* Don't put anything about top, bottom, left, and right. Does it have to be in the same position as what is on the board?

Delaney and Caitlyn's Message

-AB=3 cm

-BC=4 cm

-AC=3.6 cm

and angle A=74 degrees

Gillian's Message

AB=3cm

BC=4 cm

AC=3.6 cm

A=74 degrees

B=60 degrees

C=46 degrees

        

Nick's Message

A=74 degrees

B=60 degrees

C=46 degrees

Hans's Message

AB=3cm

A=74 degrees

B=60 degrees

Noah's Message

AB= 3cm

A=74 degrees

C=46 degrees

Jack's Message

A=74 degrees

BC=4 cm


What is the least info we need to text to get the same triangle?

What is happening in the classroom?

What does it look like and sound like?



*Direct Instruction

     -Listen
     -Look at board/Elmo
     -No side conversations
     -Thinking quietly or ideas to remember
     -No doodling if distracting
     -No fidgeting
     -Jot down notes 



*Private think/write time




*Partner Work



*Plenary-whole class discussion


    -Don't blurt out
    -Write stuff down
    -Raise your hand-so you don't interrupt
    -Everyone should participate 
    -No side conversations
    -Ah..ha moments
    -Relevant MATH ideas
    -Ask genuine questions if you get stuck
    -Use specific language 




Teacher Role:
Plenary- Guiding: Information from the students, Select people to call on, record ideas, revoice ideas, keep on topic, ask questions/prompts 
Direct Instruction:Teacher is telling you stuff




*Homework
    -Use full ability
    -All done
    -Ask for help
    -Email Ms. O'Toole
    -Call a Friend
    -Hand in on time
    -Use Planner
    -Check Work
    -Read instructions carefully



*Small group work

    -Flexible- listen to others ideas
    -Only talking to people in your group
    -Be specific and complete
    -Don't interrupt
    -Talk equally (Mrs. O'Toole could assign A,B,C to rotate tall time)
    -Relatively quiet
    -Always do observations
    - The group needs you
    -Give them a job to boost confidence
    -Share equally all the work
    -explain/have conversation
    -Give examples
       -Work on individual papers
       -Ask for observations
       -Encourage them and show them steps
    
   

*Debate
     -Show/justify your thinking
     -Don't interrupt
     -Test all ideas--Keep open mind
     -Be respectful--we are just talking about ideas not people
     -Get everyone on board
     -Don't argue
     -Listen to understand what they were thinking
     -Ask for clarification
     -Stay on topic
     -Don't bring personal stuff in