January 4, 2012

Activity in the Beckman book: (state your logic, provide needed justification, but the obvious justification)

1. vertical angles are congruent
2. __

3 things that are undefined

1. Point
   What is a point? how big is it? does it have a size? can we measure the size of a point? Can you define a point without using the word point?
2. Line
   What is a line? A line is a series of points.  Since you can't define a point, you can't define a line.  How wide is a line?  You can't measure that.
3. Plane
   You can't measure the depth of a plane.  You can measure the width and height.

Activity - Take pictures of lines, planes and points in the "real world"

Similar -

Two types of comparisons you can make in similar shapes. You can compare corresponding sides, or the dimensions within the shapes.  (You are comparing the ratios)

The angles have to be the same in similar objects.

Two types of questions that you might be asked:

1. Prove that two objects are similar
2. Find a missing side link

Finding the side of similar objects.  (I apologize that some pics are sideways)

Triangle Congruencies

Video that talks about congurent triangles

• SSS (side, side, side)
• SAS (side, angle, side)
• AAS (angle, angle, side)
• ASA (angle, side, angle)
• HL (hypotenuse leg)

Polygon Congruence

video that talks about congruent polygons

Differentiation Lesson Plan (check class syllabus to see requirements)

Measurement and Geometry

Measurement can be a difficult concept, especially for young students. Based on conversations from previous classes, we have discovered that students learn best when concepts are taught in a real world context. Teachers should focus on hands on activities to give students experience using measurement rather than just showing pictures and assigning worksheets. (Van de Walle, pg 369)

• ·         Describe everything you know about “standard units of measure."
•       Give examples of how you have used standard units of measure at home in the last week.
•       Give examples of how you have used non-standard units of measure at home in the last week.
•       Why is it important to have a standard system of measurement?

The three steps of Measurement

1. Make a Comparison
2. Concrete examples
3. Use of tools 

The Four Things we Measure

1. Time
2. Mass
   how many molecules (it is NOT weight).
   it is consistent
3. Distance or Length
4. Volume
   how much space it takes up

Geometry

• Geomoetry is a vocabulary course.
• Very important to know the definitions

1. Line
   never ending, infinite number of points
   must be straight
   no width
   
   
2. Angle
   made of two intersecting rays
   
   
   
3. Perpendicular Lines
   
   
   
4. Parallel Lines
   
   
5. Congruent
   
   
6. Degree
   
   
   
7. Postulate
   Things that can just be assumed based on general reasoning
   
8. Theorem
   must be proven
   A rule that can be used once it it proven
   
   

Parallel LinesThe slope will be the same for the parallel lines, the y intercept will be different

Perpendicular lines

The slopes are the negative reciprocal of each other.

Examples:

Transversal 

 - in class we talked about transversal being any line that intersects any set of parallel lines.  The transversal line does not have to be perpendicular.

Practice Drawing using verbal clues:

Supplementary

• two angles that add up to 180
• "supplementary makes a sunrise"

Complementary

• two angles that add up to 90
• "Compliments cause love, and love starts with an L"

Triangles:

Finding how many angles are in a triangle

This activity proves that there are 180 degrees in a triangle.

Vertical Angles

Interior Angles

Exterior Angle