| 
  • If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.

  • You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

View
 

Unit 1: Tools of Geometry

Page history last edited by Christine Koerner 4 years, 2 months ago

 

Geometry Unit 1: Tools of Geometry

Unit Driving Question 

What tools are essential to understanding Geometry? 

 

Essential Questions 

  1. How can we use multiple representations to communicate geometry notation?  
  2. How are coordinates used to prove relationships between lines/segments and within segments?

 

Launch Task 

Big Ideas for Development Lessons 

Closure & Assessment 

1 Lesson 

2 Weeks (approximately 1 week per big idea) 

1 Week

Copying a Line Segment

Click on the links below to see each Big Idea's Lesson Overview (includes links to teacher notes and student activities) 

  1. Undefined terms and Congruence are the cornerstones of geometry  
  2. Congruent angles have equal angle measure 
  3. Line segment relationships are determined by length and direction on the coordinate plane 

 

  1. Formative Assessment 1 (after Big Idea 3) 
  2. Re-engagement Activity (Not Provided)
  3. Unit 1 Assessment 

 

Big Idea 1: Undefined terms and congruence are the cornerstones of geometry.

OAS-M:  G.RL.1.1

Lessons and Additional Activities

 

Big Idea 1 Lessons 1-4 Overview (includes links to teacher notes and student activities) 

Evidence of Understanding 

 

Identify the difference between congruence and incongruence.

  • Given any two objects (non-geometric), describe what is the same and different about them

    • Example: a pen and a pencil

  • Identify and justify why two objects are the same or different

    • Distinguish “exactly the same” from “alike”

  • Discuss the difference between points, lines, rays, and line segments (undefined terms) in terms of congruence
    •  Demonstrate how a straight line segment can be drawn joining any two points (Euclid’s first postulate)

    • Demonstrate how any straight line segment can be extended indefinitely in a straight line (Euclid’s second postulate)

 

Justify which qualities are significant or insignificant for determining if two segments in geometry are congruent

  • Example: length measure vs.color of the segment, thickness, etc.

 

Construct congruent segments and justify their congruence

  • Given a line segment, create a congruent segment, and explain why they are congruent

    • Use notation to signify congruence

  • Bisect a line segment and justify congruence of both parts

    • Explain that the midpoint bisects a line segment

    • Use segment addition to explain that each part is half the measure of the whole

  • Compare methods for determining congruence and describe advantages of each type

    • Examples: paper folding, placing the segment (vertical and horizontal only) on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.

 

 

 

 

Big Idea 2: Congruent angles have equal angle measure.

OAS-M: G.RL.1.1

Lessons and Additional Activities

 

Big Idea 2 Lessons 1-3 Overview (includes links to teacher notes and student activities) 

Evidence of Understanding  

 

Describe qualities that make two angles congruent or incongruent

  • Define an angle using its vertex and rays

    • Recognize that as an angle measure increases, its arc measure increases

  • Define all straight angles as having 180° and are therefore all congruent angle measures

    • Show and describe why an angle whose arc measure is 180° is also a semi-circle

    • Show and describe why an angle whose arc measure is 360° is also a complete circle

  • Justify which qualities are mathematically significant or insignificant for determining if two angles are the same

    • Example: degree measure vs. color of the angle, length of the rays, thickness, etc

 

Construct congruent angles and justify their congruence

  • Compare methods for determining congruence and describe advantages of each type

    • Examples: paper folding, placing angles on the coordinate grid, using patty paper or online software to translate, rotate, or reflect image, etc.

  • Given an angle, create a congruent angle, and explain why they are congruent

    • Use notation to signify congruence

    • Consider and describe implications of human error

  • Bisect an angle and justify congruence of both parts

    • Use angle addition to explain that each part is half the degree measure of the whole

    • Construct congruent right angles using a perpendicular bisector

  • Perform constructions and analyze the relationships among the segments or angles created

 

 

Big Idea 3: Line segment relationships are determined by length and direction on the coordinate plane.

OAS-M: G.2D.1.5

Lessons and Additional Activities

 

Big Idea 3 Lessons 1-3 Overview (includes links to teacher notes and student activities) 

Evidence of Understanding  

 

 Analyze distance in the coordinate plane and use distance to relate points and lines

  • Calculate the distance between two points using the Pythagorean Theorem

  • Generalize methods for determining the distance between two coordinate points

    • Derive the distance formula using a right triangle and the Pythagorean Theorem

  • Explain how the distance formula can be used to find length measurements of segments (or sides of a geometric figure)

  • Find the coordinates of a segment’s midpoint

    • Prove the midpoint of a segment creates two congruent lengths

 Describe direction in the coordinate plane and use direction to relate points and lines

  • Generalize methods for determining the direction between two coordinate points

    • Determine the slope of the line

  • Identify and justify if two lines are parallel or perpendicular

  • Create equations that represent parallel lines or perpendicular lines 

 

 

 

Comments (0)

You don't have permission to comment on this page.