Download Unit Map 2012-2013 - Tindley Schools Wiki

Unit Map 2012-2013
EdPower
Shah, Ronak / Geometry (M) / Grade 9 (Tindley Accelerated School)
Tuesday, June 25, 2013, 8:29AM
Unit: Unit 3: Triangles (Week 8, 3 Weeks)
Taught Curriculum
Stage 1 - Desired Results
Established Goals
IN: CCSS: Mathematics, IN: HS: Geometry, Congruence
G-CO Prove geometric theorems

10. Prove theorems about triangles.
G-CO Make geometric constructions


12. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices,
paper folding, dynamic geometric software, etc). Copying a segment; copying an angle; bisecting a segment; bisecting an angle;
constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.
13. Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.
IN: CCSS: Mathematics, IN: HS: Geometry, Circles
G-C Understand and apply theorems about circles

3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a
circle.
IN: CCSS: Mathematics, IN: HS: Geometry, Modeling with Geometry
G-MG Apply geometric concepts in modeling situations

1. Use geometric shapes, their measures and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a
cylinder).★
Key Words/Vocabulary
Proof: A set of rigorous reasoning that guarantees the truth or falsehood of a statement.
Triangle: A polygon with three vertices and three edges.
Equilateral: A shape where all sides are line segments of equal length.
Isosceles: A triangle where two legs are line segments of equal length.
Interior Angles: The measures of the angles on the inside of a shape.
Base Angles: The angles directly adjacent to the base of a shape.
Midpoint: The point that divides a line segment into two congruent halves.
Median: The line segment joining a vertex to the midpoint of the opposite side.
Altitude: The line segment perpendicular to the base of a triangle.
Circumscribe: To draw a circle that passes through all the vertices of a polygon.
Inscribe: To draw a circle that passes through all the edges of a polygon.
Essential Questions
Understandings
When a vertex, side, or angle is changed in a triangle,
how is the triangle affected?
Students will understand…


What is the relationship between a triangle and more
complex shapes?


How can properties of triangles be modeled with realworld objects?
Key Knowledge

The circle inscribed in a polygon will always be smaller than that which
circumscribes it.
If the smaller sides of a triangle sum to the larger side, the triangle
degenerates to a line.
The properties of the sides of a triangle allow us to prove statements about
its angles.
The properties of the angles of a triangle allow us to prove statements about
its sides.
Because mathematics is a logical system, we can prove statements indirectly
by assuming the opposite and creating a contradiction.
Key Skills
Students will know that…






Students will be able to…
The measures of the interior angles of a triangle
sum to 180 degrees.
The base angles of an isosceles triangle are
congruent to each other.
A bisector separates a line segment into two
congruent line segments and an angle into two
congruent angles.
A perpendicular bisector separates a straight
angle into two congruent right angles.
The medians of a triangle meet at a point.
The bisectors of a triangle meet at a point.





Use tools to construct equilateral triangles and inscribed and circumscribed
circles.
Use a straightedge, protractor, and compass to copy and bisect angles and
line segments.
Identify patterns and make inductive conjectures about the properties of
triangles.
Use a proof to support a logical argument and prove a theorem about
triangles.
Prove a theorem using an indirect proof.
Stage 2 - Assessment Evidence
Evidence of Student Understanding
Unit 3 Test -- Triangles
Summative: Test: Standardized
Unit 3 Test and Key.pdf
Stage 3 - Learning Plan
Detailed Unit Plan
Learning Ladder
Lesson Plan
Unit 3 Calendar - Triangles.docx
Syllabi
Attach your syllabi with Links
Resources
Unit Reflection
Last Updated: Tuesday, June 25, 2013, 8:28AM
Atlas Version 7.2.6
© Rubicon International 2013. All rights reserved