|
Timeline |
Content/Topic |
Skills |
Assessment |
Standards |
|
Sept. – 6 days |
· Geometric Art
(Chapter 0) |
· Identify examples of geometry in art, nature, and world cultures
· Discover the characteristics of reflectional and rotational symmetry
· Develop observational and visual thinking skills
· Create designs with straightedge and compass
· Construct regular hexagons with compass and straightedge
· Identify van Hiele Levels |
· Group investigations
· Daily homework
· Constructions and designs
· Reflection
· Portfolio: Chapter 0 Activity
|
· A.12.1, A.12.6, C.12.1, C.12.2 |
|
Sept.- Oct. – 13 days |
· Introducing Geometry (Chapter 1) |
· Learn basic terminology and notation of geometry
· Become familiar with objects which have special characteristics
· Define basic parts of geometric objects
· Translate descriptions into diagrams and vice versa
· Develop skills of measuring angles and line segments
· Learn how to correctly mark figures
· Write definitions
· Develop critical thinking
· Develop visual thinking
· Practice construction skills
· Practice cooperative behavior |
· Group investigations
· Daily homework
· Quiz
· Definitions
· Test
· Games (Taboo, Pictionary)
· Reflection
· Portfolio Activity: Chapter 1 |
· A.12.1, A.12.2, A.12.3, A.12.4, A.12.5, A.12.6, C.12.1-3, D.12.2 |
|
Oct. – 14 days |
· Reasoning in Geometry (Chapter 2) |
· Solve problems using inductive reasoning
· Solve problems using deductive reasoning
· Generalize basic number patterns to find the nth term of a sequence
· Discover relationships between special pairs of angles
· Identify relationships of angles formed by a transversal cutting parallel lines
· Apply mathematical models to problem solving
· Practice performing investigations and writing conjectures
· Develop visualization skills and cooperative behavior
· Practice measurement and construction skills
· Review slope |
· Group investigations
· Daily homework
· Conjectures
· Quiz
· Sketchpad labs
· Test
· Reflection
· Portfolio |
· A.12.1, A.12.2, A.12.3, A.12.5, C.12.1, C.12.2, C.12.3, C.12.4, F.12.1
|
|
Nov. – 14 days |
· Using Tools of Geometry (Chapter 3) |
· Learn the rules of geometric constructions using only a compass tool with straightedge
· Duplicate segments and angles
· Perform constructions such as perpendicular bisectors, midpoints, and angle bisectors
· Use compass and straightedge, patty paper, and Sketchpad to complete constructions
· Identify points of concurrency in triangles
· Solve application problems related to various constructions |
· Group investigations
· Constructions
· Daily homework
· Conjectures
· Quiz
· Sketchpad labs
· Test
· Reflection
· Portfolio Activity: Conjectures |
· |
|
Nov.-Dec. – 21 days |
· Discovering and Proving Triangle Properties (Chapter 4) |
· Discover angle relationships in triangles
· Investigate triangle congruence shortcuts like SSS, SAS, ASA, AAS
· Learning how to show two triangles are congruent
· Applying CPCTC
· Learning how to complete flowchart proofs |
· Group investigations
· Daily homework
· Conjectures
· Sketchpad labs
· Quiz
· Test
· Project: Stained Glass Window
· Reflection
· Portfolio |
|
|
Jan. – 14 days |
· Discovering and Proving Polygon Properties (Chapter 5) |
· Discover sums of polygon interior and exterior angles
· Discover properties of kites, trapezoids, and various kinds of parallelograms
· Define and discover properties of midsegments in triangles and trapezoids
· Practice writing flowchart and paragraph proofs
· Develop reasoning, problem-solving skills, and cooperative behavior |
· Class investigations
· Patty paper investigations
· Daily homework
· Conjectures
· Sketchpad labs
· Quiz
· Test
· Reflection
· Portfolio |
A.12.1-6, C12.1-4 |
|
Jan.-Feb.
11 days |
· Discovering and Proving Circle Properties (Chapter 6) |
· Learn relationships among chords, arcs, and angles
· Discover properties of tangent lines
· Calculate arc lengths and circumferences of circles
· Prove circle conjectures |
· Group investigations
· Student presentations
· Daily homework
· Conjectures
· Sketchpad labs
· Listening quiz on Sketchpad
· Reflection
· Portfolio |
A.12.1-6, C.12.1-3, C.12.5, D.12.2, D.12.3 |
|
Feb. – 6 days |
· Transformations and Tessellations (Chapter 7) |
· Discover basic properties of transformations and symmetry
· Identify and create translations, rotations, and reflections of figures in the plane
· Learn about compositions of transformations
· Apply transformations to the coordinate plane
· Create a simple tessellation using Sketchpad |
· Daily homework
· Group investigations
· Conjectures
· Sketchpad labs
· Quiz |
A.12.1, C.12.1, C.12.4 |
|
Feb. – Mar.
15 days |
· Area (Chapter 8) |
· Review terminology for solids
· Develop area formulas through investigations for the following shapes:
o Rectangles
o Parallelograms
o Triangles
o Trapezoids
o Kites
o Regular polygons
o Circles
o Irregular shapes
· Use area formulas to solve problems
· Develop formulas to find the surface areas for the following solids:
o Prisms
o Pyramids
o Cylinders
o Cones
· Solve surface area application problems
· Practice visual thinking in three dimensions |
· Group investigations
· Sketchpad investigations
· Daily homework
· Conjectures
· Quiz
· Test
· Reflection
· Project: Design a house (room)
· Portfolio |
A.12.1, 2, 5, B.12.6, C.12.1-3, D.12.3 |
|
March
12 days |
· The Pythagorean Theorem (Chapter 9) |
· Discover the Pythagorean Theorem and the Converse of the Pythagorean Theorem
· Apply the Pythagorean Theorem and its converse
· Use the Pythagorean Theorem to calculate distances between any two points and derive the distance formula
· Derive the equation of a circle from the distance formula
· Study two special triangles:
o 30-60-90 triangle
o Isosceles right triangle
· Use conjectures related to the Pythagorean Theorem to solve problems
· Learn how to simplify and work with radical expressions |
· Daily homework
· Group investigations
· Conjectures
· Sketchpad labs
· Foldable note
· Quiz
· Test
· Reflection
· Portfolio |
A.12.1-5, B.12.3-4, C.12.1-4, D.12.1, D.12.3 |
|
Mar. – Apr.
16 days |
· Volume (Chapter 10) |
· Explore and define many three-dimensional solids
· Discover formulas for finding the volumes of:
o Prisms
o Pyramids
o Cylinders
o Cones
o Spheres
· Use volume formulas to solve problems
· Learn how density is related to volume
· Derive a formula for the surface area of a sphere
· Practice three-dimensional visual thinking and drawing skills
· Develop reading comprehension, problem solving skills and cooperative behavior |
· Daily homework
· Conjectures
· TABOO game
· Group investigations
· Quiz
· Test
· Project: Five Platonic Solids
· Drawing activity
· Volume formula chart
· Reflection
· Portfolio |
A.12.1-6, B.12.6, C.12.1-3, D.12.1-3 |
|
Apr.-May
11 days |
· Similarity (Chapter 11) |
· Review ratio and proportion
· Define similar polygons and solids
· Discover shortcuts for similar triangles
· Learn about area and volume relationships in similar polygons and solids
· Use the concepts of similarity and proportionality to solve problems |
· Daily work
· Conjectures
· Group investigations
· Sketchpad labs
· Project: Body Part Lab
· Quiz
· Test
· Reflection
· Portfolio |
A.12.1-6, B.12.2, C.12.1-4, D.12.2-3, E.12.1 |
|
May - 5 days |
· Trigonometry (Chapter 12) |
· Define trigonometry
· Discover the sine, cosine, and tangent ratios
· Use trigonometry to solve problems involving right triangles
· Create a clinometer and use it along with trigonometry to solve an indirect measurement problem |
· Daily homework
· Conjectures
· Project: Indirect Measurement
· Quiz
· Reflection
· Mini-Portfolio |
A.12.1-6, B.12.2, B.12.6, C.12.1-3, C.12.5, D.12.2-3 |
|
May-June
8 days |
· Geometry as a Mathematical System (Chapter 13) |
· Look at geometry as a deductive system
· Explore the postulates of geometry
· Discover the relationships between various conjectures
· Practice proof strategies
· Prove theorems in groups
· Connect the learning from the beginning of the course to proof |
· Daily homework
· Group proof presentation
· Individual proof
· Reflection
· Portfolio |
A.12.1, C.12.1, C.12.3 |
