Sept

Oct

Nov

Dec

Jan

Feb

March

April

May

June

Themes

Introducing Geometry

Reasoning in Geometry / Using Tools of Geometry

Using tools of Geometry / Triangle Properties

Triangle Properties / Polygon Properties / Circle Properties

Circle Properties / Transformations and Tessellations

Transformations and Tessellations / Area

Area / Pythagorean Theorem

Volume / Similarity

Pythagorean Theorem

Similarity / Trigonometry

Trigonometry

Standards

3.1b.

Develop and evaluate mathematical arguments using reasoning and proof

3.1b.

Develop and evaluate mathematical arguments using reasoning and proof.

3.1a.

Investigate relationships among plane and solid geometric figures using geometric models, constructions and tools.

3.1a.

Investigate relationships among plane and solid geometric figures using geometric models, constructions and tools.

3.2a.

Verify geometric relationships using algebra, coordinate geometry and transformations

3.2a.

Verify geometric relationships using algebra, coordinate geometry and transformations

3.3a.

Solve a variety of problems involving one-, two- and three-dimensional measurements using geometric relationships and trigonometric rations.

3.3a.

Solve a variety of problems involving one-, two- and three-dimensional measurements using geometric relationships and trigonometric rations.

3.3a.

Solve a variety of problems involving one-, two- and three-dimensional measurements using geometric relationships and trigonometric rations.

3.3a.

Solve a variety of problems involving one-, two- and three-dimensional measurements using geometric relationships and trigonometric rations.

Major Skills

1. Learn point, ray, segment, line, collinear and coplanar points, angle, and polygons.

2. Know the following triangles; acute, obtuse, right, scalene, isosceles, and equilateral.

3. Know the following quadrilaterals; trapezoid, kite, parallelogram, rhombus, rectangle, and square.

4. Know the parts of circles.

5. Three dimensional geometric objects.

1. Use inductive and deductive reasoning to find terms of sequences.

2. Angle properties of linear and vertical angles.

3. Know and use the characteristics of angles formed by parallel lines cut by a transversal.

4. Duplicate line segments and angles.

5. Construct perpendicular bisectors.

6. Construct perpendiculars to a line.

1. Construct angle bisectors.

2. Construct parallel lines.

3. Slopes of parallel and perpendicular lines relationships.

4. Construct points of concurrency.

5. Perspective drawing.

6. Triangle sum conjecture.

7. Isosceles triangle properties.

8. Side-angle inequality and exterior angle conjectures of triangles.

1. Side – side –side congruence of triangles.

2. Side – angle – side congruence of triangles.

3. Angles – side – angle congruence of triangles.

4. Use corresponding parts of triangles to prove congruence.

5. Use flowchart thinking for proofs.

6. Vertex angle bisector theorem.

7. Equilateral / Equiangular triangle.

8. Polygon sum theorems.

9. Exterior angle sum theorem of polygons.

10. Properties of kites and trapezoids.

11. Mid segment properties.

12. Parallelogram properties.

13. Properties of rhombuses, rectangles, and squares.

14. Prove the properties

1. Chord properties of circles.

2. Tangent properties of circles.

3. Arc and angle properties of circles.

4. Prove circle properties.

5. Circumference / diameter ratio.

6. Arc lengths of circles.

7. Symmetry of objects.

8. Isometric properties.

1. Combine transformations.

2. Tessellations of regular and nonregular polygons.

3. Tessellations using translations, rotations, and glide reflections.

4. Areas of rectangles and parallelograms.

5. Areas of triangles, kites, and trapezoids.

6. Areas of regular polygons.

1. Areas of circles.

2. Area of circle sectors.

3. Surface area.

4. Pythagorean theorem and its converse.

5. 45-45-90 right triangle properties.

6. 30-60-90 right triangle properties.

7. Coordinate geometry distance formula.

8. Circle formula.

9. Circles and the Pythagorean theorem.

Solid geometric objects.

2. Euler’s formulas for polygons.

3. Volume of prisms and cylinders.

4. Volume of pyramids and cones.

5. Displacement and density properties.

6. Volume of a sphere.

7. Surface area of a sphere.

8. Similar polygons.

9. Similar triangles.

1

1. Indirect measurements using similar triangles.

2. Corresponding parts of similar triangles.

3. Proportions with area and volume.

4. Proportional segments between parallel lines.

5. Paragraph and symbolic forms of proof.

6. Trigonometric ratios.

7. Use right triangles to solve problems.

1. Law of sines.

2. Law of cosines.

3. Trigonometric ratios and the unit circle.

Seminars

Building Blocks of Geometry

Seven Bridges of Konigsberg

Euler Line

Napoleaon’s Theorum

Star Polygon

Cycloids

Pick’s Formula for Area

Alternative Area Formulas

Euler’s Formula for Polyhedron’s

Five Platonic Solids: Looking for an Original Plato Reference

Textbook Chapters

Ch.1.: Introducing Geometry

Ch 2: Reasoning in Geometry

Ch 3 Using tools of Geometry

Ch 4: Triangle Properties

Ch 5: Discovery and Proving Polygon Properties

Ch 6: Discovery and Proving Polygon Properties

Ch.8: Area

Ch. :9: Pythagorean Theorem

Ch.8: Area

Ch. :9: Pythagorean Theorem

Ch 12: Trigonometry

Ch 12: Trigonometry

Coached Projects  

Draw a hypercube.

Polygonal numbers or Beehive Geometry or Map Coloring /

High – Rise complex or Block lettering or Tiled floor or Spaced Fencepost

Triangles at work or Buried Treasure

Symmetry in snow flakes or variations on the crane / The art of Pi and Race track Geometry

Parallelogram Tessellations using the midpoint method or Tessellations of T-shirts

Building a Home

Creating a Geometry flip book

Euler’s formula for polyhedras with hole or Mobius Strip or Packing effectively and Displacement / Golden Ratio

Geometry of base ball or Gothic Cathedral

Proof by math induction or Writing a logic Puzzle

Seminars

How to work well in groups.