I'm gathering up a collection of math resources and my basic plan for Natalie is to do String, Straight-Edge & Shadow: The Story of Geometry* as our main text and to supplement the chapters with relevant activities from Making Math Meaningful, Math and Science Across Cultures, Hands-On Math, and From Agnesi to Zeno, as well as biographies from Mathematicians are People, Too.
* This is usually the main text for 6th grade Geometry but we are using it to simply dive into the subject until I can see where Natalie's skills lie. Jamie York includes all the curriculum skills for this grade level in his book as well, although I haven't listed them below.
Making Math Meaningful:
A Middle School Math Curriculum for Teachers and Parents
String, Straight-Edge & Shadow: The Story of Geometry makes a wonderful text for the main lesson because it provides a continuous narrative in which to place all of the geometry information. I am cognizant, however, of the need to cover quite a lot of content!
Jamie York expresses the following goals for Geometry in 7th and 8th Grade:
Seventh Grade Geometry
Area: Shear and Stretch, Area of a parallelogram, Area of a non-right triangle
Geometric Drawing: Triangle constructions, Euclidean constructions, Geometric divisions, Star patterns with geometric division
The Pentagon and the Golden Ratio, the Golden Rectangle, the Rectangle of whirling squares, the Golden Triangle and its spiral
Angle Theorems and Proofs, corresponding angles are congruent, alternate interior angles are congruent, same side interior angles add up to 180, the Angles in a triangle add to 180, Pythagorean Theorem, Pythagorean triples, Calculating missing sides of triangles
Eighth Grade Geometry
Measuration (areas and volumes): area of a trapezoid, area of four types of triangles, area of a circle, finding the length of an arc of a circle, finding the area of a segment of a circle, cubic measurement and notation, volumes of prisms and cylinders, volumes of pyramids and cones, volume of a sphere, surface area of a sphere, surface area of a cone, plume of an octahedron and tetrahedron
Stereometry: types of polyhedra, the Platonic solids, proof that there are only five Platonic solids, Kepler's universe, the transformation of solids, examples of dual solids, the archimedean solids, the archimedeal duals, construction paper models, the possible nets for a cube and a tetrahedron, Euler's Formula
Loci: a circle, two parallel lines, two concentric circles, a perpendicular bisector, two angle bisector, a parabola, an ellipse, a hyperbola, conic sections, curves in movement, the curves of Cassini
Just when you decide to hang up your teaching hat in frustration because you'll never ever get to all of this, Jamie York goes on to say in his introduction that he has never ever with any class covered all of the material listed in his book, and not to rush through the material just for the sake of getting through the curriculum. He says that new concepts are usually introduced in main lessons but that they are continually reinforced and worked on throughout the year. He also says that, "The reader... should not simply follow instructions or carry out a plan just because it is stated in this book. As always, it is the teacher's job to develop the inner sense of what is right at a particular moment for the class and to create an effective lesson."