UNIT #1 - Congruence, Proof and Construction
Unit #1 is the most radical change brought on by the common core curriculum. For years textbooks have laid an identical pathway to introduce geometry.... (1) Basic Relationships (2) Logic & Proof (3) Parallel & Perpendicular Lines (4) Proof of Triangles (5) Triangle Relationships and (6) Quadrilaterals. It seemed like there was no other way - we were approaching it the way Euclid did, very axiomatic. Well along came the core....
The biggest change is the use of transformations to introduce this material. Congruence is developed not out of measurement but out of isometric transformations. Proof is developed by establishing relationships of symmetry and transformations to explain characteristics of shapes. . It is new and bold.... It will take some getting use to but I like it... I think many more students will get it!! |
UNIT #2 - Similarity, Right Triangles & Trigonometry
In many ways, Unit #2 is like what we have delivered for many years except that similarity is developed from a dilation standpoint. Again, the transformation introduces the relationship. Students first come to understand dilations and their characteristics and then we find that the dilation creates shapes that have proportional sides and congruent angles.... guess what... that is similarity. Similarity, as it always has, introduces great topics found in right triangles such as geometric mean, special right triangles and trigonometry.
This unit has the first of the honors-only items and it can be a big difference. The honors course is to teach the area formula using sine, the Law of Sines and Cosines and the application of those laws. These can be big concepts to teach especially the ambiguous case of the Law of Sines. I would mention that when I teach the congruence criteria of ASS back in unit #1, I discuss the cases then of which produce congruence and which ones don't. This seems to make the Law of Sines ambiguous case easier to understand at this time. |
Unit #3 - Geometric Measurement and Dimension
What surprised me here is that there is no mention of surface area in this unit. I actually cannot find the calculation of surface area anywhere in the core curriculum. I guess the understanding is that if you can calculate area, you can calculate surface area and that it doesn't need to be covered as a individual topic. We actually chose to teach some surface area because we felt that it was a glaring omission.
This unit includes some fun things... like the discovery of the volume formulas and Cavaileri's principle. Students are to develop formulas for volume and then apply them. We also look at the cross section of three dimensional objects. This is new and fresh. Students haven't had much experience with cross sections.
Finally, the understanding of volume using rotations about an axis is very fun. To contrast Cavaileri's principle of congruent slices, here we look at the revolving of a 2-D shape to form a 3-D shape. This ability to visualize and describe this process will be helpful later when they take Calculus. |
UNIT #4 - Expressing Geometric Properties with Equations
This is what once was called coordinate geometry. This is a great area of the curriculum - it links the geometric concepts to the coordinate grid and prepares students for algebra 2. A number of Algebra 2 items have moved into this course such as equations of circles and parabolas. This is nice... it seems to fit fine to investigate circles and parabolas in a geometric sense.
I also found that many of these objectives in Unit #4 can be spread throughout the year when they fit in such as; partitioning a line segment (similarity), equations of circle (circle properties), determining the name of a quadrilateral based on four points (quadrilaterals), etc... I found that I introduced some of these during the other units and then I hit them again when I covered the rest of the coordinate geometry (equation) items but in greater detail and complexity. Coordinate proof is also apart of this unit.
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Unit #5 - Circles
Not much to say here - most of the objectives are the same as to what we have done for many years. Arc length and radians were introduced as new items but they fit very nicely in the development and study of circles. We used radians to determine new formulas for the area of a triangle (using radians) and the calculation of arc length (using radians) which went very smooth. |
Unit #6 - Statistics and Probability
This is all new... at least to geometry. If anything, in previous geometry courses we would touch on geometric probabilities but nothing this involved. Was it weird teaching probability in geometry? Yes.... but did it work.... Yes... There is definitely a greater emphasis on probability and statistics in the common core and the geometry course seemed to have the space to handle some of it. These objectives focus on the basic foundational ideas of probability and prepare students for more involved statistics at the Algebra 2 level. |
