We have the same provider leading these new sessions, so I was a little worried we would end up looking for content to cut rather than incorporate. So far, that hasn't been the case. Obviously, there are certain topics that will require more focus (eg. linear relationships as opposed to exponents) but the goal has been to see how and where these supporting standards fit with the focus standards.
Our team has come up with the following units of study. We haven't reached the point where I can discuss specific activities/tasks, but I'd like some feedback on the pedagogy that motivated the clustering and sequencing.
Transformational Geometry
Use the coordinate plane to discuss transformations, congruence and similarity. Use dilations as an application of the ratios/proportions work done in grades 6 and 7. Use a graph as a tool to describe proportional relationships.
Data Analysis
Use bivariate data to create scatter plots which can then be the jumping off point for informal line of best fit (where the line may have an initial value other than zero) and an introduction for a future defining of function/non-function.
Linear Relationships
Graphing, graphing and more graphing. Take the informal line-of-best-fit and formalize the definition. Allow math to be it's own context. Graph systems of equations and look for common point (read: solution to system).
Equations
Use the work done in graphing systems to motivate more abstract symbolic manipulation required for solving linear equations.
Exponents
This was a tough one. Expressions with integer exponents and scientific notation seemed like an island unto themselves. We are still working on finding a place that fits nicely for these ideas.
Functions
Use the informal introduction to functions and formally define a function. Look at linear and non-linear functions. Compare functions using different representations (ie. graph vs. table vs. equation vs. verbal).
Pythagorean Theorem
I think this one speaks for itself.
3D Geometry
Problem solving involving the volume of cones, cylinders and spheres.
We are trying to move from the concrete/informal to the abstract/formal while allowing students to explore these ideas while creating their own formal definitions. I'm particularly interested in the sequence that runs from Data Analysis to Functions (note: Exponents look to be a unit that can be dropped in and our school calendar lends itself to having that unit kick off the second semester) as it may receive the most push-back from our high school colleagues. Traditional textbooks usually go the route of
Functions-->Equations-->Graphing-->Applications so we're going to have to have solid rationale.
No one pushes back better than you all. I'm counting on that.
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