## Project goal oriented sequencing

In our Geometry classes we have the odd situation of needing finish all the Geometry 5 weeks before the end of class, due to when our standardized-test-to-graduate is given.

Part of the time I could finish my logic unit, but that still left 3 weeks. The teachers at our school decided to start on Algebra 2. In the time span given I had great puzzlement over what to include. I didn’t want a stub of understanding that would just have to be repeated the next year.

I knew (based on requests from students who had heard of my Trigonometry classes doing the lesson) my class wanted to do the football lesson. To get there the students needed to reach systems of equations. Could they make it in 1-and-a-half weeks? (Not 3, they need time to review for the final.)

Here’s my sequence:

1. Solving multi-step equations (1-step and 2-step equations are probably the only thing from Algebra 1 they can do reliably well)
2. Rearranging equations to solve for a single variable (for example, isolating the h in $A=\frac{1}{2}bh$).
3. Systems of equations by substitution (no graphing or other solving methods).

Strangely enough, it is working. In the interests of time all the above sections I cut purely down to their abstract manipulations, with the understanding we would be applying our knowledge to the football lesson (which the students are insanely excited about). I have also been hinting how each part applies to the larger picture.

I’ve never had teaching systems of equations go so problem-free in my life. Is it because the curriculum has too much baggage in between, or is it because the students know exactly what goal they are leading to? Is dropping the Rule of Four (which I had to do here) sometimes a good idea?

### 6 Responses

1. If I had to guess, I’d say that this material being post-exam, low-stress but with a clear and interesting goal has a lot to do with it.

2. There is value to pursuing a goal without too much excess baggage, then circling back later (next fall?) to fill in any gaps and provide additional connections.

While the rule of three/four certainly helps achieve total mastery, is that really the goal when a topic is first introduced? I think it gets in the way of “telling a story”. And listening to (or better yet, participating in) a story is much more engaging for students.

So, I advocate getting the “big picture” across first. Get them to where they can do something fun/neat/impressive with the topic, and get them there as fast you can. Once they have achieved the “neat” objective, had some time to digest and start connecting the new concepts, they are in a good place to circle back and talk about variations on the theme, different starting points for the problem, different types of problems that can use the same approach, different questions that can be asked about the same situation, etc.

Many lesson plans seem to try too hard to cover every base completely as it is first passed, and students often either lose track of where we are trying to go or get bored by the trip. However, once we have reached our major destination, and they have built themselves a mental “skeleton” upon which to organize the new material, they are often surprisingly ready to productively revisit and extend topics both great and small that were left in the dust in our initial enthusiasm.

3. Can the Rule of 4 be telling the story? Which of the 4 did you drop?

• At the time of the lead up to the big lesson, the only thing we kept was symbolic manipulation.

Numeric and verbal get covered by the project itself. Graphic I don’t even know if I’ll have time for.

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