## Example Curriculum

I taught two classes of Advanced Algebra at Snowden, a Boston Public School located in Copley Square. One of my classes was 11th graders, and the other was predominantly 12th graders who were repeating the class. Each class had about 30 students in it. We were required to use a certain text and we had a Pacing Guide, but we were given great freedom in how we taught. I was very happy with this situation. When taking over these classes in January 2007, 60% of my students were receiving failing grades for the first half of the year, but only two months later, only 18% were failing.

In these two sets of four classes (of duration 57 minutes each, taught on a Thursday, Friday, Monday, and Tuesday in March 2007) I taught Circles and Ellipses. Circles were taught entirely, including their rightful place as one of the conic sections. This allowed me to teach Circles algebraically and geometrically (geometrically as both two dimensional and three dimensional geometrics).

Ellipses were introduced with the question “does our Earth revolve around the Sun in a circle?” with the revelation that it actually travels not in a circle, but in an elliptical path with the Sun as one of its two foci. The different shapes, or eccentricities, of three increasingly elongated ellipses were shown in a 12 foot wide drawing of our Earth’s revolution, and then Pluto’s, and then Halley’s comet, whose elliptical path is so eccentric that it approaches parabolic behavior and almost escapes our solar system.

The Circle was then discussed as a special case of the Ellipse. All the basics of ellipses were taught and now in the next two days I returned to firm up the students’ understanding and to place this understanding within the context of all conics.

*This material was taught over the course of four days to the 11th and 12th grade students studying Advanced Algebra at Snowden, an urban public school in Boston.*

### Handouts

Filename | Filesize | Description |
---|---|---|

Circles | 42KB | Description |

Big Picture 1 | 145KB | Description |

Big Picture 2 | 122KB | Description |

3D Conics | 155KB | Description |

3/22 Slide 1 | 150KB | Description |

3/22 Slide 2 | 132KB | Description |

3/22 Slide 3 | 124KB | Description |

3/22 Slide 4 | 151KB | Description |

3/22 Slide 5 | 114KB | Description |

3/22 Slide 6 | 94KB | Description |

Circles 3/23/07 | 41KB | Description |

Circles Worksheet | 208KB | Description |

Circles 3/26/07 | 208KB | Description |

Ellipses | 42KB | Description |