**Schema Activation**: What happens when you do two of a motion? (Same type, not necessarily the same motion.) Please guess if you don’t know.

Motions | Result-type | Know/Guess? |

Translation then a translation | K/G | |

Rotation then a rotation | K/G | |

Reflection then a reflection | K/G | |

Glide reflection then a glide reflection | K/G |

This brings up the idea of orientation both in terms of turning and in terms of face-up/face-down.

For a focus we have the following:

**Focus**: Today we’re just going to concentrate on reflections and their compositions. We have three different sketches to consider, and will also consider the questions that could be asked about each. A composition of motions is when you make one movement and then another. The combination is still a motion, as the original and image are still congruent.

We're also going to consider using questions to move us forward. The types of questions described by literacy instructors are:

- Literal - factual answer available or quickly available by recall, or can be found directly in the text.
- Application - answer found by applying known method or looking up with slight modification. The method of getting the answer is known.
- Inference - answer requires prediction or extension from known information. Can be an outright prediction or come from reading between the lines.
- Analysis/synthesis - answer requires combination or deduction from other known information, possibly requiring a method not currently known by the respondent.

**Activity**:

We discussed these sketches together. They asked about finding the center of rotation and saw a neat connection with the reflecting lines. They also saw a neat connection between finding the center of a rotation and finding the center of a circle, but couldn't remember or figure out how. They found a cool relationship between the direction and distance between parallel lines and the resulting direction and distance of the translation.

**Reflection**: What did you do during this workshop? So what did you learn? Now what would you want to consider next about motions or questioning?

Bonus: (or... extension)

Two Glide Reflections: webpage or geogebra file

**Coming Soon**:

- a tale of two lessons - why can't everything work?
- Sue's MathMama Dialogue: what's wrong with math education?

These sketches are fantastic! Thanks for sharing!! I wasn't able to open the first one though, either by webpage or by geogebra. I was able to open all the others though. Thanks again!

ReplyDeleteThanks for catching that. I just put the wrong filename in. I'm glad they're useful!

ReplyDelete