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.
|Translation then a translation||K/G|
Rotation then a rotation
Reflection then a reflection
Glide reflection then a glide reflection
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.
Two Parallel Lines: webpage or geogebra file
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
- a tale of two lessons - why can't everything work?
- Sue's MathMama Dialogue: what's wrong with math education?