The very first activity I did with my kids to start congruence was to go outside and get our hands dirty (literally).
Our medium: sidewalk chalk.
This was less of a problem and more of an activity, but it definitely sparked some great conversation. I started out with an activity for each rigid motion (reflection, rotation, translation) and then had discussion.
Have a line drawn on the parking lot. Each student draws and labels their own point. “Walk directly to the reflection line and count the number of steps it took you to get there. Now, keep walking the same number of steps and draw your new point. Label it with the same letter and an apostrophe- this is read letter prime”.
What kinds of paths did we take?
What about the distance from the line?
Are the two points we drew the same? Why or why not?
Make a point where you are standing. Now draw a circle around you and your point. Where you are facing, make a little mark on the circle and write 0. Now turn halfway around on your point. Where you are facing the circle, make another mark and write 180. Now turn halfway between your two marks. Make another mark labeled 90. Now, turn halfway around the circle, mark that 270.
Now stand on the line of your circle. Walk on the line until you get to the 90 mark.
Did we move from our point? What is the point that we are standing on?
What do these numbers represent?
What angle got us to halfway around? What angle will get us all the way around?
Whose 90 is to the left of their 0? to the right? What are these directions called in this context?
Is this still rotation? How can we know?
Where is our reference point?
Can I rotate a negative angle?
Simon says move (scholars ask move where?)
Sorry, Simon meant to say move to the right (how much?!)
Sorrrrrry, Simon really meant to say move to the right 3 steps.
Simon says move backwards 5 steps.
What clarifications did you need to follow my directions?
Did you end up the same distance from the people around you? Would you have expected to?
Why didn’t you?
The discussions were really awesome and we ended up with this sweet set of notes. We were even able to come up with perpendicular paths for reflections (a little prompting from me) and it was great to be able to refer back to the activity throughout our congruence unit.
I would love to hear your feedback- are there questions I should have asked but didn’t?