RSS

Reflecting a Point about a Line

03 Sep

Students had the opportunity to look for and express regularity in repeated reasoning while reflecting a point about the line y=x.

I sent an interactive Quick Poll so that they could move the point, observe its reflection about y=x, and then determine the image of a point not shown on the graph.

Screen Shot 2014-08-18 at 9.32.02 AM

Screen Shot 2014-08-18 at 9.33.49 AM

Then I asked students to generalize their results by determining the image of (a,b) reflected about y=x. Which responses would your students accept as correct?

Screen Shot 2014-08-18 at 9.37.51 AM

Students had a more difficult time reflecting a point about the line y=–x. 18 of 26 got it correct for the Quick Poll on which they “played”. (Show Correct Answer has been deselected.)

Screen Shot 2014-08-18 at 9.46.10 AM

But only 12 got it correct for the Quick Poll that simply asked the question.

Screen Shot 2014-08-18 at 9.43.58 AM

Would a graph help?

 

 

Screen Shot 2014-08-18 at 9.43.35 AM Screen Shot 2014-08-18 at 9.43.45 AM 

Drawing a representation of the situation is not yet second nature.

 

Then we reflected a point about the horizontal line y=–2 first on the graph:

Screen Shot 2014-08-18 at 9.53.31 AM

 

Screen Shot 2014-09-03 at 7.54.43 AM

And then we reflected a point about the vertical line x=2 on the graph:

Screen Shot 2014-08-18 at 9.58.48 AM Screen Shot 2014-09-03 at 7.54.54 AM

Next, I didn’t give them a graphical representation.

But more of them thought to create their own.

Screen Shot 2014-08-18 at 10.00.31 AM

And then the bell rang while students were submitting.

 

Screen Shot 2014-09-03 at 7.55.06 AM

 

And so the journey to provide students opportunities to develop mathematical habits of mind continues …

 

 

Advertisements
 
 

Tags: , , , , ,

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

 
%d bloggers like this: