Tag Archives: parallel / perpendicular

See, Think, Wonder #makthinkvis


For our next Making Thinking Visible chat, we were asked to read Chapter 3 and implement the first routine presented – See Think Wonder (STW) pg 55.  I realized late Wednesday evening students were scheduled off for a staff PD day on Friday.  I scrambled wondering how I could incorporate this strategy in a meaningful way.  We had worked with parallel lines / transversals and the angle relationships created.  My goal was for students to look for ways to prove lines parallel.  How could I use STW to get this accomplished?

When I searched for images of parallel lines in architecture, I ran across a picture of a building in Australia and a picture of the Illusion as well.  You can find more here Cafe Wall Illusion.

My plan was to use the optical illusion – the placement of the black and white blocks causes one to think the lines are getting closer / farther apart.  However, as I flipped through my book, I saw the routine of Zoom In and wondered if I could combine the 2 somehow.  And here is what I did:

Zoom In – Ask Students what they see, pretty standard – black rectangle.  So many ideas (some silly) of what this could actually be part of…


Slide 2 was a little more interesting, alternating black / white rectangles with several things they thought it could be a part of – keyboard, referee’s shirt, prisoner uniform, zebra…


Slide 3 eliminated some of their predictions…I did have a person actually state a building. Hmm.  I think they must have seen it before.


When I revealed the final picture – it was fun listening to their comments.  One was very perplexed “Why would anyone want their building to look that way?”  It is found in Melbourne, Australia.


After a few moments of sharing / discussion – students were comfortable.  As I shared with students that we were going to do a thinking routine called See Think Wonder – I tried to explain each step.  This is the slide I shared with students:


I went through each step, allowing time for students to record what they saw, what they thought and anything they wonder (a question they could investigate/answer).    We then shared our responses.  After the first 2 statements, I paused and revisited what we were to do for each step.  We agreed the statements would actually go to “Think.”  Here were responses:


After sharing, students were given a copy of the Cafe Wall Illusion – but not allowed to use rulers/protractors to measure anything.  You can see from the snapshots, several chose to use patty paper.

Student A traced the lines to show they were actually straight, then translated the copied lines over the originals to show they were parallel.


Student B traced the edges of the rectangles, then translated to different levels to show the lines were equidistant at all parts, thus parallel.


Student C over-layed tape, traced edges at 2 different levels, then peeled the tape and matched them up…IMG01093

One student used the pink line on the notebook paper and overlaid it to show the lines were actually straight and several traced the rectangles onto patty paper and translated to others to show congruence.

It felt a bit contrived – I’m not sure what level of thinking was achieved, but I will use See Think Wonder again.  It was a good start to model the 3 steps of the routine.  Following the activity, students could be asked – if I only had 2 lines – how could I prove they are parallel?

In discussion some responses:

  • to extend the lines to see if they ever intersect (student knows the definition);
  • measure the distant between the lines at different points (again, student understands they are equidistant;
  • draw a line perpendicular to one line, extend it, if its perpendicular to the other line, then the 2 lines are parallel (yep a student came up with that one)
  • and finally, cut both lines with a transversal, measure/compare the angles to see if the relationships exist (the understand converses/working backwards to prove).

What I appreciated about STW – I didn’t tell students what question to answer or even how to answer it.  They created their own question and chose a way to answer it.  The only problem with this – they may not wonder/choose “the question” I’m wanted them to investigate/answer.  In the end, if you can get students to make a connection with the content, give them opportunities to notice/wonder, allow them to come up with their own questions – they’ll be interested in finding the answer…

Geo-board Investigations


I was clearing out some files this weekend and ran across this packet from a presentation at KCTM in 2002.  I had just completed my initial National Board Certification earlier that spring (still didn’t know if I had certified yet) and thought these lessons were worth sharing.

I’m not sure if you’ll be able to read the first two pages – orginal files are long gone and just by happenstance I rance across this packet.  Reading through it – its almost like I was “blogging” 10 years ago – but it reminds how important reflection on your lesson will always be – how much you can learn about teaching by pausing to think about student thinking/responses.  Whether you use actual geo-boards, paper/pencil or modify to www.geogebra.org – maybe they will give you some ideas for your classroom.

Geo-board Investigations

  • Parallel & Perpendicular Investigation – use rectangle properties to find relationship with slopes
  • Amusement Park – distance between 2 points (I hate using distance formula and often allow students to find slope triangle, then apply Pythagorean Theorem)
  • Midpoint Investigation
  • Midsegment Investigation

*I used the reinforcement tabs for students to write coordinates/label points on geo-boards.  BUT don’t let them peel and stick…just leave on paper and drop over the geo-board tab.