# Pythagoras, His Formula and a Teacher Who Didn’t Teach

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So a simple lesson today.

A segment on a grid and asked students to find the length of it. Yep, most sketched in their right triangles and pulled out the Pythagorean Theorem.  But what if we don’t have a grid? How can you find the distance between the two points without graph paper? Or if one of your points is (543, 97)?

After their sharing, while practicing, some wondered, “Is it okay to use the slope if its in lowest terms?”

Good question.  Does it matter?  What could you do to determine if it matters?

And their suggestion:

…with their finding.  Makes me smile when they answer their own questions.

Best part of lesson today?  Their INB notes.  A post by @justinaion made me wonder how I could be more purposeful in student notes.  Today’s notes…after completing the lesson, students put their whiteboards away, and created their own notes.  Some had step by step instructions.  Others had pictures drawn, paragraphs with a couple of examples.  But in the end, they wrote what was important to them.

I loved the question a student asked while walking out the room.  “How am I supposed to find the distance with three coordinates in space?”

My response, How are you supposed to find the distance with three coordinates in space?  A smile with an a-ha look on her face…you just…yes, child, you knew how all along.

A day when I didn’t teach a thing but my students left knowing something new (well, except for the kid who sulled up because I wouldn’t TELL them ‘the formula’, use your device) …its been a good day.

Even better, a FB post from a former student-

# Developing Definitions

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I’m back!  Nearly 2 months? Yikes. Some fellow teachers on Twitter were committing to blogging once each week.  I think  that’s reasonable – besides, usually my best reflection comes during the moments I blog.  Reflection – seems to be the first thing I push aside when I just don’t have the time.  Yet, its the most valuable use of my time.

I’m sharing some successes from Kagan Geometry (one of my favorites by the way).

I was going to be out for a number of days due to being seated on the jury for a trial (give me 100+ teenagers over the courtroom anyday!).  I wanted to leave something productive.  I did short videos (<10 minutes) filling out certain pages in the INBs in addition to other activities.

The first Kagan activity was for vocabulary.  Each strip of paper included examples and counter-examples for each term.  I modified from the round-table recording it suggested.  Students were asked to pair up (a new partner for each new term) and develop their own definitions.  I loved it simply because most were terms students had previously been exposed to in middle school.

When I returned to the classroom, I ran through all I had left during my absences to address any concerns/questions.  Several students commneted how they liked (appreciated) doing the definitions this way.  Their comments ranged from – ‘You actually had to think about the terms; Talking with someone about it really helped you process what it was before writing it down;  The pictures of examples / nonexamples really helped understand the word better.’

Yesterday, we developed more definitions about angles.  When I told them what we were doing – they were excited about the activity.  Listening to the conversations – I was very happy with their discussion / questions / specifics they included in their definitions.

I remember several times in the past doing examples / non-examples, especially when using Frayer Models.  I believe taking it out of my hands/mouth and giving them the opportunity to work in pairs really enhanced their understanding of the terms.  Even when discussing HW  today – they used appropriately terminology.  Yeah!

Another Kagan activity I used as a LHP activity

from Kagan Geometry

– very similar to Everybody Is a Genius’  Blind Draw.  Students were placed into small groups and given 12 cards with written directions.  Person 1 chose a card, read the directions, gave others time to think and draw a diagram with labels.  The reader confirms/coaches/praises others’ work.  A new person chose a new card and the rounds continued until all cards had been used.  One thing I appreciated about this – another card asked students to draw a ray from E through M.  This allowed students to realize differences in very similar diagrams.

Again, when I returned to the classroom, students shared how this activity was different from anything they’d done before, saying it was both challenging but helpful in that it helped to clarify certain misconceptions they had; especially with labeling the diagrams.

I have learned the Kagan strategies help students develop and process concepts.  There are “game like” activities where students must find their match and discuss.  Visual, Auditory, Kinesthetic – something for everyone.  Its not an end all – be all resource.  But the amount of HW / practice is minimal when I’ve used these strategies correctly.  I am a firm believer that they help start a strong foundation to build upon.  Hey – if students are smiling and laughing while “doing definitions” – its gotta be good.