Category Archives: distance

Purple Circle Card Sort


Last spring, I placed equations of circles after distance between 2 points.  The idea came from a mini-investigation in my Discovering Geometry book (formerly Key Curriculum, now Kendall Hunt). 

Earlier in the semester a new colleague shared the success her students experienced with the Formative Assessment Lesson Equations of Circles 1.  I decided to use this lesson…

In my early geometry class yesterday, we literally stared at circles.  It felt like a wasted class.  No matter what example I referred back to, or what question I asked, it just didn’t work.  Thankfully, I had planning immediately following and I was able to reflect very quickly.  For my last geometry class of the day, I adjusted my sequence of leading examples.  Reviewing our previous work from last week. 


The remainder of the lesson went smoothly.  A quick white-board quiz at the beginning of class today allowed me to address some small errors.  Once again, I had them create their own notes/examples in their INBs.  Yes, a few are still lacking, but the majority are very thorough in what they are including.  Asking questions about specific what-ifs, like one student brought up none of our examples today had a center located at the origin, so I asked the class if they could remind her.  Several went on to include a similar example on their page.

The lesson continued with a collaborative pair.  They were given 12 equations to sort by center and radius.  There were 4 blank blocks in their grid that required them to create their own equations.  At the beginning, some were “cheating” so I stopped them to remind them 1 person picked a card, explained why they were placing it, the other person had to agree and understand before taking their turn.  They are getting better at disagreeing and telling why when their partner is making a mistake.


Their assignment was to create an artistic picture incorporating 5 different circles and listing their equations on the back. Short, sweet, simple.  Can’t wait to see them.

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


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-


Distance & Midpoint on a Map


Been playing with this idea for a couple of days – here’s a rough sketch.  Rather than having students work a gazillon problems – I’ve decided to use a school map.  I ran a copy of grid paper on a transparency and overlayed on a map of school – copied, added a rough set of axes.  Placed points throughout.


Questions range from:

  • Calculate the distance between Room 137 & Room 114.
  • Find the coordinates between Room 137  & Room 114.  What room are you closet to at this point?
  • Connect Ag, Kitchen, Cafeteria & Workshop.  What type of quadrilateral have your formed?  How do you know?   Prove it.  We have not covered types quads – but they can use their BYOD to find this information if needed, right?
  • Connect Library, Room 128, Room 116 and Room 114.  Is it a rectangle?  Or a square?  (LOL) How do you know.  This always comes up in discussion – I must say I love the “disagreements”.
  • Connect Room 145, Room 142 and Band.  What type of Triangle have you created?  How do you know?  Prove it.
  • Connect the Gym, Library and Tan Hall – Find the perimeter & area of this triangle.
  • What about having them “map” out their schedule and calculate “as the crow flies” distances between their destinations.

Anyone else have better ideas?  Other uses for this?

I’m thinking it was @k8nowak who did a scavenger with other geometric concepts.