Category Archives: July14 Challenge

Circles Part 2: Angle Relationships


Once similarity intuition has been built with circles, we can start getting into more specific relationships with angles and segments.  This post will look at using visual information from central angles and inscribed angles.

Pi Charts

Students sometimes lack intuition for the measure of something.  Andrew Stadel has developed this idea into a thorough curriculum on estimation. In my classes we started reasoning through similar exercises.  Once we had a decent understanding of circle parts and whole, we moved on to other types of angles.

Non-Central Angles

At this point most students have the common sense that a circle has 360 degrees, and a triangle is half that at 180 degrees.  Built with this intuition in mind, we look at a triangle created by inscribed angles.

The next day we get to see the formula that collapses 3 ideas down to 1.

Dynamic Angles in…

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Circles Part 1: Similarity Intuition #JulyChallenge2014 5/31


All circles are similar, right?

Okay, maybe it’s not given.  In fact, it needs to be proven.  This proof is yet another that is so easily demonstrated with dynamic math tools (like desmos and geogebra

Circle Similarity with Desmos

So long as you can move one center onto the other (translate) and dilate one radius to equal the other, similarity is achieved.  This works for every circle.  The perfect proportional balance achieved with circles lays the foundation for most of not all relationships found in them.

Proportional Measures

Similarity gives us a simple system for comparing measures in multiple figures.


You can even explore this with repetition of congruent triangles:

Dimensional Analysis with Scale


Below are a couple of applications that push further with exploring the measures of circles, proportionality, and relationships in the measures.

Pizza Pi 

This activity was first inspired by a posting on John Stevens‘ website .  It looks at proportions…

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What’s Your Short Term? #JulyChallenge2014 4/31

I just spoke with my brother, @jakebutler, just catching up on the latest. We eventually go into a conversation about concept development, and how it accelerates as history progresses.  The gist was something like Moore’s law applied to the topic of impactful ideas.


A standard long term example he posed was the idea of language and documentation, tracing from spoken, to written, automated, then digital, and now multimedia.  The next big thing comes faster than the last, and sometimes it feels like we’re always playing catch up.  My brother works for an awesome company based out of Boston that focuses on a lot of the social aspects of healthy living, especially in the realm of technology integration.


He told me that they have long term goals, but when it comes to comprehensive and detailed planning, each of their sub teams never looks further out than 2 weeks.  We started applying this format to technology in general and I in turn added the context of education and #edtech.  For the most part, I would argue (as would my brother) that successful technology enhancements have gone away from the secret projects behind closed doors that take at times years to reach a level worth any public reveal, and instead have more of a micro step process.  Upgrade a few things, and often.  The short term plan to update and implement smaller, more frequent changes has been a necessary adaptation to the accelerating progress of technology in general.

As teachers are upgrading their curriculum and technology for near future integrations I think we need to consider the value of this short term cycle.  Instead of having an entire year planned out to the day, we can maintain long term bench marks with the intention on updating our planning through small frequent upgrades.  I doubt that teachers trying to implement formative and interactive technologies in the classroom would have predicted the introduction of @peardeck (read more here).

This hard for an educator to manage.  We already have plenty on our plate between and the hard requirements and soft skills necessary to achieve them.  If a teacher truly wants to match the current culture of technology and conceptual progression we need to have an appropriate design for our planning.  We need to anticipate the change and build in the flexibility so that we can adapt on the fly.

I don’t know if I’d take it as far as this guy…

…but refusing an adaptive attitude is assuming we can predict the future of every step in growth of our students.  And that sounds silly.


I’d love to hear how others have integrated this adaptive planning, with small frequent updates, into their classroom planning (tech and non-tech contexts)

Teacher Cook #Julychallenge2014 3/31

Teaching is like [fill in the blank]

This is just one more to add to the pile, and I’d like to throw my in my thoughts from last night.

Just as I was wrapping up #ggbchat last night, I started to turn my attention to dinner . After dinner I made some awesome blueberry coffeecake for the morning. This coffeecake is a common recipe for my family passed down from my mom who stole it from the side of a box back in the day.
This recipe is so familiar that I never look it up anymore. I also don’t use exact precision in the measurements for flour, sugar, spices and powders. I know about how much to use, and I kind of like not being exact.

Then I thought about teaching. The first time you try a recipe, it’s good to have plenty of detail and structure. As we get better in facilitating the experience, simmering the students into something awesome, we can take some liberties (pun intended for tomorrow’s celebration). In fact, without trying some experimentation, even delicious food can progressively become more bland. So I encourage the teachers out there to experiment with their recipes, and also appreciate that we even have such recipes.

Best of luck as you cook up something good.

Start – Stop – Continue 1/31#MTBoS

Just read about a blogging challenge for the month of July.  I tried this with #MTBoS30 and only got up to 12.  This time around I’m going to divide and conquer across four blogs I have various levels interactions with:, DailyDesmos, and #ggbchat.

For post 1 of 31, the theme is a derivative from others and it focuses on the past, present and future goals with 3 items for each of the Start, Stop, and Continue theme.


  • Desmos API:  I am so excited about this one.  I’m a huge fan of @geogebra and @desmos (and pretty much any other dynamic math visualization tool).  After an open invitation from Chris Lusto, I’m excited to learn from others.
  • Books: I read one book this summer so far.  Looking forward to the next.  There’s something about the raw nature of a book that balances out my passion for and interaction with technology (my wife would probably say it leans more toward addiction).
  • Cross Curricular: Late in the year this last season of school, I spoke with a science teacher about integrating geogebra applets into a physics setting.  There’s too many overlaps with math and science NOT to exploit the potential collaboration opportunities. With the CCSS Standards for Mathematical Practice we are also seeing an increased focused in constructing arguments, organizing evidence, and making sense of problems.  These type of frameworks lend to collaboration with Humanities.  This conversation of cross curricular collaboration is too far overdue.


  • Driving (as much as possible): My car, a lovely Buick that has passed from my grandparents, to my great aunt, and now onto me, is nearing it’s end.  I only live 6.5 miles from work.  There is also a Super Target less than a mile away.  I like to ride my bike, and I feel like I don’t show it the love that it deserves.  Time to stop driving (when possible) and start riding more.
  • Frustrations with Growing Pains in CCSS: There is plenty of argument and frustration with the changes in education.  Progress and growth doesn’t jive well with those who have established systems in place.  Education is a continual evolution that I’ve learned to embrace.  Those that resist this change often take plenty of shots at new ideas.  I will concede that new ideas without proven track records can be a gamble.  However, I feel that the mantra, “If it ain’t broke, don’t fix it” has little place in education.  I feel it’s better to apply a growth mindest and look at education as “Don’t knock it till to try it.”  Learning that something doesn’t work is still learning, and that should be our focus, learning.
  • Playing Candy Crush: Level 140 has been stuck on my phone for a month.  Seriously, why do I continue.  I’m done.


  • CCSS: it’s not that I have to re-learn math, or teaching, or learning.  This label is probably overused if nothing else.  I look at recent transitions in education, especially in math, and am glad for the increased coherence and creativity.  My most recent ambition is learning more about the progressions.
  • Geogebra:  Recently a group of colleagues and I started a #ggbchat on twitter.  I’ve only been using this software for about a year, but the potential has only grown the more interactions I have with it.  I plan to get more organized with my work, especially in ways that makes the applets more user friendly for students.
  • #MTBoS: OHHHH, EMMMM, GEEEEE.  If you’re reading this post, hopefully you’re already aware of the gold mine that exists out there on the net.  Get plugged in, buckle up, and try not to blink.  You will be overwhelmed, and it will be awesome.

So now, your turn: What do you plan to Start, Stop, and Continue?

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