Defining Circles


There is a High School in the district I worked  in for my entire career that is notorious for putting math content questions on their list of interview questions if you are interviewing to be a math teacher there.  A favorite question of this type for many years (until word got out that they used this question) was, ‘What is the definition of Pi?‘.  Off the record and according to several people who were part of these interviews, more than half of all secondary licensed math teachers who applied struggled with this question.  They could talk about the number pi (3.14159….) & that this number is irrational.  They mentioned ‘Pi Day’ and named formulas for the circumference of a circle and the area of a circle, but when pressed for more they could say little.  How sad that so many math teachers struggle with a basic concept in mathematics.

I would say I was surprised by this lack of understanding, but I have my own evidence of math teachers lack of understanding of mathematical concepts.  We are addicted to teaching skills – we can talk all day about how to use pi in formulas, but we struggle to see and talk about it as a ratio (circumference to diameter) or anything else like this.  11 years ago I started a job at my district office as the K-12 math lead.  On a visit to a local alternative middle school I noticed a new math teacher hired was given room 314.  I said to her, “Lucky you, you got the Pi room”.  She looked at me and said, “What is pi again?  Is that the golden ratio?”  UGH!!!

Image result for palm face gif

Since I’ve learned of the HS’s interview questions and seen it for my eyes – math teachers lack of understanding of circles and ‘pi’, I’ve been on a mission to make sure my students would never have the lack of understanding some math teachers have around ‘pi’ and circles.

As you know, I believe our students are way more engaged when #mathMovement is a part of our classes.  My students move every single day.  I’ve written about numerous ways students move on my blog.

This post is about how I incorporate movement and mathematical discousrse into how I introduce the concepts of circles, pi and all the vocabulary connected to circles.  I use these same ideas if I am reviewing these concepts.  I’ve used this in Middle School when students first learn about pi and in High School Geometry and Trigonometry.  I would also use these ideas with elementary students.

My goal always to create the experiences in my classrooms so that students will SEE what I want them to SAY.  Below are THREE videos describing how I used movement to support my students mathematical discourse around circles.

Video 1 is about students defining circles!

Video 2 is about how you make the ratio of the circumference to the length of a circles diameter come alive!  (Hello Pi!)

Video 3 is about how I help students develop a circle vocabulary.

One word of warning – this blog post is a bit different.  To get all the information – you need to watch the videos below. 

Video 1 of 3:  What is a ‘Circle’?  – with Movement & Mathematical Discourse.

Watch this first video to see how I have all my students move to form a circle without ever using the word ‘circle’!

Watch this 1st video to learn about a really cool ‘Math Language Routine’ from the University of Stanford that incorporates #mathMovement!

Watch this video to see how students engage in discourse to build a definition of a circle.

Video 2 of 3:  What is a ‘Pi’?  – with Movement & Mathematical Discourse.

I have a love/hate relationship with Pi Day!  The hate part is seen in this tweet thread from Dan Meyer.

Too much of how Pi Day is celebrated is connected to low level memorization and not the beautiful relationships in Pi.  There are so many other wonderful things you could do on March 14th – than just memorizing digits of Pi.  If you need one small way to start this – Check out video #2 where I have students start to build an intuitive idea of Pi – you could expand the ideas in this video to really do something special with Pi.

In Video #2 you will see why having rope/yarn of 3 different colors can quickly help your students see the relationship between the circumference and diameter of a circle.

In Video #2 – it is all about ratios and comparisons!  Check it out….2 great ideas for building the beginning ideas of ‘pi’.

Video 3 of 3:  Circle Vocabulary  – with Movement & Mathematical Discourse.

Since most of my career has been teaching lots of Immigrant students and many others who have a low academic vocabulary – Video 3 is set up to connect Circle Vocabulary with Movement & Discourse.  The goal the entire time is for students to say the definitions for all kinds of circle words way before I say them.

BONUS – my favorite #mathFail is in this video.  It is one I got from the amazing Greta Bergman!

I hope, after watching these 3 videos, you have lots of ideas to build into your practice #mathMovement, having students engage in discourse (they say it before you do) connected to concepts – and in the case of this blog – the concept is ‘CIRCLES’!  If you like adding movement connected to mathematical concepts into your classroom and want more ideas – comment below and say ‘Sara, I want more!’.  I have more ideas for you on lots of other topics.

Teaching Circles

When you start getting ready to teach circles – make sure you are using resources that are conceptually rich.  I love, love the Illustrative Mathematics Materials.  Check out 7th grade Unit 3 and Geometry Unit 7 on Circles.  See the button below to download links to rich curriculum.  I also included an oldie but a goodie and connected you to the IMP curriculum’s resources on Circles – again, click the button below for more.

Here is one small curriculum teaser for you.  IM has a movement activity on day 3!  It is similar to my videos above but for defining ‘perpendicular bisectors’….so, so good.  Check it out HERE:  Illustrative Mathematics (IM) HS Geometry, Unit 1 Lesson 3 Activity 2 – Human Perpendicular Bisector (as found at Kendall Hunt website)


If you would like the power point I used in the 3 videos above – or resources on ‘Math Language Routines’ or get links to conceptually rich curriculum for Circles – CLICK the button below to gain access to a Google folder full of resources for you!

Click HERE to gain access to a Google folder of resources about Circles, Movement and Discourse.

How are you using #mathMovement do review or introduce mathematical concepts like ‘Circles’ in your classroom? Comment below or tweet at @saravdwerf or using the hashtag #mathMovement. I’d love to hear your ideas and/or questions.

CLICK the links below for more movement ideas for your classroom.
Sara VanDerWerf

I am Sara Van Der Werf, a 24-year mathematics teacher in Minneapolis Public Schools. I have taught math in grades 7-12 as well as spent several years leading mathematics at the district office. I currently teach Advanced Algebra at South High School and I'm also the current President of the Minnesota Council of Teachers of Mathematics (MCTM). I am passionate about encouraging and connecting with mathematics teachers. I'd love to connect via twitter.  Join the community.  Tweet me @saravdwerf.

Click Here to Leave a Comment Below 4 comments