By Derrick Brown (follow on Twitter @dbrowndbrown)
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Rigid Transformations: A Lesson on Movement and Growth (785 Words)
By Derrick Brown (Join Our Mailing List!)
In geometry, a rigid transformation is simple enough to define … you can slide, flip, or rotate a figure, but its size and shape do not change.
What begins as a triangle ends as a triangle.
Same length.
Same angles.
Same measure.
Different position … same object.
Today’s lesson on translations, reflections, and rotations became more than math. It became metaphor.
The Triangle Shuffle
As I stood before them, I introduced my classes to a large triangle … one that belonged to my high school geometry teacher.
I glided across the floor while holding it … using a dance move called the “shuffle.”
A translation.
The classroom chuckled.
A few students rolled their eyes, but they were listening.
That shuffle was not just a movement across the grid.
It was an invitation to see math … and themselves … differently.
Mirrors and Windows
Next, I flipped the triangle across the x-axis.
“Reflection,” I said.
Then I pushed deeper … “This is like looking in a mirror … or like looking
through a window.”
The room was still for a moment.
Reflections force us to ask … what do we see in ourselves, and what do we see in others?
At its best, teaching is always about both.
360 Degrees of Trouble
Then came the part that always gets a reaction.
I rotated the triangle in a full circle.
“Now imagine your boo tries to appease you by saying, ‘I’ll change. I’ll do a complete 360.’
What should you do?”
Without missing a beat, CW in first block and KS in third block shouted, “Run!”
The class erupted.
Then I said … “Exactly. Because they just told you they’ll go through the motions, but stay the same. They will put on a whole show … but will not grow.”
That joke, wrapped in humor, was really a lesson.
A rigid transformation can move you around.
But if you do not change inside, you are still the same figure … same angles, same lines, same struggles.
The Work Session
The rest of the day was less glamorous.
Students struggled to plot points, manage integer arithmetic, and follow transformation rules.
The Desmos Transformation Calculator I designed became both a scaffold and a mirror … some used it to get started, while others used it to check themselves.
My message was simple … “If you learn to use it well, you may discover you do not need it. That is a good thing.”
As we checked on our Unit 2 Test grades, some students pleasantly surprised me.
ZV’s quiet competence earned her public praise, and her face lit up.
SW glowed when her work was acknowledged.
Even JS, who resisted checking her test score, eventually sat beside me, listened, and nodded.
That moment of reconciliation … silent but sincere … brought me peace.
Even in rigidity, there was movement.
My Own Reflection
Rigid transformations are not just math.
They are my life in the classroom.
I move from one lesson to another, from one year to another, from one set of students to the next.
But what has changed in me?
Am I just rotating through routines, or am I actually transforming?
I am in my “last days” as a high school teacher.
The murmurs, the boundary testing, the administrative meddling and performative leadership … it is all weight I no longer want to carry.
Yet moments like today remind me that even if I am weary, the work still has meaning.
Students laugh at my jokes, roll their eyes at my metaphors, struggle through their problems, and … once in a while … thank me with silence, humility, or joy.
That is enough to keep showing up, even in the rigidity.
Lessons Beyond the Classroom
Rigid transformations teach three truths that matter beyond math:
1. Movement is not growth. You can change your position without changing your nature. True transformation requires more than a 360-degree rotation.
2. Tools are scaffolds, not crutches. Calculators, metaphors, even teachers—we all help students start, but the goal is independence.
3. Recognition reconciles. Sometimes, the smallest acknowledgment … public praise, a private nod … moves a student (and a teacher) more than a great lecture ever could.
Closing the Circle
When I asked students to describe the final position of the triangle after a 360-degree turn, they eventually said … “It’s in the same place it started.”
That was the “math” answer.
But it was also the “life” answer.
Sometimes we rotate in circles.
Sometimes we put on “shows” of change.
Sometimes we return to where we began.
The question is not whether we have moved.
It is whether we have grown.
And in that silence between my students and me today, I felt the whisper of an answer … even in rigidity, there are glimpses of transformation.
Selah.
(The "Follow The Leader (changED - Volume 2)" Audio and Video Album / Mixtape is also available at TeachersPayTeachers.com)
(The "changED (Volume 1)" Audio and Video Album / Mixtape is also available at TeachersPayTeachers.com)
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I am a “standup storyteller.”
I fuse rap, spoken word (poetry), oration (traditional public speaking), singing, and teaching into messages of hope, healing, and change that I write, direct, and produce to help people who help people.
Everything must change - and stay changED.
Tradition begins and ends with change.
Change begins with me and the renewing of my mind ... then continues through efforts to effect small-group discipleship (equipping others to equip others) with audiences that respect and embrace mentoring, mediation, and problem solving as tools of change.
I am the product of my mentoring relationships, peacemaking (and peacekeeping), and problem-solving ability.
My education began when I finished school.
After school, I enrolled in a lifelong curriculum that includes classes in ministry, entrepreneurship, stewardship, literacy, numeracy, language, self-identity, self-expression, and analysis / synthesis.
My projects execute a ministry that has evolved from wisdom earned through lessons learned.
I want to share this wisdom to build teams of "triple threat" fellows - mentors, mediators, and problem solvers.
We will collaborate in simple, powerful ways that allow us to help people who help people.
I now know that power is work done efficiently (with wise and skillful use of resources, interests, communication, and expertise).
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