My Geometry Course

This work by Andrew Shauver – Ingham Intermediate School District is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Some highlights from our instructional video website

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Intro: I taught geometry from 2008-2014, here are some sample lessons that I use to lead my students through the learning of geometry. Since that time, I continue to search, find, explore, and post any new and dynamic ideas I see in classrooms. So, recognize that this page is always… ALWAYS… under construction. So check back again another time and there might be something new up here.

Our geometry course is aligned to the Common Core State Standards as is required by the state of Michigan. Anything I post here is creative commons licensed and free for you to use. If you should take something and improve upon, please send it back. I like my stuff, but I love great stuff regardless of who makes it.

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I’m really glad you’re here: I look forward to you exploring the different activities. Also, I really, really encourage stuff like THIS from Dan Burfeind. Or THIS from Jennifer Wilson. When you use something you find here, share, share, share! The more of this stuff that gets used, the better it will get! We’re all on the same team, here.

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A word about PROOF: When I arrived in my math classroom in 2008, Geometry was one of the most universally-hated classes at the high school where I taught. Proofs were a huge reason why. I set out to change that and we made some significant progress. You’ll see our philosophy on proof permeate lots and lots of the activities that appear below, largely because we believe that good proofs don’t start getting written until the structure and purpose are really internalized by the students. But, it would be unfair of me to not give you a chance to further explore our thoughts during the transition. So, here are two posts that I wrote during those stretches that can give you a window into our thinking.

Proof and Consequences from October 2013

Proof: The Logical Next Step from Nov 2012

I also feel like it is okay to use measurements tools as proof at the beginning of the process. Here’s a bit on that: When measurement is okay… from Dec 2012.

Let me know (andrew.shauver@gmail.com) if you have any questions or want to see any more examples or discussion on the way we used and taught proof in our geometry class.

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Dan Meyer and Desmos: Some activities will have the term “3-Act” next to it. That is a reference to a lesson design model describe by Dan Meyer. It would be helpful if you read this short article as an introduction to 3-Act Activities if you don’t have any experience with them. In a couple of places, you’ll see me reference activities called “Desmos Polygraph”. Here’s a little introduction to those activities.

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A word about Instructional Tech: I taught in a 1:1 classroom and that means that I got comfortable with a fairly wide variety of teaching, learning, assessment, and presentation technologies. I summarize these in my ongoing “Instructional Tech in Under 3 Minutes” podcast. (They’re short on purpose. No one has time for a long podcast.) Check those out for ideas on how to build experiences for your students.

                                                                                                                                                                  

All right, ready? Here’s we go!

Day One: Best Circle (from Dan Meyer)… although I use this a little bit differently. Because it’s Day 1, I don’t necessarily lead toward maximizing-area-per-perimeter, which is the direction that Acts II and III lead. My goal is simply to get the students having conversations about what a circle is, what ways there are to verify the “betterness” of one attempted circle against another, and converting definitions and ideas into actions with results we could use to make decisions. It usually makes for a darn good hour.

Unit 1 – Introduction to Transformations

Disclaimer: You pick where you think it will fit best, but during this unit you absolutely MUST do Dan Meyer’s Magic Octagon with your students. It’s a must. It is too wonderful an opportunity to let slip through your fingertips.

Introductory Vocabulary Exploration (complete with a Google form to gather the collaborated responses, also, for some of the trickier vocab words, Wordle can help a bit. – Mrs. Sheila Orr used Wordle for her vocab exploration.)

Activator for Reflections

Activator for Rotations – Circles from Cedar Street – Possible solution using Geogebra

Introduction to Transformations (featuring function notation)

Rotations and Reflections (Check out how Dan Burfeind used this handout)

Rotation Practice and Reflection Practice

3 -Act Best Reflection

Reflections in the Coordinate Plane (using Desmos)

Desmos Activity Builder – Reflections (Excellent from MathyCathy)

Desmos Activity Builder – Pizza Delivery (Excellent from Scott Miller)

3-Act Best Translation (Act I) (Act II and Act II) (Act III)

3-Act Best Rotation (Act I) (Act II and Act II) (Act III)

Transformation Vocabulary Exploration

Transformation Polygraph (Desmos – Excellent from Julia Finneyfrock)

Transformations Figures onto Themselves

 

Unit 2 – Rigid Motions and Congruence

Rigid Motions vs. Non Rigid Motions

Congruence and the beginnings of proof

Tips for Proving Rigid Motions

 

Unit 3 – Angles, Triangles, and Parallelograms

Desmos – Laser Challenge

Putt-Putt Golf Problem (excellent from Fawn Nguyen)

3-Act Best Midpoint (excellent from Dan Meyer)

Investigating Lines and Intersections

Divisible by 3 – Transversals, Tape, and Stickies

The Pizza Delivery Problem (Thanks Illuminations)

Desmos Polygraph Polygons (Excellent from Ryan Brown)

3-Act Best Triangle (excellent from Dan Meyer)

3-Act Hershey Bar Problem

Investigating Triangles

3-Act Best Square (excellent from Dan Meyer)

Parallelograms in the Coordinate Plane (Using Desmos)

Investigating Parallelograms – (Dan Burfeind put this one into action)

Movin’ In Problem

Desmos Polygraph Basic Quadrilaterals

Desmos Polygraph Advanced Quadrilaterals

Desmos Polygraph Hexagons

 

Unit 4 – Triangles and Similarity

Student-made Video Solutions Guide to Unit 4 Practice Test

The Snickers Problem

The Giant Flip-Flop Problem

Introduction to Dilations (Original Handout)

Working with Dilations (Desmos – from Mr. Rothe)

Dilations Practice

Connecting Dilations to Similarity (coordinate-heavy)

Angle-Angle Similarity Practice

Intro to Triangle Proportionality Theorem

Scale Model Floor Plan

 

Unit 5 – Trig or Treat

Introduction to Special Right Triangles 

3-Act Boat on a River (Excellent from Andrew Stadel)

Introduction to Trig Ratios

Right Triangle Trig Review (with Kahoot! Quiz to go with it… I explain it here.)

Practice on Special Rights with Sine and Cosine (Geogebra – Designed by Sam Shah)

Midterm Review Kahoot! Midterm Review Quiz

Wouldn’t it be cool if your students made THIS as an assessment?

 

Unit 6 – 3-D Geometry

3-Act Filing Cabinet (Excellent from Andrew Stadel)

Cubes and Prisms with KEVA Planks

You Pour, I Choose (Excellent from Dan Meyer)

Intro to circles (including π, area, and circumference) and cylinders (including volume and surface area).

Ritz Cracker Problem, Episode I.

The Wedding Cake Problem with a possible alternate hands-on version and also a possible Desmos extension.

Problem-Solving with Spheres, Cylinders, Cones, and Pyramids

Spinning Rings and Coins

 

Unit 7 – Circles

Desmos Activity Builder – Measuring Circles (Excellent from Kate Nowak)

NPR wants to advise your pizza order… (with possible literacy activity using NPR article linked in the post)

The Hovering Circles Problem (inspired by @jamestanton)

Introduction to Similarity of Circles

The Grill Fries Problem

The Art of Mathematics: Kolams

Geogebra Activity – Arcs and Angles Exploration

How Radians Work (Video File tweeted by @ThingsWork)

 

Unit 8 – Year-End Wrap-Up

Wrap Battle (Discussed in Designing Engagement and Collaboration)

The Lake Superior Problem (discussed in Multiple Approaches to The Lake Superior Problem)

This work by Andrew Shauver – Ingham Intermediate School District is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.