Unit 1 - Geometric Transformations

During this unit, students will begin to develop detailed definitions. The work they will do will help them to explain the geometry in the world around them, communicating to solve problems. Geometric Transformations can be found in many careers, and I often take the time to point them out as often as possible.

  • Week 1 – Definitions (G.CO.A.1 & 2)
  • Week 2 – Rotations, Reflections, and Translations (G.CO.A.3, 4, & 5)
  • Week 3 – Congruence (G.CO.B.6)

Common Core State Standards for Mathematical Content

Congruence — G-CO
A. Experiment with transformations in the plane
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on
The undefined notions of point, line, the distance along a line, and distance around a circular arc.
2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs.
Compare transformations that preserve distance and angle to those that do not (e.g., translation
versus horizontal stretch).
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections
that carry it onto itself.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,
e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that
will carry a given figure onto another.
B. Understand congruence in terms of rigid motions
6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid
motions to decide if they are congruent.

Common Core State Standards for Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.

 

Unit 1 - Geometric Transformations

 

Creating A Visual Dictionary for Geometry Vocabulary

Moving to the Common Core for Geometry.

High school geometry students are expected to know far more than they used to. Curriculum standards that used to be taught at the high school level have been moved to advanced 6th and 7th grade.

Your students are “expected” to know many geometry terms when they enter your class, which is why I recommend starting the year with the Visual Dictionary project.

Creating the Visual Dictionary

The goal of this activity is to understand what the students retained and what would I have to re-address.

Your students can use tablets or computers for this project, but technology isn’t required.

The Project

The students are placed in groups of two, so they can learn to start working in groups at the beginning of the year.

Acute angle - Geometry

A real-world example of an "acute" angle.

They have a list of about 25 words. For each word, they have to find a mathematics definition and a real world picture of the word. One teacher I know had one student sign out a camera and take the pictures, which turned into a cool final result.

Give the students about a day and a half in class and five days overall. That amount of time gives the students the opportunity to produce quality work and to really be creative.

Once the projects are complete, they upload the pictures to a tool like Glogster, Prezi, or Google presentation. Then you can refer to the projects the rest of the year when you are working on specific standards and vocabulary.

The following week, you can share all of the pictures with the class so all of the students can see what other groups found.

Vocabulary is so important for students to know, use, and understand, the two in-class days for this project are definitely worth it.

 

 

π Day is coming!

I love pi day.

This past Christmas I received a π cake mold from my oldest daughter. She knew I would love it and she was right! (I added a link to it below. It works great!)

I celebrate the pi day at school and home every March 14, so imagine the fun I have put this day together.

The following video begs the question, how many dominoes is that? Spoiler alert: the second (needed information) and third act (the answer) are at the end. This would be a great way to begin class.

Pi Day In Math Class

Is there any better day in the life of a math geek? Ok, that might be a little bit of an exaggeration, but it is a very fun day to be a math teacher.

In my class, we always eat pie on pi day. The kids bring it in, and I supply the cups, juice and paper goods. We always have a great time discovering the ratio of pi and enjoying the wonder of the randomness. The students always seem to gather interest in the wonder of numbers. Isn't that what it is all about?

The class is set up as stations with different activities depending on the mathematical level of my students. When they walk in, I am playing Pi Songs. They circulate through stations ranging from creating the music pie to measuring and finding the common ratio of pi, to pinning the tongue on Einstein. Don't forget that he shares his birthday with pi! And of course, the end of class has a memorization of the pi contest.

I always want to try something new with pi day and therefore have made necklaces by assigning each digit a different color bead, found our birthdays within pi and we have sung pi day songs. The next day, when the sugar buzz has worn off we discuss what we discovered and observed, the kids always amaze me at how much they take away from a day that would look like nothing more than high school kids at recess. I hope they have great memories of Pi day and a deeper understanding of pi.

There are some great resources online. Some of my favorites are below

Do you have a favorite π day activity that you do with your students? Please add it to the comments below! Thanks!

Interesting find while searching online 
To type the π symbol, you can use your number pad on your keyboard. Hold down the alt key and type 227 on your number pad. Let go, and you have a pi symbol. Amazing. For more helpful tips on inserting math and science symbols into your documents, you can see my list here.