Mr. Cook's Geometry
Overview
In our ever-increasing technological world, a rich study of logic and mathematical proof is fundamental for reasoning and good decision making. The study of geometry offers students the opportunity to develop skill in reasoning and formal proof. Additionally, it helps students to describe, analyze, and recognize the underlying beauty in the structures that compose our world. Geometric thinking is a powerful tool for understanding and solving both mathematical and applied problems and offers alternate ways of reasoning mathematically beyond algebra, including analytical and spatial reasoning.
Geometry builds on a number of key geometric topics developed in the middle grades, namely relationships between angles, triangles, quadrilaterals, circles, and simple three-dimensional shapes. It is expected that students beginning geometry are able to recognize, classify, and apply properties of simple geometric shapes, know and apply basic similarity and congruence theorems, understand simple constructions with a compass and straight edge, and find area and volume of basic shapes.
Students studying geometry in high school further develop analytic and spatial reasoning. They apply what they know about two-dimensional figures to three-dimensional figures in real-world contexts, building spatial visualization skills and deepening their understanding of shape and shape relationships. Geometry includes a study of right triangle trigonometry that is developed through similarity relationships. These topics allow for many rich real-world problems to help students expand geometric reasoning skills. It is critical that connections are made from algebraic reasoning to geometric situations. Connections between transformations of linear and quadratic functions to geometric transformations should be made. Earlier work in linear functions and coordinate graphing leads into coordinate geometry.
The study of formal logic and proof helps students to understand the axiomatic system that underlies mathematics through the presentation and development of postulates, definitions, and theorems. It is essential that students develop deductive reasoning skills that can be applied to both mathematical and real-world problem contexts.
Throughout geometry, students experienced geometric thinking and reasoning techniques as accessible and powerful tools that can be used to explore the concept of mathematical proofs as well as to model and solve real-world problems. At the end of the year, students are able to put together what they have learned into one of two projects described below.
Geometry builds on a number of key geometric topics developed in the middle grades, namely relationships between angles, triangles, quadrilaterals, circles, and simple three-dimensional shapes. It is expected that students beginning geometry are able to recognize, classify, and apply properties of simple geometric shapes, know and apply basic similarity and congruence theorems, understand simple constructions with a compass and straight edge, and find area and volume of basic shapes.
Students studying geometry in high school further develop analytic and spatial reasoning. They apply what they know about two-dimensional figures to three-dimensional figures in real-world contexts, building spatial visualization skills and deepening their understanding of shape and shape relationships. Geometry includes a study of right triangle trigonometry that is developed through similarity relationships. These topics allow for many rich real-world problems to help students expand geometric reasoning skills. It is critical that connections are made from algebraic reasoning to geometric situations. Connections between transformations of linear and quadratic functions to geometric transformations should be made. Earlier work in linear functions and coordinate graphing leads into coordinate geometry.
The study of formal logic and proof helps students to understand the axiomatic system that underlies mathematics through the presentation and development of postulates, definitions, and theorems. It is essential that students develop deductive reasoning skills that can be applied to both mathematical and real-world problem contexts.
Throughout geometry, students experienced geometric thinking and reasoning techniques as accessible and powerful tools that can be used to explore the concept of mathematical proofs as well as to model and solve real-world problems. At the end of the year, students are able to put together what they have learned into one of two projects described below.
Origami Mobile Project: Some Assembly Required!
This project claims to “require some assembly”. This means that students must be able to create this origami mobile without the help of the teacher. For the rest of students’ lives, they cannot take a teacher out of the pocket and ask what to do in these situations. Instead, this project requires the following of instructions, collaboration of students, reverse engineering and all sorts of problem solving skills!
The purpose of this project is to make a sustainable mobile of origami solids that can be hung in my classroom. Paper for use will be provided but students were free to use their own paper if they think they can improve upon a current design. Ultimately, the mobile will have two main parts: the platform to hold all solids (this could just be the octagon star if made strong enough) and the origami solids themselves.
Below is a slide show of what students have created since the spring of 2010.
The purpose of this project is to make a sustainable mobile of origami solids that can be hung in my classroom. Paper for use will be provided but students were free to use their own paper if they think they can improve upon a current design. Ultimately, the mobile will have two main parts: the platform to hold all solids (this could just be the octagon star if made strong enough) and the origami solids themselves.
Below is a slide show of what students have created since the spring of 2010.
Digital Story Project
“Digital Storytelling” is the practice of using computer-based tools to tell stories. As with traditional storytelling, most digital stories focus on a specific topic and contain a particular point of view. However, as the name implies, digital stories usually contain some mixture of computer-based images, text, recorded audio narration, video clips and/or music. Digital stories can vary in length, but most of the stories used in education typically last between two and five minutes. The topics that are used in Digital Storytelling range from personal tales to the recounting of historical events, from exploring life in one's own community to the search for life in other corners of the universe, and literally, everything in between.
Purpose: The purpose of this assignment is for a student (and 1 partner if they choose so) to create your own 2-5 minute digital story. While the topic for your digital story is up to the student, I would like them to craft a story based on any subject that we have gone over in geometry from the year. The story could be based on how the student(s) made sense of a mathematical concept or it could be a story where the math that was used is a significant part of the story line.
Below are some digital stories created by students since the spring of 2011 to now. I hope to add a few more in the future!
Purpose: The purpose of this assignment is for a student (and 1 partner if they choose so) to create your own 2-5 minute digital story. While the topic for your digital story is up to the student, I would like them to craft a story based on any subject that we have gone over in geometry from the year. The story could be based on how the student(s) made sense of a mathematical concept or it could be a story where the math that was used is a significant part of the story line.
Below are some digital stories created by students since the spring of 2011 to now. I hope to add a few more in the future!