The following learning progression is based on meeting the cluster on High School: Functions under ‘Understand the Concept of a Function and use Function Notation’ standard under the Interpreting Functions math domain. This cluster has been taken from the Common Core State Standards for Mathematics. The book where some of the activities or homework problems were taken from is called AGS Publishing: Algebra 2 by Siegfried Haenisch. The activities are focused on assuming this is a 10th grade class; however, this may vary.
Author: carmonma
Learning Progression for HS ‘Solving Equations and Inequalities in One Variable’
The following learning progression is based on meeting the cluster on Algebra under ‘Solving Equations and Inequalities in one Variable’ standard under the Reasoning with Equations and Inequalities math domain. This cluster has been taken from the Common Core State Standards for Mathematics. The book where I got activities or homework problems from is called Algebra I: Expressions, Equations, and Applications by Paul A. Foerster. The activities are focused on assuming this is a 9th grade class; however, this may vary.
Teaching a Specific CCSS for High School Students Using GeoGebra
Different types of technology are available these days. Students are more engaged and inclined to do work when it involves technology. Since students are surrounded by technology every day a lesson on technology would be more beneficial than a lecture. A type of technology that students will find engaging and interesting is GeoGebra. This is a free and interactive website for students to work with in geometry, for example. The link to download GeoGebra is the following:
http://www.geogebra.org/cms/en/
The following link contains tutorials on how to get started:
http://wiki.geogebra.org/en/Tutorial:Main_Page
The use of GeoGebra would be great for a lesson for high school students about circles in Geometry. The standard CCSS.Math.Content.HSG-C.A.3 states that students should be able to Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Using GeoGebra for a lesson on this could bring many benefits. To start off the lesson involves going to the computer lab, which is already exciting to students since class will be held outside the usual classroom setting. Students will feel motivated to do the work and experiment on their own.
On GeoGebra students can create, erase, and move around objects in a 2-dimensional plane to visually “prove” to themselves a property. The students’ learning will be enhanced because they will be able to move objects around by dragging them. Sometimes it is better to actually see inscribed and circumscribed circles in a triangle or a quadrilateral inscribed in a circle instead of just learning the steps to constructing them. The teacher can have students create a variety of diagrams using the “Tools” in GeoGebra. The lesson will be easier to teach since the teacher will have already caught their attention and students will feel confident and curious to learn more.
The teacher then, will be able to explain the properties of angles and how to prove them. She can refer to the work done on GeoGebra and ask students to explain their reasoning based on their experiments. Students will also be able to self-assess themselves by referring to their work done on this interactive site. Since GeoGebra is a free site, those students who need more time or want to keep “playing” with it, will be able to do so by downloading the software onto their computer. Lastly, GeoGebra is easy to use; each command has its own name such as “perpendicular bisector” or “parallel line”; thus, students know what the command will do. Therefore, teaching with technology has become easy, effective, and fun for students and teachers.