Author: cardenad

Statistics and Probability According to the Common Core Standards

cardenad CCSS-Math Learning Progressions, HS Statistics & Probability

This learning progression is a focused on statistics and probability in a 7th grade middle school mathematics classroom. There are many ways probabilities can be taught, this progression will use models and data collection. There are three levels of functions that are taught at the high school level: Compare probabilities from a model to observed frequencies, Develop a uniform probability model by assigned equal probability to all outcomes and use the model to determine probability events, and Develop a probability model by observing frequencies in data generated from a chance process. Probabilities describe the extent to which something is probable; the likelihood of something happening or being the case. In the progression of Interpreting Statistics and Probability students learn how to understand and develop probability events, how to observe and  interpret collected data, and formulating questions, designing studies, and collecting data about a population through random sampling allow us to make inferences and compare data.

 

Learning Progression-Probability Modeling Statistics and Probability Lesson Plan

Functions and Sequences According to the Common Core Standards

cardenad CCSS-Math Learning Progressions, HS Functions

This learning progression is a focused on functions in high school mathematics classroom. The many ways functions can be taught, how discrete this concept is, and the understanding that this is a concept that will continue to show up in all respective classes. There are five levels of functions that are taught at the high school level: Introduction, interpreting functions, building functions, linear, quadratic, and exponential models, and trigonometric function. Functions describe situations where one quantity determines another. Functions usually have numerical inputs and outputs and are often defined by an algebraic expression. In the progression of Interpreting Functions students learn how to understand the concept of a function and use function notation, they interpret functions that arise in applications in terms of the context, and they learn how to analyze functions using different representations.

Learning Progression

Using Geogebra to teach Geometry

cardenad HS Geometry, Technology Teaching Issues

Incorporating technology into lessons has become a requirement for many curriculums. With technology evolving and being an influential part of a person’s everyday life. By incorporating technology into the classroom it sparks an interest in the students, no matter what grade level it is. Using technology to teach a concept also makes the class relevant to the students because they are moving away from traditional lecture classes. In a geometry class, students are experimenting with transformations in planes and learning the similarities in terms of similarity transformation. Several students struggle with geometry because they have issues visualizing the triangles and planes. By using Geogebra, this free application allows students to work with shapes and visualize planes.

Geogebra is available for free download at www.geogebra.org. The standard CCSS.Math.Content.HSG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Geogebra would be excellent to teach this standard because it allows students to create triangles, edit them, move them around and enhance them. By using this technology it allows visual representation of triangles as an alternative explanation. When students can visually prove to themselves that two triangles are similar or congruent it allows them to remember the concept long term.