Standard+Equation+of+a+Circle+(High+School+Algebra+2+-+Geometry)

Contributing Teacher(s): Mrs. Nicole Hardison
Resources:

Content:
CLE 3103.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. CLE 3103.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution. CLE 3103.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies. CLE 3103.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models. 3103.3.20 Understand the relationships between the equations of conic sections and their graphs. SPI 3103.3.11 Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph.

ISTE Technology:
Students apply digital tools to gather, evaluate, and use information. Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students demonstrate a sound understanding of technology concepts, systems, and operations.

Introduction/Problem:
I would like to students to explore each of the following conic sections, circle, ellipse, parabolas, and hyperbolas.

Procedures:
Here is an attachment for Worksheet A that the students will use in this lesson.

Step 1 - The students will watch the following Video -Conic Sections once the students finish watching the video they should be able to define how each conic sections is made. The students can now answer the questions 1-4 on Worksheet A.

Step 2- For this lesson we would like to focus on the circle. The students will go to the following website to write down what the standard form of a circle. [|Circle- Standard Form] They can write this on Worksheet B under question 1.

Steo 3- The students will then go to a circle applet where they can explore the properties of the standard form of the equation of a circle, They will be able to form an opinion, investigate, and test their conjunctures to see if they can understand each part of the circle. The students can now continue to work on Worksheet B. Here is a copy of Worksheet B

Step 3- At this time the teacher will discuss with the students the formula and what each part of the formula represents and how it effects the circle.

Step 4- The student will go to the following page interactmath practice and answer the first 7 questions about writing the equation of a circle. They can answer this question on the bottom of one of their worksheet B to save time.