Monday, April 11th, 2011

More than One way to Slice a Cone

Objective: Learners will be better able to identify the various conic sections and where they originate from. 

Standards met:  G1.7.2 Identify and distinguish among geometric representations of parabolas, circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones.

Materials: computers, question sheets

Instructional Sequence:

Attendance and Settling in (5 min)

Slicing a Double Cone (15 min)

First in small groups then together as a class, students will discuss what sort of shapes slicing a double cone could create.  We will generate a list of possible shapes and provide names for any new shapes. 

Computer Investigation (40 min)

Students will then work in pairs on the laptops exploring what is needed to make each of these shapes.  They will answer a series of questions on each curve in the process.  During this time I will circle and observe student work picking out the groups that I want to ask to present their solutions in the next portion of class. 

Break (5 min)

Group Debrief (25 min)

I will ask different groups to come forward and demonstrate what they learned using the projected computer screen.  This will include four groups since there are four shapes.  Other students may pose questions to the groups at this time and if they do not then I will.

Homework: 10.1 (18, 20, 29, 30, 33, 49)

Tuesday, April 12th, 2011

Patty Paper Parabolas

Objective: Learners will be better to write and transform equations of parabolas and draw parabolas given a foci and directrix. 

Standards met:  A3.3.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate information.

A3.3.2 Identify the elements of a parabola (vertex, axis of symmetry, direction of opening) given its symbolic form or its graph, and relate these elements to the coefficient(s) of the symbolic form of the function.

Materials: quiz, patty paper, parabola folding handout   

Instructional Sequence:

Attendance and settling in (5 min)

Homework Questions (≤15 min)

Students will have a chance to pose any homework questions from the night before in preparation for the quiz.

Quiz (5 min)

10.1 (30)

Parabola Basics (10 min)

Before beginning the activity we will go over the basics of parabolas including the definition, the general equation, and the basic shape.  This should all be a review from Algebra B, but I want to go over it again to make sure everyone is on the same page. 

Break (5 min)

Patty Paper Parabolas (40 min)

Students will work though an investigation where they are folding patty paper to make a parabola and answering questions.  These questions will lead them through proving the shape they have made is a parabola and derive the equation of an untranslated parabola. 

Debrief (≥10 min)

This tile will be used to make sure that everyone reached the same point and then we will look at the general form and identify the translations. 

Homework: 10.2 (36, 39, 45, 56, 58)

Wednesday, April 13th, 2011

In a Round About Way

Objective: Learners will be better able to write equation for circles and ellipses and describe the difference between the two. 

Standards met: G1.7.1 Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius.

G1.7.3 Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations.

Materials: quiz, string, tape, tacks, paper, pencils, misc. classroom supplies

Instructional Sequence:

Attendance and settling in (5 min)

Homework Questions (≤15 min)

Students will have a chance to pose any homework questions from the night before in preparation for the quiz.

Quiz (5 min)

10.2 (36)

Circle and Ellipse Basics (30 min)

I will go over the general equations, definitions and basic shapes of each of these conic sections before we begin.  This will likely be a review for circles, but new for ellipses and our definitions are more precise this time in both cases.  Then we will use the definition of a circle to create several methods of drawing a circle.  Going into the next portion I will challenge students to use the definition to do the same for an ellipse 

Ellipse Compass (30 min)

Students will work in small groups using the definition of an ellipse to find a way to draw one accurately.  I will offer suggestions and guidance if they are stuck.  Students may use any of the classroom resources to complete this task. 

Regroup (≥5 min)

This is just a chance to make sure that students are finishing up and got what they needed out of the activity today and have a successful group explain what they did. 

Homework: 10.3 (39, 45, 54, 68) 10.4 (34, 39, 41, 44, 56. 65)

Thursday, April 14th, 2011

Hyperbola Magic

Objective: Learners will be better able to draw hyperbolas, write their equations and describe real world events that would create them. 

Standards met: G1.7.3 Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations.

Materials: quiz, CBR’s, calculator cords, lab handouts

Instructional Sequence:

Attendance and settling in (5 min)

Homework questions (≤15 min)

Quiz (5 min)

10.4 (56)

Lab Description (10 min)

I will explain the lab and have a student help me model the activity before students try and complete it on their own. Because some of this technology is new I will have to show them how to set it up on their calculator. At this point I will also go over the basics of hyperbolas. 

Lab (30 min)

Students will work in groups to collect data and then find equation to fit that data. 

Debrief (≥25 min)

After making sure that all groups found an equation I will go over how to graph a hyperbola by hand.  We will try a few of these until the end of the hour. 

Homework: 10.5 (23, 28, 36, 48)

Friday, April 16th, 2011

My Favorite Conic Section

Objective: Learners will be better able to talk about a specific conic section in a variety of ways.  They will also improve their abilities to work with others as this is a group project. 

Standards met: none

Materials: quiz, project materials as requested

Instructional Sequence:

Attendance and settling in (5 min)

Homework questions (≤15 min)

Quiz (5 min)

10.5 (23)

Project Work Time (60 min)

Students will begin (or continue) work on their projects about a specific conic section.  I will check in on progress and answer any questions that arise. 

Reminders (≥5 min)

Before students leave I will remind them when this project is due and what is coming up next week.

Homework: none

Monday, April 18th, 2011

A Slide to the Left and a Step to the Right

Objective: Learners will be better able to translate equations of conic sections by using the general form of the equation

Standards met: A2.2.2 Apply given transformations to parent functions, and represent symbolically.

Materials: quiz, translation activity

Instructional Sequence:

Attendance and settling in (5 min)

Equations (10 min)

We will make a list of all of the general equations complete with spots for translation on the board. 

Translations and Practice (20 min)

A brief reminder on how to use h and k should be enough and then students will practice this with the translation activity

Break (5 min)

Project Work Time (50 min)

Students can continue and hopefully almost finish their projects from Friday.  Anything not completed today in class must be done as homework. 

Homework: 10.6 (26, 29-32, 37-39)

Tuesday, April 19th, 2011

Putting on a Show

Objective: Learners will be better able to present their knowledge to their classmates. 

Standards met: none

Materials: project evaluation cards, group participation sheets

Instructional Sequence:

Attendance and settling in (5 min)

Homework Questions (≤15 min)

Quiz (5 min)

10.6 (39)

Group Presentations (65 min)

Each group will give a 5-10 minute presentation of their conic section to the class.  They must also rate the other groups and evaluate the participation within their own group. 

Homework: none

Wednesday, April 20th, 2011

A Unit in Review

Objective: Learners will be better able to evaluate their understanding of conic sections and fill in any gaps that exist.

Standards met:

Materials: review sheet, practice problems

Instructional Sequence:

Attendance and settling in (5 min)

Final questions (15 min)

Review (70 min)

Students will work independently or in small groups to review for tomorrows test.  I will pass out a review sheet made from their projects with my additions and a set of practice problems.  Students may also use the time to make up missing work or prepare a note card to use on the test.  Note cards may be no larger than half an 8.5”x 11” sheet of paper and may be written on only on one side. 

Homework: none

Thursday, April 21st, 2011

A Final Test

Objective: Learners will be better able to demonstrate their knowledge of conic sections. 

Standards met: none

Materials: test

Instructional Sequence:

Attendance and settling in (5 min)

Last minute questions (≤10 min)

Test (75 min)

Student will work on the test until completed.  If they finish early they may do other work quietly or sleep until the end of the hour. 

Homework: none