Reflection for Presentations on 4/4/07

I thoroughly enjoyed the presentation on the manipulation websites. I found a lot of resources from the team's Wikki posts as well as their tutorials through the various sites. The team was very knowledgeable on their topic and had a very organized presentation. I could definitely see myself using manipulation devices in my classroom -- especially Geometer's Sketchpad. The team offered some useful tips on how to use the devices as well as how to implement them into the classroom. Since their presentation I have tried out some of the websites on their Wikki post and found them to be very easy to navigate through and have come up with some ideas on how to use them in a lesson.

Reflection on Presentations

The manipulation group did a great job of demonstrating the use of different sites and ways they could be integrated into the classroom. I really liked them because, not only do they have representation of mathematical symbols, as well as pictures and graphs to help students make connections and build understanding. One idea I had was going to the computer lab for manipulations once every other week or so. This will give students a chance for a change of atmosphere, and keep them more engaged. Also, by using the computers sparingly students will be more engaged than if they were being used every day.

Our Team's Map

Maps of our homes!



Lesson Ideas
--Students could pick a location and find the quickest route to get there.
--Students could use the Pythagorean theorem to find the shortest distance between two locations.
--Teachers could give students a particular radius or diameter around a given location, and students could list all the places they could go within that radius or diameter.
--Students could estimate distances using a scale.
--Students could locate the midpoints between two locations.
--This can be connected to latitude and longitude lines.

Technology Lesson Plan Ideas

Lesson Plan Idea #1

Target Audience: Algebra II Class

Big Idea: The big idea of this lesson is to introduce graphing technology and/or improve student ability with graphing technology

Goal: The goal of this lesson is to test the advantages and limits of using graphing technology with functions.

Standards: A1.4.1 - Graph a linear equation.
A1.8.1 - Graph quadratic, cubic, and radical equations.
A2.1.4 - Graph relations and functions with and without graphing technology.

Possible Resources: Algebra II Textbook, Graphing Calculator


Lesson Plan Idea #2

Target Audience: Geometry Class

Big Idea: The big idea of this lesson is to let students know how fun Geometer’s Sketchpad makes geometry.

Goal: The goal of this lesson is to introduce Geometer’s Sketchpad while transferring students’ knowledge of circumscribed angles and inscribed angles from paper to software.

Standards: G.6.4 – Construct tangents to circles and circumscribe and inscribe circles.

Possible Resources: Geometry Textbook, Geometer’s Sketchpad Software


Lesson Plan Idea #3

Target Audience: Pre-Calculus/Trigonometry Class

Big Idea: The big idea of this lesson is to let students have fun and communicate their ideas about trigonometric functions.

Goal: Goals of this lesson include: analyzing and examining appropriate methods of solution for trigonometric functions, practice manipulating trigonometric functions, and working in small groups to encourage peer discussion.

Standards: PC.3.1 Solve word problems involving right and oblique triangles.
PC.3.2 Apply the laws of sines and cosines to solving problems.
PC.4.1 Define sine and cosine using the unit circle.
PC.5.1 Know the basic trigonometric identity cos2x + sin2x = 1 and prove that it is equivalent to the Pythagorean Theorem.
PC.5.2 Use basic trigonometric identities to verify other identities and simplify expressions.

Possible Resources: Textbook, Handouts, Calculators, Transparencies http://illuminations.nctm.org/LessonDetail.aspx?ID=L383

Technology Lesson Plan Ideas

Lesson Plan Idea #1

Target Audience: 7^th grade math students

Big Idea: I am going to utilize CPS to help students review for a quiz. A jeopardy type game can be used so every student gets to practice their skills while still having the element of competition.

Goal: The goal of this lesson is to help students to review the material for their exam and to know what they still need to study for their exam.

Possible Resources:

• Textbook
• Internet

Lesson Plan Idea #2

Target Audience: Pre-algebra students (8^th graders)

Big Idea: The students are learning about relations in class. Relations can be represented as ordered pairs, on a graph or in a table. To have students check their graphing skills, graphing calculators are a perfect way for the students to see on a standard axis how the relation should appear.

Goal: The goal of this lesson is to have students represent relations in the three different forms and to utilize the graphing calculator to check their graphs.

Possible Resources:

• Textbook
• Internet

Lesson Plan Idea #3

Target Audience: Geometry students (high school)

Big Idea: Students will combine their knowledge of geometry and sketchpad to make an animated Ferris wheel. Students will practice their skills while doing something out of the ordinary. Let’s face it, geometry can get pretty boring so anything teachers can do to make it more interesting will help the students be more engaged in the lesson.

Goal: The goal of this lesson is for the students to have fun with sketchpad while practicing their geometry skills and applying their knowledge of sketchpad.

Possible Resources:

• Textbook
• http://mathforum.org/dynamic/jrk/ferris_dir/
• Geometer’s Sketchpad

Reflection #7

Lesson 1: Hitting the Bull’s Eye
Target Audience: 10th and 11th grade Algebra II students
Big Idea: To use graphing calculator technology to teach experimental probability and make connections with geometry and algebra.
Goal: The students will learn a different use of a graphing calculator other than to just graph and do arithmetic.
Standards:
A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.
A2.1.4 Graph relations and functions with and without graphing technology.
A2.4.1 Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).
A2.4.2 Graph conic sections.
Resources: Graphing calculators for class.

Lesson 2: Geometer’s Sketchpad
Target Audience: 9th and 10th grade Geometry students
Big Idea: Use Geometer’s Sketchpad to determine properties of quadrilaterals.
Goal: The students will visualize quadrilaterals in an engaging activity, and make conjectures about specific kinds of quadrilaterals and their properties.
Standards:
G.2.2 Find measures of interior and exterior angles of polygons, justifying the method used.
G.3.1 Describe, classify, and understand relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite.
G.3.2 Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.
G.3.3 Find and use measures of sides, perimeters, and areas of quadrilaterals. Relate these measures to each other using formulas.
G.3.4 Use coordinate geometry to prove properties of quadrilaterals, such as regularity, congruence, and similarity.
G.8.3 Make conjectures about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.
Resources: Geometer’s Sketchpad

Lesson 3: Exploring Linear Data
Target Audience: 8th and 9th grade Algebra I students
Big Idea: Use either a graphing calculator or the Illuminations website to construct a scatter plot and estimate/find the lines of best fit.
Goal: Students will be able to create meaningful data and use the data to describe a possible relationship between points in a scatter plot.
Standards:
A1.3.1 Sketch a reasonable graph for a given relationship.
A1.3.2 Interpret a graph representing a given situation.
Resources: Graphing calculators or Internet access to the Illuminations website

Reflection 7: Lesson Plan Ideas

Lesson Idea 1:

Target Audience -- Middle School Students

Big Idea and Goals -- To familiarize students with adding polynomials using a "Gizmo" (an interactive simulation that makes concepts easier to understand and fun to learn) on the Learning Center Website. The students will be able to explore exponents on their own and work in small groups in order to research the main concepts through the use of this internet software.

Resources -- http://www.explorelearning.com/


Lesson Idea 2:

Target Audience -- Higher Level Calculus Students

Big Idea and Goals -- Students will explore the topic of Extreme Values on their graphing calculator. They will be given a functions and their intervals to graph. They will then need to sketch their findings, compare the graphs' maximum and minimum values, and then use F '(x) in order to compare the functions' extreme value. The students will need to present their calculations in order to get credit for showing their work.

Resources -- Texas Instruments Graphing Calculators


Lesson Idea 3:

Target Audience -- High School Geometry Students

Big Idea and Goals -- Students will use Geometer's Sketchpad to guide them while exploring, identifying, describing, and comparing triangles. They will get acquainted with the shapes on paper and then will be working in collaborative groups in order to come up with a tangible idea of the different triangles that can be constructed.

Resources -- Geometer's Sketchpad