Meagan Vickers

PBI – 10am

September 30, 2005

Lesson Plan 1

Title of Lesson: Introduction to Sundials

Date of Lesson: Day 1 of Unit

Length of lesson: 50 minutes

Description of the class: Pre-Calculus, regular or honors

TEKS addressed:

c2c: investigate identities graphically and verify them symbolically, including trigonometric identities

3. The student uses functions and their properties to model and solve real-life problems.

3d solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas.

The Lesson:

Overview- The students will get an introduction to sundials in order to become familiar with the unit that will take up the rest of the six-weeks. Students will watch a benchmark video illustrating the importance of sundials and how they could be useful if all the clocks in the world were to break. Students will also work on computers to access a website that simulates sundials in order to get acquainted with some of the concepts that relate to them.

Performance/Learner Outcomes: Explore real-life applications of mathematical concepts, use technology to increase competence with specific topics

Materials, Resources, supplies needed: computers with Internet access

Supplementary materials, handouts: worksheet for Internet activity, benchmark video and technology to show it

Five-E Organization

Teacher does: Student does:

Engage: Teachers explain that for the next four weeks, students will be learning about the components of, and building sundials. Teacher shows benchmark video about sundials. The video highlights “what would happen if all the clocks in the world stopped? How would we tell time?” Teacher points out that the world thought that all computers would crash at the turn of the last century Teacher gives students more explanation on the project on the horizon, tells students not to worry, specifications and more explanation will come later as the unit progresses. Notes that things will be taken a day at a time. Groups will be assigned at this time.

Respond to introduction with questions about sundials, when they were used, why they are useful in today’s society, etc. Students respond to video with comments that the idea of “all the clocks breaking at the same time” would never happen.

Teacher does: Student does:

Explore: Teacher allows students to break from their desks and work on the computers. Teacher hands out the worksheet and has the students begin exploring the website with the sundial simulation. Teacher walks around the room, asking questions and checking on students. Make sure that they are on task. Encourage students to jot down any questions they may have about sundials because it may come in handy later, as well as be useful in classroom discussions. It is important that students correctly record all data collected from the program.

The students are working at computers with the simulation on sundials. Students are answering as well as asking questions about the project, addressing them with classmates, and brainstorming about what they might need to know for their sundial sketches and constructions.

Evaluate –

Teacher is assessing students understanding, taking note of common questions among students, asking probing questions to get students to think more about the upcoming project.

Explain: Teachers will also go over the worksheet and have students make a list of the questions they came up with on the board. Teacher can ask students if different types of sundials would work for example, would a sundial made of a vertical pole be useful in telling time? The teacher then explain why it’s so important to know the math behind sundial construction, how triangles and circles are the basis for an effective sundial, and mathematical concepts and terms are important in understanding time.

Students will listen to questions that other students formulated, make a list on the board, and all contribute in answering them. Students will answer, or be told, that the shadow of a vertical object does not fall in the same direction nor extend to the same distance at the same time on successive days. This is because the Sun passes across the sky each day on a path which rises and falls with the changing seasons.

Evaluate

Teacher is assessing students understanding, taking note of common questions among students, asking probing questions to get students to think more about the upcoming project.

Extend/Elaborate: Teachers will briefly explain different mathematical concepts that will be required for their sundial projects (how latitude effects the gnomon and how law of sines and cosines will be helpful with other aspects of the project). If time allows, teachers can explain more about the correlation of graphing and sundials. Teachers should also ask students (as well as on the worksheet) what they learned from the simulation and what they hope to learn from the sundial project. The teacher can also elaborate on how sundials tell Sun Time, which may be different from the time told by a watch. This is due to the fact that the circular motion of the sun varies in speed with the time of the year. Sun Time and time told by a watch can differ up to 16 minutes!

Students will moan and groan that they don’t know what the teacher is talking about, but will be reassured when the teacher reaffirms that things will be taken slow, and all the mathematical concepts needed for the project will be taught before hand. Having students think about what they have learned and what they hope to learn will assist the teacher in highlighting topics that interest the students as well as enable the teacher to identify misconceptions early on.