Untitled Document


Day 1 Teacher Notes: Classroom Lesson 1


This lesson begins a theme on positioning systems which will continue through Day 3.
Differentiated Objective:
Graphs and identifies ordered pairs in the coordinate plan and relates it to locating one's position on a map.

Approach to Differentiating: The objective was differentiated by adding the analytic element of comparison between the various positioning systems.

Lesson
Description:

As a class, students will create a labeling system for a large grid taped to the classroom floor and practice naming the position of objects placed on it. The discussion will center on the necessity of having a system that delivers a unique name for every position--and why! The teacher will solicit ideas for other labeling systems, which should naturally lead to a discussion of the Cartesian coordinate system and a review of its characteristics and properties.

Textbook homework assignments for the duration of this unit will be handed out to the students.

Lesson Sequence | DCU Home Page



Day 2 Teacher Notes: Web Lesson 1


This lesson continues the positioning theme begun with yesterday's lesson

Differentiated Objective:
Graphs and identifies ordered pairs in the coordinate plan and relates it to locating one's position on a map.

Approach to Differentiating: The objective was differentiated by adding the analytic element of comparison between the various positioning systems.

Lesson
Description:
Working in groups of two, students are to visit a web site devoted to global positioning systems and choose two of these systems to investigate. The students will print out a guide sheet of tasks to accomplish in the course of their investigations. These tasks include describing the systems, comparing the systems to the Cartesian coordinate system, and preparing for an oral presentation about one of their systems.

Time Line: The web activity should be completed in one class period. The presentations, subsequent discussion, and collection of written work and self-evaluation forms will follow the next day.

Materials: The Lesson Guide Sheet and the Self-Evaluation form are to be printed from the lesson home page by the student. No other materials are required.

Evaluation: Each group will be evaluated by the teacher on the oral presentation of a system and on their written responses to the lesson guide questions. In addition, each group will do a self-evaluation on their presentation. For the grading rubric, see the lesson guide sheet.

Differentiation
Approach:
The lesson offers differentiation in...

content, which is complex and varied.
process, by allowing students to discover, use higher level thought, and encouraging freedom of choice as well as group interaction.
product, by presenting a real problem, by requiring communication with peers and written analysis of knowledge.
evaluation, by using appropriate prestablished criteria and by offering opportunity for self-evaluation

Addressing
Student Needs:
This lesson meets the student's cognitive needs by expanding his knowledge base, and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.

WL1 Home Page | WL1 Guide Sheet | | Lesson Sequence | DCU Home Page


Day 3 Teacher Notes: Classroom Lesson 2


This day's activities concludes the positioning systems theme of Days 1 & 2.

Differentiated Objective:
Graphs and identifies ordered pairs in the coordinate plan and relates it to locating one's position on a map.

Approach to Differentiating: The objective was differentiated by adding the analytic element of comparison between the various positioning systems.

Lesson
Description:
Each group will present one of the positioning systems they investigated yesterday to the class. The presenters will be expected to answer questions from the class and from the teacher about their system. The last 10 minutes of class, the students will learn how to do searches on the internet for their activity tomorrow.

Lesson Sequence | DCU Home Page



Day 4 Teacher Notes: Web Lesson 2


This lesson begins a 4-day themed unit on Rene Descartes and characteristics of mathematicians.
Differentiated Objective:

With classmates, collaboratively investigates the life and times of Rene Descartes and creates a visual (picture, tableau, puppet show, web page, power point presentations,etc.) of some aspect of Descartes' life.

Approach to Differentiating: The objective was differentiated to include analysis, organization and valuing through the investigation of the personality and achievements of Descartes.

Lesson
Description:

The students will work in groups of three doing web research on Rene Descartes. To narrow the scope of the research, each group will be randomly given one of these topics to focus on: (1) Rene from birth to 1604, (2) Rene from 1605-1623, (3)Rene from 1624-death (4) Rene the mathematician (5) Rene the philospher.

The first phase of the lesson requires the each group to take notes from each of 4 web sites. After gathering information from the web sites, the students will work on a visual displaying the results of their research. This display may take one of many forms: skit, comic strip, power point display, overhead transparencies, etc.

Time Line: The web research should be completed in one class period. Preparation of the visual display will begin on day 5 and continue through day 6 as time allows. Students will be expected to work on these presentations as homework along with their text book assignments. The presentations are scheduled for day 7.

Materials:
The Lesson Guide Sheet is to be printed from the lesson web site by the students.

Solicit information from students regarding the equipment and materials they will need for their visuals so that it can be collected and used tomorrow.

Evaluation: Each group will be graded on site notes as well as the visual display. See the lesson guide sheet for details on the grading rubric.

Differentiation
Approach:
The lesson offers differentiation in...

content, which is complex, varied, and focuses on the study of a person and his methods.
process, by allowing students to discover, use higher level thought, and encouraging freedom of choice as well as group interaction.
product, through variety, self-selected format, and communication with peers.
evaluation, which uses approriate preestablished criteria.

Addressing
Student Needs:
This lesson meets the student's cognitive needs by expanding his knowledge base and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.

WL2 Home Page | WL2 Guide Sheet | | Lesson Sequence | DCU Home Page


Day 5 Teacher Notes: Classroom Lesson 3


This lesson continues the theme started on Day 4 investigating Rene Descarte and the characteristics of mathematicians

Differentiated Objective:

With classmates, collaboratively investigates the life and times of Rene Descartes and creates a visual (picture, tableau, puppet show, web page, power point presentations,etc.) of some aspect of Descartes' life.

Approach to Differentiating: The objective was differentiated to include analysis, organization and valuing, through the investigation of the personality and achievements of Descartes.

Lesson
Description:

The majority of this class period will be used by the students to work on their visuals. The last 15 minutes or so of class time will be spent on homework and a discussion of positioning concepts as preparation for a quiz tomorrow.

It is expected that the student will finish up their visuals outside of class.

Lesson Sequence | DCU Home Page



Day 6 Teacher Notes: Classroom Lesson 4

This lesson continues the themed unit on Descartes.

Differentiated Objective:

With classmates, collaboratively investigates the life and times of Rene Descartes and creates a visual (picture, tableau, puppet show, web page, power point presentations,etc.) of some aspect of Descartes' life.

Approach to Differentiating:

The objective was differentiated to include analysis, organization and valuing.

Lesson
Description:

During the first half of the period, there will be a quiz on the Cartesian Coordinate system and on positioning systems in general. The last half of the class will be devoted to a discussion of Descartes and the characteristics that made him such a great mathematician and philospher. We will then consider whether we know anyone that has those same characteristics, including ourselves!

Students should finish up preparations for their visual presentation as homework tonight.

Lesson Sequence | DCU Home Page


Day 7 Teacher Notes: Classroom Lesson 5


This lesson concludes the themed unit on Descarte.

Differentiated Objective:

With classmates, collaboratively investigates the life and times of Rene Descartes and creates a visual (picture, tableau, puppet show, web page, power point presentations,etc.) of some aspect of Descartes' life.

Approach to Differentiating: The objective was differentiated to include analysis, organization and valuing.

Lesson
Description:
Each group will present their visual. During the last part of class, the students will work together to do a "treasure hunt", filling out a fact sheet about Descartes.

Lesson Sequence | DCU Home Page


Day 8 & 9 Teacher Notes: Web Lesson 3 & 4


This is two-day investigation of a web site devoted to linear equations.

Differentiated Objective:

Distinguishes the different characteristics (slope, intercepts, equations) of a horizontal line, a vertical line and a line that's neither.

Approach to Differentiating: The objective was differentiated by including the higher mental process of analysis through distinguishing the differences between

Lesson
Description:

This lesson takes advantage of a web site designed to instruct and test students on interpreting and graphing linear equations. At the site, students will go through a set of topics and a quiz each of the two days. If time allows, they will have opportunity to investigate other aspects of the web site as well.

Most of the students will have been exposed to much of this material in Algebra I. This allows them the opportunity to review/relearn the concepts at their own pace while prepare them for their current homework assignments and the next lessons on writing equations.

Time Line: This lesson is to be completed in two days.

Materials: The Lesson Guide Sheet is to be printed from the lesson home page by the students. No other materials are needed.

Evaluation: Self-evaluation through the quiz taken at the web site each day. Each question of the quiz is graded as soon as an answer is selected. The students can look at a hint or refer back to the topics when he/she has a wrong answer and re-enter a correction.

Differentiation
Approach:
The lesson offers differentiation in...

content, which is varied and abstract.
process, which is self-paced and allows students to discover while using higher level thought.
evaluation, which has preestablishid criteria and is controlled by the student.

Addressing
Student Needs:
This lesson meets the student's cognitive needs by requiring higher level mental processes and skills in a self-paced format.
WL3/4 Home Page | WL3/4 Guide Sheet | | Sequencing of Lessons | DCU Home Page




Day 10 Teacher Notes: Classroom Lesson 6

This lesson continues the student's investigation of linear equations.

Differentiated Objective:	Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line).
Approach to Differentiating:	The objective was differentiated to include analysis by comparing and contrasting the different forms of equations.
Lesson Description:	The first part of the class period will be used to review homework and important concepts from the previous two days web work. The last part of the period will be used to compare and contrast various forms of linear equations and the information necessary to write them. This discussion will be continued tomorrow.

Lesson Sequence | DCU Home Page


Day 11 Teacher Notes: Classroom Lesson 7


This lesson continues the student's investigation of linear equations.

Differentiated Objective:

(1)Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line).
(2)Uses computers and calculators to investigate linear functions.

Approach to Differentiating: The objective was differentiated to include higher level thought through comparison of different forms of equations and using calculators and computer software to experiment with the effects of changing the slope or the intercepts on the graph of the equation.

Lesson
Description:
The first few minutes of the class period will be used for answering homework questions, to finish up yesterday's comparison of different forms of equations, and to practice writing equations that characterize given relationships of two variables, such as found in word problems. During the last part of the class period, students will use calculators and computer software to investigate these equations.
Lesson Sequence | DCU Home Page


Day 12 Teacher Notes: Web Lesson 5


This lesson continues the student's investigation of linear equations.

Differentiated Objective:
Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line).

Approach to Differentiating: The objective was differentiated to include higher level thought through comparison of different forms of equations.

Lesson
Description:
Working in pairs, students will visit the PBS website "Mathline" and do portions of two lessons as instucted on their lesson guide sheet. From these lessons they will generate data. One of the lessons features linearly related data; using this data, the students will write an equation and graph the relationship. The other lesson features non-linearly related data which the students will graph and recognize as non-linear in nature.

Time Line: The students will work on this assignment during class and complete it as homework to discuss tomorrow.

Materials: Graph paper. The lesson guide sheet will be printed off the web by the students.

Evaluation: The assignment will be graded by the teacher according to a preestablished set of criteria. See the lesson guide sheet for evaluation details.

Differentiation
Approach:
The lesson offers differentiation in...

content, which is complex and varied.
process, by allowing students to discover, to use higher level thought, and by encouraging group interaction.
product, by offering real problems, and communication with peers.
evaluation, which uses approriate preestablished criteria.

Addressing
Student Needs:
This lesson meets the student's cognitive needs by expanding his knowledge base, and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.
WL5 Home Page | WL5 Guide Sheet | | Lesson Sequence | DCU Home Page


Day 13 Teacher Notes: Classroom Lesson 8

This lesson concludes the student's investigations of the coordinate plane and linear equations.

Differentiated Objective:
Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line).

Approach to Differentiating: The objective was differentiated to include higher level thought through comparison of different forms of equations.

Lesson
Description:

The students will discuss yesterday's exercise. Possible questions: Do all the graphs for exercise 1 look the same? Was the relationship in exercise 2 linear or non-linear? How do you know?

The last half of the class period will be spent on text homework questions and a general review of important concepts of the last 2+ weeks for the test tomorrow.
Lesson Sequence | DCU Home Page


Day 14 Teacher Notes: Classroom Lesson 9



Lesson
Description:
The students will use the class period to complete a written test on the Cartesian coordinate plane and linear equations.
Lesson Sequence | DCU Home Page



Day 15 Teacher Notes: Classroom Lesson 10


Today's lesson begins a themed unit examining mathematicians and mathematics as a career.

Differentiated Objective:
With parental permission, views two or three movies/documentaries that portray mathematicians. Compares those portrayals with that of the stereotypical "nerd". Compares the life of a mathematician in today's world to that of mathematician in Descartes' day. Discusses mathematics as a career option.

Approach to Differentiating: The objective was differentiated to include higher level thought through comparison of different portrayals of mathematicians/scientists and to emphasize the affective elements in our perceptions of mathematicians/scientists and ourselves.

Lesson
Description:
The class will watch the movie "A Brief History in Time" about Stephen Hawkings. As homework over the next two days they are to watch two other movies about mathematicians ("Stand and Deliver" "It's My Turn" or "Sneakers") so that we can discuss stereotypes vs charcteristics, mathematics as a career, etc.

Lesson Sequence | DCU Home Page

Differentiated Objective:	Graphs and identifies ordered pairs in the coordinate plan and relates it to locating one's position on a map.
Approach to Differentiating:	The objective was differentiated by adding the analytic element of comparison between the various positioning systems.
Lesson Description:	Working in groups of two, students are to visit a web site devoted to global positioning systems and choose two of these systems to investigate. The students will print out a guide sheet of tasks to accomplish in the course of their investigations. These tasks include describing the systems, comparing the systems to the Cartesian coordinate system, and preparing for an oral presentation about one of their systems.
Time Line:	The web activity should be completed in one class period. The presentations, subsequent discussion, and collection of written work and self-evaluation forms will follow the next day.
Materials:	The Lesson Guide Sheet and the Self-Evaluation form are to be printed from the lesson home page by the student. No other materials are required.
Evaluation:	Each group will be evaluated by the teacher on the oral presentation of a system and on their written responses to the lesson guide questions. In addition, each group will do a self-evaluation on their presentation. For the grading rubric, see the lesson guide sheet.
Differentiation Approach:	The lesson offers differentiation in...
Differentiation Approach:	content, which is complex and varied. process, by allowing students to discover, use higher level thought, and encouraging freedom of choice as well as group interaction. product, by presenting a real problem, by requiring communication with peers and written analysis of knowledge. evaluation, by using appropriate prestablished criteria and by offering opportunity for self-evaluation
Addressing Student Needs:	This lesson meets the student's cognitive needs by expanding his knowledge base, and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.

Differentiated Objective:	With classmates, collaboratively investigates the life and times of Rene Descartes and creates a visual (picture, tableau, puppet show, web page, power point presentations,etc.) of some aspect of Descartes' life.
Approach to Differentiating:	The objective was differentiated to include analysis, organization and valuing through the investigation of the personality and achievements of Descartes.
Lesson Description:	The students will work in groups of three doing web research on Rene Descartes. To narrow the scope of the research, each group will be randomly given one of these topics to focus on: (1) Rene from birth to 1604, (2) Rene from 1605-1623, (3)Rene from 1624-death (4) Rene the mathematician (5) Rene the philospher. The first phase of the lesson requires the each group to take notes from each of 4 web sites. After gathering information from the web sites, the students will work on a visual displaying the results of their research. This display may take one of many forms: skit, comic strip, power point display, overhead transparencies, etc.
Time Line:	The web research should be completed in one class period. Preparation of the visual display will begin on day 5 and continue through day 6 as time allows. Students will be expected to work on these presentations as homework along with their text book assignments. The presentations are scheduled for day 7.
Materials:	The Lesson Guide Sheet is to be printed from the lesson web site by the students. Solicit information from students regarding the equipment and materials they will need for their visuals so that it can be collected and used tomorrow.
Evaluation:	Each group will be graded on site notes as well as the visual display. See the lesson guide sheet for details on the grading rubric.
Differentiation Approach:	The lesson offers differentiation in...
Differentiation Approach:	content, which is complex, varied, and focuses on the study of a person and his methods. process, by allowing students to discover, use higher level thought, and encouraging freedom of choice as well as group interaction. product, through variety, self-selected format, and communication with peers. evaluation, which uses approriate preestablished criteria.
Addressing Student Needs:	This lesson meets the student's cognitive needs by expanding his knowledge base and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.

Differentiated Objective:	Distinguishes the different characteristics (slope, intercepts, equations) of a horizontal line, a vertical line and a line that's neither.
Approach to Differentiating:	The objective was differentiated by including the higher mental process of analysis through distinguishing the differences between
Lesson Description:	This lesson takes advantage of a web site designed to instruct and test students on interpreting and graphing linear equations. At the site, students will go through a set of topics and a quiz each of the two days. If time allows, they will have opportunity to investigate other aspects of the web site as well. Most of the students will have been exposed to much of this material in Algebra I. This allows them the opportunity to review/relearn the concepts at their own pace while prepare them for their current homework assignments and the next lessons on writing equations.
Time Line:	This lesson is to be completed in two days.
Materials:	The Lesson Guide Sheet is to be printed from the lesson home page by the students. No other materials are needed.
Evaluation:	Self-evaluation through the quiz taken at the web site each day. Each question of the quiz is graded as soon as an answer is selected. The students can look at a hint or refer back to the topics when he/she has a wrong answer and re-enter a correction.
Differentiation Approach:	The lesson offers differentiation in...
Differentiation Approach:	content, which is varied and abstract. process, which is self-paced and allows students to discover while using higher level thought. evaluation, which has preestablishid criteria and is controlled by the student.
Addressing Student Needs:	This lesson meets the student's cognitive needs by requiring higher level mental processes and skills in a self-paced format.

Differentiated Objective:	(1)Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line). (2)Uses computers and calculators to investigate linear functions.
Approach to Differentiating:	The objective was differentiated to include higher level thought through comparison of different forms of equations and using calculators and computer software to experiment with the effects of changing the slope or the intercepts on the graph of the equation.
Lesson Description:	The first few minutes of the class period will be used for answering homework questions, to finish up yesterday's comparison of different forms of equations, and to practice writing equations that characterize given relationships of two variables, such as found in word problems. During the last part of the class period, students will use calculators and computer software to investigate these equations.

Differentiated Objective:	Compares and contrasts the different forms of equations for a line and writes and graphs equations of lines given various information (such as slope, intercepts, points on the line).
Approach to Differentiating:	The objective was differentiated to include higher level thought through comparison of different forms of equations.
Lesson Description:	Working in pairs, students will visit the PBS website "Mathline" and do portions of two lessons as instucted on their lesson guide sheet. From these lessons they will generate data. One of the lessons features linearly related data; using this data, the students will write an equation and graph the relationship. The other lesson features non-linearly related data which the students will graph and recognize as non-linear in nature.
Time Line:	The students will work on this assignment during class and complete it as homework to discuss tomorrow.
Materials:	Graph paper. The lesson guide sheet will be printed off the web by the students.
Evaluation:	The assignment will be graded by the teacher according to a preestablished set of criteria. See the lesson guide sheet for evaluation details.
Differentiation Approach:	The lesson offers differentiation in...
Differentiation Approach:	content, which is complex and varied. process, by allowing students to discover, to use higher level thought, and by encouraging group interaction. product, by offering real problems, and communication with peers. evaluation, which uses approriate preestablished criteria.
Addressing Student Needs:	This lesson meets the student's cognitive needs by expanding his knowledge base, and by requiring higher level mental processes and skills. More importantly, it meets his affective needs through group interaction and cooperation with his peers.

Differentiated Objective:	With parental permission, views two or three movies/documentaries that portray mathematicians. Compares those portrayals with that of the stereotypical "nerd". Compares the life of a mathematician in today's world to that of mathematician in Descartes' day. Discusses mathematics as a career option.
Approach to Differentiating:	The objective was differentiated to include higher level thought through comparison of different portrayals of mathematicians/scientists and to emphasize the affective elements in our perceptions of mathematicians/scientists and ourselves.
Lesson Description:	The class will watch the movie "A Brief History in Time" about Stephen Hawkings. As homework over the next two days they are to watch two other movies about mathematicians ("Stand and Deliver" "It's My Turn" or "Sneakers") so that we can discuss stereotypes vs charcteristics, mathematics as a career, etc.