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MATH 409 MATHEMATICS THROUGH COMPUTERS ELAINE REED FALL 2007PowerPoint Presentation

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MATH 409 MATHEMATICS THROUGH COMPUTERS ELAINE REED FALL 2007

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MATH 409

MATHEMATICS THROUGH COMPUTERS

ELAINE REED

FALL 2007

CLICK TO OPEN PORTFOLIO

Table of Contents

About Me

Article Critique

Lesson Plans

WebQuest

Reflections

Resume

Education Classes Taken

Philosophy of Education

Table of Contents

I am currently in my junior year at Central Connecticut State University and in my second semester in the Education Program. During this semester I was enrolled in Mathematics through Computers, MATH 409. In this class I was exposed to different ways that technology could be integrated with mathematics instruction.

Elaine Reed 182 South Main St. reedelm@ccsu.edu

Marlborough, CT (860) 295-9454

Education

About Me

High School

RHAM High School, Hebron, CT 2000-2002

-Received honors each year

S:t Eskils Gymnasium, Eskilstuna, Sweden 2002-2003

-Exchange student for 10 months with AFS

Education Classes Taken

RHAM High School, Hebron, CT 2003-2004

-Graduated with honors

College

CCSU New Britain, CT Spring 2005- present

Philosophy of Education

-Dean’s List Spring 2006

-Dean’s List Fall 2006

-Dean’s List Spring 2007

-Kappa Delta Pi Honors Society Spring 2007-present

-Golden Key Honor Society Fall 2007-present

Table of Contents

Work Experience

Marlborough Country Bakery Fall 2003-present

-Counter staff

Tutor for Sixth Grader Fall 2005- Spring 2006

Marlborough Elementary Child Care Association Summer 2006

-After school care and summer camp Volunteer

Marlborough Elementary Child Care Association Fall 2006-present

-Before and after school care and summer camp daycare provider

Special Skills

CPR Certified

First Aid Certified

Child Care Certified

MathematicsStructures of Math I: Number Systems

Structures of Math II: Probability and Geometry

Structures of Math III: Number Patterns

Structures of Math IV: Development of Geometry

Topics in Elementary Math: Proof and Logic

PsychologyGeneral Psychology

Life Span Development

Childhood Development

Educational Psychology

TechnologyIntroduction to Educational Technology

Developing Educational Materials

Technology Through Computers

ReadingComprehensive Reading Instruction I

Comprehensive Reading instruction 2

Theoretical Introduction to Education and Learner Exceptionalities

Education and Teaching Leadership- Diverse Learning

Effective Elementary Teaching

PracticumDiLoreto Magnet School, New Britain, CT Third Grade

Webb Elementary School, Wethersfield, CT Fifth Grade

Dwight School, Hartford, CT Fourth Grade

About Me

Resume

Philosophy of Education

Table of Contents

Through personal experience as well as my classes at Central Connecticut State University I have developed certain philosophies about how students learn and foster their knowledge. These are just some of the main points that I have noticed though the semesters I have spent in the education program.

To start, I have recognized that all students learn differently. Students are like snowflakes, there are no too that are alike. But, there is one thing that all of the students have in common; all students are capable of learning. To have this learning occur, material needs to be presented in a variety of ways. There are eight multiple intelligences according to Howard Gardner, and all eight of these intelligences should be incorporated in to learning.

I also believe that students do not always have to learn from the teacher. Students can teach themselves and teach others. By having the students work in cooperative groups, the students are able to teach each other, as well as learn and grow socially.

Another belief of mine is that students learn by doing. In order for the majority of students to learn about the Pythagorean theorem, they would have to be actively engaged in the lesson. This could be through drawing out the theorem, finding the theorem in real world situations, or by completing a WebQuest on the subject.

My last thought for now is that diversity in the classroom plays a key part in classroom dynamics. By having a diverse classroom there is a variety of view points. These view points lead to better learning and understanding about any topic. The different view point and the diversity should be fostered, and definitely not ignored.

My philosophy of education is always changing and expanding as I learn more through my classes and from the students that I see.

About Me

Resume

Classes Taken

Table of Contents

Article Read

Critiquing this article was a positive experience for me. It exposed me to a multitude of different ways to incorporate technology into lessons in the classroom. The technology that this article focused on was the use of virtual manipulatives in the classroom to enhance the understanding of students.

PowerPoint Presentation

List of Links

Table of Contents

Article Critique

Virtual Manipulatives

Examples of Static vs. Dynamic Virtual Manipulatives

Visual Fractions

Room 108

Manipula Math

Useful Sites with multiple Virtual Manipulatives

Utah State University National Library of Virtual Manipulatives

Arcytech

Article Read

PowerPoint Presentation

Table of Contents

Data Analysis

As part of this course we were required to write four lesson plans. Four each of these lesson plans we focused on a different area of mathematics. These areas were Data Analysis, Number Systems, Geometry, and Algebra. For each of the lessons we also incorporated technology into the lesson. This was helpful in understanding the importance technology to learning. I was able to see how the different technologies could be used to enhance a lesson, not just be added to a lesson.

Number Systems

Geometry

Algebra

Table of Contents

Topic:

Data analysis

Technology use

Environmental learning

Grade Level:

Second Grade

Lesson Objectives:

The students will demonstrate their ability to make a column graph by using excel and making a chart including 3-4 categories of litter.

Standards:

Record and analyze data using charts and bar graphs

Purpose:

Creating graphs is a useful way to convey messages, enabling visual representation as well as effectively summarizing large amounts of data. In this lesson the graphs are being used to show the amount of litter that was found and collected at a local park.

Materials and Equipment:

Computers equipped with Microsoft Excel

Group data that was previously collected

Printer

Letters to students

Anticipatory Set:

Send all students a “call to duty” letter to help save the planet by spreading the word about the need to cut back pollution, specifically littering.

Bring in newspaper and magazine clippings of bar graphs or charts that relate to topics the students would be interested in. Have the students look at the clippings to get an idea of how graphs and charts can be used to convey messages.

Lesson Plans

Number Systems

Geometry

Algebra

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Data Analysis

Time Estimate:

Receiving and reading letters: 5 minutes

Looking at clippings: 10 minutes

Break into groups move to computer stations: 2 minutes

Organize data into charts: 13 minutes

Instruction and Make into bar graphs: 10 minutes

Print graphs and put into folders: 5 minutes

Total time: 45 minutes

Prior Knowledge:

Students have previously visited a park and collected litter. The litter was recorded and recycled by the students. The groups that are to be used for this lesson were assigned at the park according to the area where they were collecting the litter. Students have already encountered graphs on a small scale and they have created bar graphs using paper and pencil. The students have had science lessons that focused on the damage that pollution can cause.

Important Terms (Vocabulary):

Column graph (bar graph)

Chart

Litter

Pollution

Environmentalist

EPA Environmental Protection Agency

Data

Teaching Model/ Learning Environment:

Working with cooperative groups of about 3-4 students with one computer per group. Computers are stationary, so the students will be gathered around an assigned computer.

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Number Systems

Geometry

Algebra

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Data Analysis

- Differentiated Instruction:
- For the multiple intelligence, we have addressed the following intelligences in the following ways:
- Visual- Demonstration by teacher
- Logical- analyzing graphs
- Spatial- creating graphs
- Bodily Kinesthetic- Gallery tour
- Interpersonal- working groups
- Intra personal- coming up with your own ideas about graphs, looking at the clippings
- Naturalistic- Environmental concerns
- For Bloom’s taxonomy we are at the Synthesis level of the cognitive scale. The students are creating their own graphs. For the affective domain our students will be demonstrating internalizing values. This is because they will be active members in a group and demonstrating problem solving.
- Procedure:
- 1. Deliver the “call of duty” letters to the students. Allow time for the students to read the letters.
- a. What could we do to help?

- 2. Come up with an idea of how they could help the EPA solve the problem of pollution by spreading the word of pollution.
- a. How can we reach a large number of people quickly?

- 3. Present the other graphs and discuss how a graph is an effective way to deliver a large amount of information very quickly.
- a. What do you notice about all of these graphs?
- b. What do they have in common?
- c. What are some differences?

- d. What graphs are easier to understand than others?

- a. What do you notice about all of these graphs?
- 4. Break the students into their groups and give out what their data was that they have collected. Have the students move to their computer station.

Lesson Plans

Number Systems

Geometry

Algebra

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Data Analysis

- 5. Show students how to use excel to organize their data into 3-4 groups by combining the categories they have previously made. Include on every chart a title (where that group collected the data), types of litter, and the amount of each type of litter.
- a. What is a title?
- b. Where are the types of litter?
- c. Where are the amounts?
- d.What categories could we make that would include what we found?
- i. Think of recycling groups.

- 6. Highlight all of the cells that have information in them.
- 7. Click on insert, and then the icon with the column graph. Allow students to select what graph would best represent their data.
- a.What would be the best representation of your data?

- 8. Double check the graphs and make sure that all of the components of a graph are there. (Title, labeled axis, numbers are correct.)
- Assessment:
- We will know how the students understood the concepts that were presented by watching the students making their graphs and charts. Also at the end of the lesson there will be a gallery walk to look at all of the different graphs that were made for the different areas of the park. The students will then discuss the graphs with their groups.
- Closure:
- After the gallery walk the students will discuss what they have seen today in a large group and
- how the graph can be used to show other students in the school about the problems of pollution.
- References and additional Resources:
- Parker, D L (March 2003). Take care of mother earth: technology and the environment. Teaching Children Mathematics, 9, 7. p.414(6). Retrieved October 03, 2007, from General OneFile via Gale:http://0-find.galegroup.com.csulib.ctstateu.edu:80/itx/start.do?prodId=ITOF

Lesson Plans

Number Systems

Geometry

Algebra

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Topic: Bases for Number Systems and creating individual number systems

Subject or Grade Level: Fourth Grade Mathematics

Lesson Objective: Students will be able to understand numbers in bases other than base 10 by creating another number system using a different base.

Standards: Understand numbers, ways of representing numbers, relationships among numbers, number systems (NCTM Standards of Number and Operations Standard for Grades 3- 5).

Purpose: Learning about numbers in different bases is useful because although in our culture base ten is considered the norm, in other cultures this is not always used. Understanding this is important not just in mathematics, but in all facets. Along with this, students should make the connection that what we see as the standard in our culture may be looked at by different perspectives from other cultures and vice versa. Children will realize that learning from other cultures is beneficial.

Materials and Equipment:

Paper (poster sized)

Pencil

Colored Pencils

Computers with Internet Access (one per student)

Pictures of different tropical island (one per group of four)

Anticipatory Set: Hand out the images of different tropical islands. Ask the students to imagine that they are stranded there and they need to develop a number system other than base 10. Since the island is their habitat, brainstorm ideas of things that it may be a good idea to keep track of i.e. bananas, coconuts. These things may serve for the basis of a new number system. For example, you could say that since you usually find 3 coconuts per tree that 3 is the new base number. While the students are brainstorming there will be background music of island music to help set the mood of the brainstorming.

Lesson Plans

Data Analysis

Geometry

Algebra

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Time Estimate:

Split into Groups of Four: 3 minutes

Hand out images/ Anticipatory Set: 7 minutes

Explore link provided (individually): 10 minutes

Hand out Colored Pencils and Paper: 2 minutes

Groups Collaborate and make Posters: 15 minutes

Present Posters: 15 minutes

Total Time Estimate: 52 minutes

Prior Knowledge: This lesson should be a follow-up to a previous lesson on numbers in different bases. It allows children to explore, personalize, and enrich their understanding of the previous lesson. The students had a good understanding of how the bases worked after the prior lesson.

Important Terms (vocabulary):

Base numbers

Culture

Number Systems

Numerals

Teaching Model/ Learning Environment: The children are going to be working in groups for the value of collaboration. Each group will represent their own island with different number systems from the rest of the class. The groups will be of about four students. While the children are exploring the provided website, however, they will be working alone for the purpose of understanding the lesson on their own terms.

Lesson Plans

Data Analysis

Geometry

Algebra

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- Differentiated Instruction:
- Gardner’s Multiple Intelligences:
- Linguistic- Presenting number systems to the rest of the classroom. Students will use words effectively to explain and defend their ideas.
- Intrapersonal- Students work independently at the computers, investigating the website.
- Interpersonal- Working in the groups of four, learning through interaction
- Musical- There will be music playing in background while they are brainstorming and working in their groups
- Visual-Spatial- Creating the poster
- Bodily-Kinesthetic- The groups will be getting up to present in front of the class
- Logical-Mathematical- Thinking abstractly to devise a number system. The students will use reason to choose an appropriate base number.
- Naturalistic- Using nature to create a number system
- Blooms taxonomy:
- Cognitive- The lesson is at the Evaluation Level. The students will be presenting their uniquely created number systems, explaining them, and making connections to the meaning as a whole.
- Affective- The lesson reaches the Organization Level. The students will organize and prepare a poster. Then, the students will present, explain, and defend their ideas.
- Psychomotor- The lesson is aimed towards the level of Adaption. The students will be adapting new numerals and bases for the specific task.
- Lesson Design/Procedure:
- 1. Split the class into groups with four students in a group.
- 2. Hand out the pictures of the islands to the groups and tell them that they are stranded on this island and they do not know how to count. In their groups they need to find a way to count that is not in base ten. At this time the students will think which base will work best for their island.
- a. Who remembers what we learned last class?
- b. What are some other bases that we have learned about?
- c. How would we go about picking a different base?
- d. What is important to consider?

- e. What do you see in your picture that could help you decide what base might be most useful to
- have?

Lesson Plans

Data Analysis

Geometry

Algebra

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Lesson Plans

- 3. The students will go to the computers and explore the website http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html. At this website the students should be able to see how adding and subtracting can work in the different bases as well as how many different numerals would be needed for each of the bases.
- a. How are these bases different from the base ten that we are used to?
- b. How many numerals would be needed for base 5? 3? 7?

- 4.The students will meet back up in their groups and come up with their numerals and discuss how their number system will work.
- a. Why did you choose those numerals?

- 5. The groups will create their posters.
- 6. The groups will present their posters and explain why they chose the base that they did as well as the numerals that they did. They will then demonstrate how their number system would work by adding and subtracting.
- Assessment:
- The students will make a poster of their numerals and demonstrate to the class how their number system works (what base they chose and why). The poster will include all of their numerals for their number system, a name for the number system, one addition equation done out both in their numerals and drawn with base blocks, and one subtraction problem done out both in their number system and in base blocks.
- Closure:
- Refer back to the groups the students were placed in. Note that each group’s work on number systems is unique. Make the conclusion that cultures may be different in how they do things, but this is not a bad thing. Then ask question such as what makes a number system, and are there some number systems that are better than others?
- References and Additional Resources:
- http://nlvm.usu.edu/en/nav/frames_asid_152_g_2_t_1.html
- “Culture in the Curriculum: Enriching Numeration and Number Operations.” Teaching Children
- Mathematics 8.4 (2001): 238.

Data Analysis

Geometry

Algebra

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Topic:

Geometry

Subject:

Tessellations grade 4

Lesson Objective:

Students will be able determine what is needed to make a tessellation. They will explore a website about tessellations that will guide the students in making tessellations. After testing what they think is needed, the students will be able to make their own tessellations.

Standards:

NCTM Math curriculum scope and sequence standard 6.2 for the fourth grade states that students will “make and test conjectures about geometric properties and relationships involving shape, position, movement, subdivision, tessellation, and transformations.”

Purpose:

The purpose of this lesson is to show that our whole environment is made up of tessellations. There are tessellations in architecture, nature, and art work.

Materials and Equipment:

Computers with internet access

Index cards

Tape

Scissors

Colored Pencils

Pictures of tessellations

Pencils

Paper

Anticipatory Set:

Gather the children in a group and have them seated. Tape pictures that you’ve previously collected of tessellations found in architecture, in nature, and in artwork (Try to use interesting, and colorful examples. When picking out artwork with tessellations, use at least one piece by Escher). Ask the children what they see in each picture or what it is a picture of, and if they notice any type of patterns. Recall what tessellations are and ask if the pictures are also tessellations. This discussion should guide children to discovering that tessellations are all around us. Depending on the classroom, ask the students to look up at the ceiling (or on a wall, or at the tiling on the floor) and ask them again what they see. End the discussion by telling them that today they are going to get the chance to explore tessellations, and then create their own.

Lesson Plans

Data Analysis

Number Systems

Algebra

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Time estimate:

Anticipatory set 5 minutes

Transition to computers and get to website 4 minutes

Explore website 13 minutes

Hand out index cards, colored pencils, paper, tape, and scissors 3 minutes

Create tessellations (guided) 8 minutes

Create and begin coloring tessellation on own 12 minutes

Gallery tour of tessellations 5 minutes

Total Time: 50 Minutes

Prior Knowledge:

The students will have already been introduced to “identifying polygons in various orientations including combining, subdividing, sliding, rotating and reflecting” In the previous year (NCTM grade 3).

Important Terms:

Tessellation

Rotation

Sliding

Tiling

Plane

Learning Environment:

The learning environment being created will be a combination of whole class and individual work. The students will collaborate as a whole class during the Anticipatory Set. At this time the children will listen to each others’ responses about the images of tessellations as an aid to understanding the bigger idea. After the anticipatory set the students will work individually at the computers and then independently at their desks to construct the tessellations.

Lesson Plans

Data Analysis

Number Systems

Algebra

Table of Contents

Differentiated Instruction:

Gardner’s multiple intelligences:

Linguistic- reading on the website

Logical mathematical- creating the tessellation

Spatial intelligence- planning out the tessellation

Bodily kinesthetic- gallery tour

Interpersonal- whole group questions

Intrapersonal- individual work

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- Bloom’s taxonomy:
- This lesson allows the student to synthesis their own meaning of what a tessellation is, while they create their own tessellation. It is also motivating to move through the different stages of the tessellation website. The students also have to use their motor skills to operate the computers as well as to cut, copy, and color their tessellations.
- Lesson Design:
- 1. Gather students to the front of the classroom where you have displayed the examples of tessellations from architecture, from nature, and from artwork.
- a. What are these pictures of?
- b. What do you notice in common in all these different pictures?

- 2. Distinguish which tessellations are architecture, which are from nature, and which are artwork. Suggest that tessellations are a part of everyday life and are all around us.
- a. Who can tell me what other picture is from nature/architecture/artwork?
- b. Ask the children to look up at the ceiling (or walls or floor). Ask if they recognize a pattern. Is
- this also similar to the tiling of a plane? We can see tessellations around us every day if we look.

- 3. Tell the children that they are going to individually explore a website to see how building a tessellation would work, and after this they will have a chance to create their own original tessellation.
- 4. Break from whole class to individual seats at computers with internet access
- 5. Do a demo on an overhead projector to guide them to the website http://www.mathcats.com/explore/tessellationtown.html
- 6. Explain how the website works, highlighting the clouds that contain information.
- 7. Children will explore the website on their own. Be sure to walk around to assist any students having difficulties and to be certain that all students are on task.
- 8. After the students have had some time to practice creating tessellations on the internet, hand out paper/index cards/tape/scissors/colored pencils. Announce that now the students will create their own original tessellations.

Lesson Plans

Data Analysis

Number Systems

Algebra

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- Do a demo on how to create a tessellation out of an index card
- Choose one side of the index card to begin with. Tell students to cut out some type of design that begins and ends at the top and bottom of that side
- Tape that side to its corresponding parallel side
- Repeat these steps for the remaining two sides
- Tell the children to trace their new shape onto the paper, filling the plane. You can relate it to a puzzle piece to make a connection of what the children are doing. Walk around to help any students who might it.
- Color the tessellation after it is traced. *Note that some children may spend a very long time on coloring, so stick to the amount of time set aside for this and be aware that it is okay if a few children do not finish coloring.

- 10. The students leave their tessellations on their desks and then move around the class to view all of the other tessellations that were made in a gallery presentation.
- 11. Hand in Tessellations
- Assessment:
- You will be able to tell if the students understand the concept of tessellations by assessing the tessellations that they create individually. You also want to check that each students’ tessellations is unique in order to make sure that students were not just copying a design they saw their neighbor create. Although the finished project will look like a tessellation, if it is not original then the student did not understand the concept expected.
- Closure:
- After the gallery tour the students will discuss what they saw and what makes up a tessellation. To extend knowledge and thinking about tessellations we will ask if there are any reflections, rotations, or slides in the tessellations that were made.
- Reference:
- http://www.mathcats.com/explore/tessellationtown.html

Lesson Plans

Data Analysis

Number Systems

Algebra

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Topic

Algebraic Patterns

Grade Level

Second Grade

Lesson Objectives

The students will be able to see number patterns and expand a given number pattern by making charts and seeing the relationships.

Standards

“Use tables and graphs to display pattern data and explore a variety of ways to describe and write rules for patterns. Explore and describe number patterns. Model situations that involve addition and subtraction of whole numbers using objects, pictures, and symbols, including open number sentences. Analyze observable changes using qualitative and quantitative descriptions.” (NCTM Standards of Algebra and Functions for Grade 2)

Purpose

This lesson promotes real-world thinking and problem solving. The students will learn that their observations of patterns can lead to a greater understanding of relationships around them.

Materials and Equipment

1 Laptop per pair equipped with Microsoft Excel

Pattern blocks (equal number of trapezoids and squares, one triangle per group)

1 T- Chart with columns of “Years Old” and “Number of Pattern Blocks” as headings per pair (on Microsoft Excel)

Ancient Ones: The World of the Old-Growth Douglas Fir, a book by Barbara Bash

Printer

Anticipatory Set

Explain to the students that today we are going to read a story. The story that we are reading is about tall trees that grow in forests, and all of the animals that live in the forests. Tie the lesson in with the science unit of ecosystems. Explain that we are going to pay close attention to how the trees in the story grow into these tall trees.

Time Estimate

Anticipatory Set- 5 Minutes

Reading story- 15 Minutes

Going over what was read- 3 minutes

Splitting into pairs- 2 minutes

Lesson Plans

Data Analysis

Number Systems

Geometry

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Building trees and recording number of pattern blocks used- 10 minutes

Making chart into a graph- 5 minutes

Finding a pattern and closure- 5 minutes

Total Time Estimate: 45 minutes

Prior Knowledge

The students have been learning about ecosystems in their science unit. They have also previously used Microsoft Excel for recording data and making graphs. The students have had little practice finding patterns in numbers, but they have found patterns using objects before.

Important Terms

Pattern

Growth

Ecosystem

Graph

T-Chart

Learning Environment

The students begin the lesson on the classroom rug to listen to a story and for the anticipatory set. After the story the students break up into pairs and find a spot in the class where they are comfortable to work. Each pair then receives a laptop computer that they can use in the spot that they chose. For finding the pattern and the closure the class will come together in a central area with their laptops to discuss what patterns were found.

Differentiated Instruction

This lesson is differentiated due to the number of multiple intelligences that are being used.

Linguistic- The students are listening to a story

Bodily Kinesthetic- Building the trees out of pattern blocks

Interpersonal- Working with a partner

Intrapersonal- Listening to the story and thinking about how the trees grow

Naturalistic- Learning about natural growth and ecosystems

Spatial- Making the graphs

Logical Mathematical- coming up with a pattern, making a chart

Lesson Plans

Data Analysis

Number Systems

Geometry

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- This lesson is also differentiated because it utilizes different aspects of Bloom’s Taxonomy.
- Affectively- this lesson allows the students to value the different ecosystems and how patterns are found in different places.
- Psychomotor- the students develop motor skills by building with the pattern blocks.
- Cognitive- The students analyze a pattern to determine what the pattern is and then use the pattern to see if it holds true in test cases.
- Lesson Design
- 1. Anticipatory set, explain what is going to be done and introduce the book that is going to be read.
- a. What have we been learning in Science class?
- b. Has anyone ever noticed how a tree grows?

- 2. Read the story to the students. Have them pay particular attention to the size of the trees at different stages in their lives.
- 3. Go over what was read.
- a. Did anyone notice any patterns with how the trees grow?

- 4. Have the students break into pairs and explain what is going to be done. The students will take turns growing the “tree” that is made out of the pattern blocks. The first year tree is made out of one square (for the trunk), one trapezoid, and then a triangle on the top of the trapezoid, forming a tree. For each year the students will add one square to the bottom and one trapezoid to the body of the tree. This will make the tree grow each year. While one student is making the tree grow, the other student is recording how many pattern blocks are being used for each year. The students will take turns with these two tasks.
- a. What patterns are you noticing?
- b. Each year, how many more blocks are added?

- 5. Use the chart that was made on Excel and make a line graph. Look at the graphs that were made.
- a. What do these graphs look like?
- b. Is the line curved or straight?
- c. By how many pattern blocks do the trees grow each year?

- 1. Anticipatory set, explain what is going to be done and introduce the book that is going to be read.
- 6. Print off both the charts and the graphs.

Lesson Plans

Data Analysis

Number Systems

Geometry

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Assessment

The teacher assesses students by collecting their charts and graphs. During the lesson the teacher will also ask questions such as, “What patterns do you see” in order to gain some insight into which students are picking up the lesson and which may need more help.

Closure

Ask questions such as:

What patterns did we find? How many blocks were added each year? How many bocks would be used for a tree that was 25 years old?

What would happen if the trees grew by two trapezoids and one square each year? What would this pattern look like? Would it look similar or different?

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Data Analysis

Number Systems

Geometry

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WebQuest

This WebQuest assignment was designed to show us how easy it is to put together a motivating lesson for students to take learning into their own hands. The WebQuest is a good format for a lesson such as this. It allows the students to learn both on their own and with a group. This WebQuest is on Pythagoras, his life and his theorems.

Reflection

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During this class we had the opportunity to reflect on what we were doing. The two assignments that we reflected on were our lesson that were taught to the class and our WebQuest that we created. Reflection is an important aspect to teaching because it allows the teacher to see what worked well during the lesson. This will allow the teacher to see possible ways to reconstruct the learning. Reflection also allows the teacher to see areas that did not work so well and areas that could be improved. This is especial useful for a beginning teacher, but should be continued throughout the career.

Data Analysis Lesson Reflection

WebQuest Reflection

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When starting this WebQuest I already knew what it was all about. I have previously made a WebQuest using Zunal.com. Previously I did not enjoy making the WebQuest. I found it boring and unimaginative. The way that the website had the constructer build the WebQuest did not leave room for any variation. This, I suppose, is a good think for a first timer, but I did not enjoy the experience. When we made the WebQuest for Math 409, we used Microsoft PowerPoint. There was no template to use and there were hardly any guidelines to follow. This made for a more creative page that could engage the students better.

Working on this WebQuest was a group effort. We all worked together to have this come to fruition. There was not a member of the group that did not participate equally. Ideas were flowing between our group freely. There was also not any animosity between the members and all of the members were able to voice their opinions.

Looking back there would not be too much that I would change. The topic was a bit dull, and we tried spicing it up as much as we could. I think if we put more effort into coming up with a premise for the WebQuest we would have been able to find a more realistic scenario for the students to feel engaged.

Over all I feel that we did a good job making an engaging WebQuest for our imaginary class to use to learn more about Pythagoras.

Reflections

Data Analysis

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The first area to look at was how we addressed our lesson objectives. We did state what our lesson objectives were, the only problem with this was that we did not state our objectives at the beginning of our lesson. There was reason behind this decision though; this reason was because we wanted to student to come up with the idea to make the graphs. If we were to state at the beginning of the lesson that we were going to make bar graphs to show why it was important not to litter, then the students could not have thought for themselves of the best way to show what they wanted to show. This lesson was part of a larger project and the project was one for the students to take charge of.

Another area to look at was how we addressed the standards. This area I believe we had them complete. There was only one standard that applied to our lesson that we could find and in this standard there was only a portion of the standard that applied to our lesson.

Still another area to examine would be our purpose. I think we did a good job showing how graphs can be used in the real world and also giving the students a reason to make the graphs. I think that it is important to link graphs to something that the students are interested in. If I were to do this again I would not change how we made the graphs meaningful for the students.

The next area to look at would be the anticipatory set. This is the part of the lesson that I liked the most. We got the attention of the students by writing them a letter from the EPA. This idea I believe would have worked better if the students were actual second graders instead of college students that were pretending to be second graders. I would not change this if I were to teach this lesson to a class. What I might try to do would be to go to the local DEP headquarters and ask if they could actually write a letter about cleaning pollution. This I think would be more realistic than a letter made up by myself.

If I were teaching this lesson in an actual classroom I would ideally want laptops so that the class could be spread out. I would still want the students to be in groups. I think it is important for the students to be in groups and working together to learn a new technology. I remember when I was in elementary school, the teacher would have the whole class go to the computer lab and each work individually on a computer. I would not always know what to do, when other people were jumping ahead of the lesson. This would often frustrate me and I would end up asking my peers for help. If the students can start out in groups, then they are already in a position to teach each other.

Reflections

WebQuest

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An area that could use improvement would be our directions and our procedures. I feel that we were not as clear as we could have been when it came to giving directions. We did not fully think through all of the directions that we would have to give. An example of what I am talking about is when we were preparing the class to begin the gallery tour. Here we did not specifically say where to go to look at the different graphs. Overlooking these details leads to confusion in the classroom. Next time I will try to map out exactly what will take place and anticipate problems.

I do not feel that our transitions were smooth. Again, we did not plan extensively on how we would deliver our transitions. This I believe comes with more practice and with watching what other people do.

I enjoyed our assessment. The gallery tour allowed for each group to share what they came up with for a graph and to show what they accomplished at the park. It also allowed Joey and myself an opportunity to see what groups had an understanding of the bar graphs and all of the aspects that went into the graph.

A problem that we were faced with was the difference in Excel between the version that we are used to and the version that is now on the computers at Central. When we were planning and practicing our lesson on our own computers, forgetting that the school had a different Excel. If I were to teach this lesson again, I would make sure I tried out the lesson on the actual computers that will be used to find out if there are any differences.

We used technology as a tool to make our graphs. Or lesson was designed for a second grade class and they most likely would not have the background to make the graphs on their own. Some guidance by the teacher would be needed. I do not see how this lesson could be carried out with a group of second graders without going through how to make the graphs each time for at least the first few times. This lesson was however intrinsically motivating. Most students at this age that I know feel passionately about pollution issues and they want to help the environment.

Throughout the lesson we attempted to create discussion. This did not work very well. The class did not seem willing to participate in the discussions. This seems to be typical of presenting lessons to college age students. If I were to attempt this again, I would attempt to facilitate discussion by having the students first talk in small groups and then ask them to share with the class. This might work better to get some discussion going.

There were many areas in our presentation that could use improvement, but there were also some good areas. The areas that need the improvement need to have a solution thought about. It does not good to simply say “I need improvement,” but then to give mo plan of action to improve.

Reflections

WebQuest

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