Math Curriculum Guide

By

Amaranta Perez

SED 720ÝÝÝÝÝÝÝ Dr. CooksÝÝÝÝÝÝÝ 12/5/02ÝÝÝÝÝÝ SFSU

Articles

Article 1:

URL: http://www.leeds.ac.uk/educol/documents/00001634.htm

Summary:Ý This article titled ìDeveloping Algebraic Activity in a ëCommunity of Inquiresí,î by Laurinda Brown, Alf Coles, Rosamund Southerland, and Jan Winter isÝÝÝ about answering the following question:

ÝCan we develop a school algebra culture in which pupils find a need for algebraic symbolism to express and explore their mathematical ideas?

The researchers worked with four seventh grade mathematics classrooms in secondary schools in the UK.Ý In this article the researches analyzed a transcript from an observed classroom from four different perspectives: metacommenting, teaching strategies, algebraic activity, and pupil perspectives.Ý In the part of metacomments the researcher noted comments that had to do with students asking their own mathematical questions and their answers to those questions.Ý In the section of teaching strategies the researcher noted patterns in data across the four classrooms and teaching strategies related to the studentsí development of Algebra. In the section of pupil perspectives the researcher noted the studentsí perspectives of what mathematics they learned. In the section of algebraic activity the researcher noted activities in the following algebraic categories: generational, transformational, and global.Ý One of the conclusions of this research was that studentsí ìcreativity is supported as they are encouraged in asking of their own questions.î

Connection to Literacy: This article investigates how seventh graders develop algebraic language.Ý It gives good examples of students discovering how to write mathematical patterns and how to approach a mathematical problem.

Significance: This article shows teachers how to encourage students to come up with algebraic language by themselves. This is important because in order to understand mathematics one must know the meaning and concepts behind symbolism. To illustrate, there is an example in the article of students coming up with the community property all by themselves.

Article 2:

URL: http://www.leeds.ac.uk/educol/documents/00001883.htm

Summary:Ý The article titled ìAspects of English and Turkish studentsí performance in trigonometry tasksî by Ali Delice is a ìcomparative study of English and Turkish senior high school students' understanding of trigonometry.îÝ Delice investigates studentsí performance in different areas, some of which are the following: student manipulation of trigonometric identities, formulas, simplification of trigonometric expressions, mental models of word problems.Ý Delice also investigates how teachers teach trigonometry in both countries, what resources they use, textbooks, and curriculum.Ý Some of the results of this study are the following. Turkish students answered correctly more algebraic problems compared to English students.Ý English students answered correctly more application problems compared to Turkish students.Ý ìBoth English and Turkish students were better at algebra than trigonometry.îÝ Delice concludes that what is meant by trigonometry in both countries is not the same, so whatever area is emphasized in the curriculum that is where students are going to do better.

Connection to literacy: Delice writes that in the answers of tests that she gave to many students, students did not know the language of trigonometry, for example, angle of depression. She writes that misuse of the language or misunderstanding of the problems led to wrong solutions in the tests. This shows that is important for teachers to teach vocabulary and standard mathematical language to students so they can perform better in tests.

Significance: Research comparing different educational systems is important because we can improve our own education classroom by looking at what is working for other teachers.Ý Students benefit greatly when they are exposed to different perspectives, books, and curriculum.

Article 3:

URL: http://www.csci.educ.ubc.ca/publication/insights/archives/v06n01/swanson.html

Summary: The article ìTeaching Mathematics in Two Independent School Contexts: The Construction of ëGood Practiceíî by Dalene Swanson is about her experience of teaching at two different schools, in different countries, and different cultures.Ý Swanson taught at a high school in South Africa and a middle school in Canada.Ý Swanson writes that good teaching had different meanings at both schools and that the attitudes of the parents at both schools were very different.Ý In the first school a student who is not doing well in school is perceived as not putting sufficient effort in school or lacks the ability to do well. In the second school the fault that the student is not doing well in school is placed on the teacherís strategies of making the student feel good.Ý For example, a parent suggested that if the teacher would give his son a better grade, regardless of his mathematical performance, his son would feel better and as a consequence do better in school.

Connection to literacy: This article shows the importance of teachers doing research on the community that they are going teach in order to create lesson plans that work with that student population.

Significance: This article shows the importance of the teacher getting to know the community in which he/she is going to teach in order to be able to teach better and be able to handle parents concerns.

Article 4: ìProof as a tool for Learning Mathematicsî by Erick J. Knuth, Mathematics Teacher, Volume 95, Number 7, October 2002, Pages 486-492: NCTM.

Summary:ÝÝÝ This article is about the importance of showing high school students proofs that promote mathematics understanding.Ý The article states that there are proofs that merely demonstrate and proofs that explain.Ý Knuth says that proofs are only covered in geometry in high school and he encourages mathematics teachers to use proofs that explain in all math classes to increase mathematical understanding.Ý The author gives examples of different proofs of the same theorem to illustrate his point of proofs that explain.Ý He shows algebraic proof, geometrical proofs, and pattern proofs to prove his point.

Connection to literacy: In the mathematical world being literate means knowing how to do proofs.Ý So it is important that high school students learn how to do proofs in high school or at least get exposed to proofs, not only because it helps in their understanding, but also because knowing why a theorem works its mathematical power.Ý Students also improve their writing skills and critical thinking skills by doing mathematical proofs.

Significance: This article shows the importance of students learning to do mathematical proofs in high school to develop mathematical understanding. Students that know how to use mathematical language like doing a proof in high school have an edge in college over students that have not been exposed to proofs, since college mathematics involve proofs.

Article 5: ìBuilding Studentsí Sense of Linear Relationships by Stacking Cubesî By Diana Underwood Gregg, Mathematics Teacher, Volume 95, Number 5, May 2002, Pages 330-336: NCTM.

Summary: This article is about helping students make sense of lines and linear equations.Ý Gregg describes the different stages of her activity of stacking-cubes. First how stacking-cubes become towers in increasing order and students are to figure out how many cubes ìthere would be in the tenth tower, without drawing all the towers in between.î After this students are to figure out the pattern of the height of any tower. The next step is to figure out the rate of change between the towers. The next stage of her activity is to describe the towers as points.Ý Afterwards, the next step is to explain to the student that the term slope is used for change, and that the ìheight of the zeroth building was called the y-intercept.îÝ The teacher should also make the distinction of discrete and continuos data.Ý The author concludes that many of her students learned well from this activity and that they now understand the algebraic meaning of linear equations.

Connection to literacy: This article shows how teachers can explain linear equations to their students in a way that students conceptualize mathematics in their heads. The author shows an innovative approach to teaching linear equations that makes the language of mathematics more accessible to many more students.

Significance: This article is a great resource for a teacher that is going to teach linear equations, since students greatly benefit when they understand mathematics.Ý The article contains graphs and figures that explain her activity step by step.Ý

Critiques of Lesson Plans

Critique 1:

URL: http://ofcn.org/cyber.serv/academy/ace/math/cecmath/cecmath028.html

Summary: This lesson plan is for a high school math class.Ý The lesson is about figuring out at what angle does a water hose eject water at a greatest distance.Ý This is an interesting geometry application problem that can help track athletes think about their performance and how to maximize their jumps.Ý

Positive Aspects: The author gives a good procedure for the teacher to follow.Ý The lesson plan also comes with questions that students should answer at the end of the activity. These questions make students think about and explore different angles.

Development Areas: The negative aspect of this lesson plan is that many gallons of water will be wasted in learning about which angle gives a maximum distance.

How would I adapt this lesson for my classroom? I like the purpose of this lesson plan, but I donít like wasting water.Ý The same activity could be done with tennis balls and a racquet.Ý Students could hold a ball with one hand and with a racquet throw the ball at different angles with the same force.Ý Doing this activity this way might be a little less accurate, but still students will figure at what angle the ball achieves a greater distance.

Critique 2:

URL: http://school.discovery.com/lessonplans/programs/numbersnature/

Summary:Ý This lesson plan is designed for a high math class dealing with number theory.Ý The lesson is about getting students introduced to the Fibonacci sequence and how Fibonacci numbers are found in nature.Ý The lesson plan first gives a story of how Fibonnaci came up with the Fibonnaci sequence, then the teacher is to let students explore by themselves a problem to come up with the Fibonacci sequence.Ý After that students are to find Fibonacci numbers in nature.

Positive aspects: This lesson plan is easy to read and well written.Ý The author did good research about the Fibonacci sequence and came up with a classroom activity that relates math to numbers in nature. The lesson plan includes good discussion questions and a helpful rubric.

Development Areas: This lesson plan from my point of view needs very little development. It is well written so a substitute can follow and teach it.Ý

How would I adapt this lesson for my classroom? I like this lesson plan, so I plan to use it in my classroom as it is.

Critique 3:

URL: http://mathforum.org/alejandre/frisbie/locker.html

Summary: This is a problem-based lesson for middle or high school students.Ý The problem is the following.Ý Imagine that there are 1000 lockers in the school and that a student opens every locker. Then a student closes every other locker. The third student changes the state of every third locker beginning with number 3. (If the locker is open the student shuts it, and if the locker is closed the student opens it.)

The fourth student changes the state of every fourth locker beginning with number 4. Imagine that this pattern continues, at the end, what lockers would remain open and close?

Positive aspects: This is a very good problem for students to look for patterns and investigate numbers.Ý The lesson plan uses manipulatives like cardboard boxes to simulate lockers so students can explore the question using their hands if they need to.Ý The lesson plan suggests that students could use spreadsheets to simulate the activity, which could be helpful for some students.

Development areas: Having solved this problem myself in a math class, I think that the teacher should emphasize to the students to solve the problem their own way.Ý Manipulatives and technology should only help the student solve the problem not distract the student from the problem.

How would I adapt this lesson for my classroom? I plan to use this lesson plan in high school, so I do not plan to use cardboard boxes to simulate locker because it might be to distracting for my students.Ý I do plan to show them how to come up with their own way of symbolizing that a locker is closed or open, so they can explore the problem on paper.

Critique 4:

URL: http://math.rice.edu/~lanius/pro/richte.html

Summary: This is a problem-based lesson for 4-9 grades.Ý The problem is the following what payment would you choose out of the two options? This first option is that you will get pay 1 cent on the first day, 2 cents on the second day, and double your salary every day thereafter for the thirty days.Ý The second option is that you get 1,000,000 dollars flat payment for thirty days.

Positive aspects: This is a good introductory problem to exponential growth.Ý The lesson is also good to practice finding patterns.Ý It is an interesting problem that adolescents like.

Development areas: The author of the lesson plan when introducing the problem tells the students that a guy choose option two and that the students need to figure out if he was smart in choosing option two.Ý There is no necessity of including a third person in the problem.Ý The problem should be posed directly to the student to see what they would choose.

How would I adapt this lesson for my classroom?Ý I plan to use this problem in one of my lessons.Ý I plan to ask my students directly the question and not introduce unnecessary material.Ý

Critique 5:

URL: http://score.kings.k12.ca.us/lessons/teamwins.htm

Summary: This statistics lesson plan is for the grades 8-12.Ý In this lesson students are to figure out in how many ways a team can win a 7-game series.Ý The lesson includes an example of how many ways a team can win a 5-game series.Ý Students are expected to use the internet and to go to specified web sites to collect data on 7-game series just to get an idea of how 7-game series have been won.Ý The author includes a list of several web sites for students to look at.

Positive aspects: This lesson plan is a good exploration for student to become familiar with sample spaces of 5 and 7-game series.Ý This lesson plan brings to the classroom popular culture making a interesting lesson for adolescents.

Development areas: The procedures in this lesson plan could be better explain, otherwise the plan is a good one.

How would I adapt this lesson for my classroom? I plan to use this lesson plan as it is with minor adjustments.Ý First I am going to ask my students to explore how a team can win a 3-game series, 5-game series, and then a 7-game series.Ý I am going to limit the use of internet searching because one can get an idea of how a team can win without having to surf the net.

Original Lesson Plans

Lesson Plan 1:

I created this lesson plan on taskstream.com. It can be found at:

http://lesson.taskstream.com/lessonbuilder/v.asp?LID=fvh@zbfpcxhgzu

Student handout that goes with the above lesson plan:

How to make a soccer field map using Geometerís Sketchpad

Instructions:

1. To open a new sketch on Geometerís Sketchpad go to File-New Sketch.
2. Use straightedge tool found on the left palette to draw a horizontal line.
3. ÝLabel the endpoints of this segment A and B using the Text tool (looks like a hand).
4. To measure the length of AB go to Measure-Length.
5. Use the selection arrow tool (arrow) to extend or shrink segment AB so its 3.33 inches long.
6. Draw two perpendicular lines each 5.05 inches long to segment AB at points A and B to make the sidelines of the soccer field with the straightedge tool.
7. Complete the rectangle ABEF with the straightedge tool.Ý This rectangle is the boundary of the soccer field.
8. Construct the midpoint of AB by clicking on this segment with the selection arrow tool then going to Construct-Point at Midpoint.Ý Label the midpoint j.
9. Create midpoints at all sides of the rectangle.
10. Construct the midpoint between AJ.Ý To do this first you need to create segment AJ.Ý Click on points A and J while holding the shift key, then go to Construct-Segment.
11. Create the midpoint of the segment JB.
12. Create the penalty area boundaries, and the goal area following the steps above.
13. Connect the midpoints of AF and BE to construct the midfield line.
14. Create the center circle using the compass tool.
15. Follow steps 2-12 to create the other side of the soccer field.

A sample of the soccer field map done on Geometerís Sketchpad following the above directions:

Lesson Plan 2:

ÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Amaranta Perez

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Grade: 9^th-10th

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Class: Geometry

ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Number of students: 22

Time: 1hr

PROBLEM-BASED LESSON

1. Purpose of lesson: Students will be able to use similarity of triangles to be able to measure the height of a tree.

Students already know the definition of similarity and know the criteria for similarity of triangles like AAA and SAS.Ý In this problem we be using these ideas.

In the next lesson students will compare answers and prove to their group why they think they are right.

2. Rationale:Ý It is important that students see how the ideas of similarity are used in a real life problem.

3. Prerequisites: Students already know the definition of similarity, they know about the ratios, and know criteria for similarity of triangles like AAA and SAS.

4. Standards addressed:

Standards NCTM:

Explore relationships (including congruence and similarity) among classes of two and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.

CA Standards:

Standard 5.0: Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

Standard 1.0: Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:

Ý
Benchmark or Example 1.1: Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).

Benchmark or Example 1.2: Construct and read drawings and models made to scale.

Benchmark or Example 1.3 (Key Standard): Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

5. Materials:

12-inch ruler,

binder paper,

yardstick,

pencil.

6. Lesson Outline:Ý

Launch:Ý Initially I will give my students the following problem on a piece of paper to each group of four students.Ý Then we will read it aloud to explain it and answer questions.Ý

Problem:Ý Today we are going to the park to do some measurements.Ý Your job is to approximate the height of a tree with only a 12- inch ruler, paper, pencil and a yardstick.Ý You are not allowed to climb the tree or use other type of instruments.Ý Think about what you have learned in the last few days and apply those ideas to solve this problem.Ý Draw diagrams on your paper to help you figure out how you are going to approximate the height of the tree.

Investigation: I take my class to the park and show my students which tree I want them to measure.Ý The students will work in-groups of four to come up with their own way to approximate the height of the tree.Ý First I will let the students explore by themselves the problem.Ý After 10 minutes I would start giving students clues about how to do use ratios.Ý For example, one way to solve this problem is to put the ruler in front of your eyes and see what measurement corresponds to the height of the tree.Ý Then in the same way see what measurement corresponds to the width of the trunk of the tree and measure its actual width. Another way to solve this problem is to measure your shadow and the shadow of the tree.Ý I could also provide mirrors and have them measure similar angles that way.Ý I would have students write down the measurements in a diagram that showed similar triangles.

Summary: After all measurements have been taken we would return to class and I would ask my students to calculate the height of the tree.Ý To do a write up and to show how why their method works.

7. Strategies: I want my students to think of many different ways to solve this problem.Ý I want them to apply all kinds of criteria for similarity of triangles and other geometry that they have learned.Ý I am going to encourage students to try their own methods or give them ideas of how to use some method if they are stuck.

8. Assessment: I will collect a report from each group about how they calculated the height of the tree.Ý That report will contain a diagram that showed how they used similar triangles, what method they used, and their final approximation.

In the next lesson, groups will present their solutions to the class.Ý So everyone can see different ways and see what approximations are more accurate.

9. Literacy aspect: Students that participate in this lesson will practice angle notation.

Lesson Plan 3:

Amaranta Perez

Class: Algebra 1

Grade:8-9

Number of students in class: 22

Time:1hr

Objective:

… Students will be introduced to the idea of a function.

… Students will explore different types of relationships and decide if they are functions or not.

Purpose :Ý The purpose is to introduce students to the idea of a function.

ÝÝÝÝÝÝÝÝÝÝÝ

Materials: Paper and pencil

Anticipatory Set:Ý (8:00AM-8: 10AM)

ÝÝÝÝÝÝÝÝÝÝÝ First I will write on the board two sets with numbers.Ý These two sets will be related in some way.Ý Students are to figure out what is the relationship between them.

Instruction: (8:10AM-8: 20AM)

ÝÝÝÝÝÝÝÝÝÝÝ Students are already familiar with order pairs.Ý I will remind them of the definition of order pairs (x, y) where x is an element of set A and y is and element of set B.Ý Then I will introduce the idea of a function as a set of ordered pairs.Ý Then I will explain to my students the definition of a function. (There are two sets A and B.Ý There is a relationship between these two sets represented by order pairs where every element of A is pair with an element of B, and no element of A is used in two different pairs.)ÝÝÝÝÝÝ

Guided Practice: (8:20AM-8:40AM)

ÝÝÝÝÝÝÝÝÝÝÝ Students will work in-groups of four. I will give students different types of relationships and they are to figure out by themselves if they are functions or not. Then they are to discuss their results with their group mates.

Closure: (8:40AM-8: 50AM)

ÝÝÝÝÝÝÝÝÝÝÝ Students write out a definition of a function in their own way.Ý Students write about relationships or rules that occur in their lives.

Homework:

Students come up with mathematical functions of the relationships that occur in their own lives and say whether they are functions or not.

Assessment:Ý Below is a quiz that I would use to see if students understood functions.

Directions:Ý Below are several sets, you are to connect the elements in one set to the elements in the other set to form a relationship.Ý The type of relationship that you are ask to create is written below the sets.Ý Also if it is a function give its domain, range, and codomain.

Ý

FunctionÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Not a function

Explain why is it a function?ÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝExplain why is not a function?

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ _______________________

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ _______________________

Domain =ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ

Range =ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ

Codomain =

Ý

FunctionÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Not a function

Explain why is it a function?ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Explain why is not a function?

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ _______________________

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ _______________________

Domain =

Range =

Codomain =

Ý

FunctionÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝFunction

Explain why is it a function?ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Explain why is a function?

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ _______________________

______________________ÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ_______________________

Domain =ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Domain =

Range =ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ Range =

Codomain =ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ ÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝCodomain =

Literacy aspect: Students will be introduced to function notation, syntax, and concepts.

ÝLesson Plan 4:

Amaranta Perez

Class: Geometry

Grade: 9^th

Number of students in class: 22

Time: 1hr

Objective:

… To learn when two polygons are similar

… To learn AAA criterion for similarity of triangles

… To learn SAS criterion for similarity of triangles

Purpose :

ÝÝÝÝÝÝÝÝÝÝÝ The purpose of this lesson is to know what similar figures are, and to discover the different criteria for similarity of triangles.

Materials: paper and pencil

Anticipatory Set:Ý (8:00AM-8:10AM)

ÝÝÝÝÝÝÝÝÝÝÝ Show students a slide with different types of polygons, some similar to each other.Ý Ask students which ones they think are similar and why.Ý On a piece of paper students write their reasons of why they think the figures are similar.Ý Then we have a discussion about which figures are similar.

Instruction: (8:10AM-8:20AM)

… Define similar in geometric terms

… As an example use similar rectangles

Guided Practice: (8:20AM-8:40AM)

ÝÝÝÝÝÝÝÝÝÝÝ Break students up into groups of four each and give them a worksheet that is going to guide them to discover the different criteria for similarity of triangles that is AAA and SAS.

Closure: (8:40AM-8:50AM)

ÝÝÝÝÝÝÝÝÝÝÝ Explain to students what AAA and SAS to reinforce what they have discovered.

Homework:

ÝÝÝÝÝÝÝÝÝÝÝ Students will measure the ratio and angles of similar triangles to prove that they are similar.Ý Also student must identify if they could have used AAA or SAS to show that they were similar.

Assessment: Teacher collects and grades homework.

Literacy aspect: Student is taught the notation of similar angles and congruence.

Lesson Plan 5:

Amaranta Perez

Grade: 10-12

Class: Trigonometry

Time: 1hr

Number of students in class: 22

Objective: Students are introduced to spherical coordinates and are to practice using spherical coordinates using a basketball.

Materials: paper, pencil, and 2-3 basketballs for the entire class

Anticipatory set: (8:00AM ñ8:10AM)

I am going to show my students a basketball and I am going to pose the following situation.Ý Imagine that you were an ant on the surface of this ball and you had a friend that was lost in the forest.Ý Your friend calls you on your cell and asks you to give her directions to your house.Ý How would tell her to come to your house? ÝRemember you are now living on a circular surface, there are no flat areas.Ý Students are to write their responses on journals.

Instruction: (8:10-8:20) I am going to define spherical coordinates.

Guided Practice: (8:20-8:40) Students are to answer the problem in the anticipatory set with given coordinates.Ý Students need to give directions in spherical coordinates and write it down on a piece of paper.

Closure: (8:40-9:00) Students will go to the board to present different solutions, since there are many ways of getting from one point to another point.

Homework: Students are to create and solve a similar problem at home.

Assessment:Ý Teacher collects and grades homework.

Literacy aspect: Students are introduced to spherical notation and syntax.

Resources

Resource 1:

URL: http://www.terragon.com/tkobrien/algebra/

Summary:Ý This website is a great resource for Algebra 1 teachers and students.Ý It is an online textbook that comes with a graphing program.Ý It allows students to graph functions as in a graphing calculator.Ý This resource comes with quizzes and test that the teacher could print to use in the classroom.Ý This website has detail examples that students could read to understand how to graph linear equations.

Positive aspects: The graphics features in this website are easy to use and give the reader a clear view of the graph.Ý The website comes with helpful aids such as a calculator, crossword puzzles, and a glossary.

Development areas: The program is a little slow when it comes to graphing functions.Ý The user could benefit from examples of how to graph a function on this program.

How would I use this resource in my classroom?Ý In case the high school that I work for does not have a computer lab with the software Mathematica, then I plan to use this website to show my students how to graph functions. As the teacher I plan to use its quizzes and tests with my students.

Resource 2:

URL: http://members.ozemail.com.au/~petehobson/

Summary: This website is a great resource for high school math teachers who are looking for low cost/no cost computer mathematical software.Ý The website comes with six categories of resources: graphical designs, assessment items, spreadsheets, functions, modeling, and shareware.Ý In each of these categories the author gives examples of material that the teacher could use in a classroom and gives links in how to find that particular software.

Positive aspects: This website gives the teacher great ideas about creating interesting lessons with computer software.Ý Most examples are easy to read and are mathematically meaningful.

Development areas: The reader would have a better idea of how the spreadsheets look like if the author had included an actual sample.

How would I use this resource in my classroom?Ý I plan to use this website to enhance my lessons with technology.Ý I plan to use the examples in this website in my classes as well as the suggested software.

Resource 3:ÝÝÝ

URL: http://math.rice.edu/~lanius/misc/

Summary: This is a great website for Geometry teachers who want to learn how to use Geometerís Sketchpad. This website comes with step-by-step directions about how to do ìPinwheel rotationsî.Ý Following these directions one learns how to do rotations, translations, and reflections on Geometerís Sketchpad.Ý The website comes with a link to math lesson plans.

Positive aspects: If one follows the websiteís directions for its Geometerís Sketchpad activity one learns the powerful features of this software.Ý The website also comes with good questions for students to answer after they have finished the activity.

Development areas: Some of the links in this website donít work.

How would I use this resource in my classroom?Ý I plan to use this activity in Geometry classes to make my lessons more interesting.Ý Movement and color will certainly make geometry sketches more fun.

Resource 4:

URL: http://www.enc.org/weblinks/math/

Summary: This website is a collection of math resources. It contains links to websites by subject area within mathematics, for example, Numbers and Operations, Algebra, Geometry, etc.Ý The website also contains links to curriculum resources, professional development, parents section, and other links.

Positive aspects: This is a great starting place for math teachers to do research on the internet about a specific subject since it contains many links to math websites.Ý This website has a great search engine that allows the user to look for specific material.

Development aspects: This website does not have any direct links to websites about women involved in math.

How would I use this resource in my classroom?Ý I plan to use this website as a starting point to do research about information that I could use in my lesson plans.

Resource 5:

URL: http://www.nctm.org/

Summary: This is the website for the National Council of Teachers of Mathematics, an association of math teachers dedicated to provide national leadership in math education.Ý The website contains the national math standards for K-12 grades.Ý It contains information about grants for math teachers.Ý It has a section of publications, which include online journals like Mathematics Teacher and On-Math.Ý It has a section called Student Math Notes, which includes math activities for the math classroom.Ý It also has a family section and conference section.

Positive aspects: This is an organization that promotes excellence in mathematics. It is an organization that writes national standards that make sure students not only know the basics, but also know the concepts and how to think critically. This organization also supports teachers by offering grants to special projects.

Development areas: This organization should promote more often that all students should have qualified teachers especially in the inner city schools.

How would I use this resource in my classroom?Ý I already subscribe to Mathematics Teacher and have the book of all the K-12 NCTM standards, and of course I am a member of NCTM.Ý I plan to use this website as a recourse to find activities for my lesson plans.Ý I also plan to read the electronic journals to keep up with the latest research.