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Mathematics Portfolio. MAE 4360 Teaching Middle and Secondary School Mathematics Fall 2006 . Grading Criteria. Cover Design with Name,Class, Title............……… +5 _______ Binder/PowerPoint/ or other Electronic Presentation.. +10 _______

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mathematics portfolio

Mathematics Portfolio

MAE 4360

Teaching Middle and Secondary School Mathematics

Fall 2006

grading criteria
Grading Criteria

Cover Design with Name,Class, Title............……… +5 _______

Binder/PowerPoint/ or other Electronic Presentation.. +10 _______

Organized/Neat/Easy to Read.................................… +10 _______

Table of Contents/Cover Letter with Summary......... +10 _______

Includes all Sections Mentioned Above..................... +10 _______

Math Auto. and Philosophy Bullets........................… +10 _______

Research Articles on Math Ed./Websites…………… +10 _______

Professional Section with Resume, etc....................… +10 _______

Quality Presentation/Demonstration of Effort............ +20 _______

Above and beyond minimum (Tech., Org., Qual., & Pres.) +5 _______

Possible Portfolio Grade = 100 ______

  • Table of Contents
table of contents
Table of Contents
  • Grading Criteria
  • Summary
  • Chapter Reflections
  • Problem SolvingSample
  • Classroom Brochure
  • Lesson Plan
  • Calculus Textbook Review
  • Teacher Observations
  • Tessellation Extra CreditSample
  • Math Autobiography
  • Final Exam Questions
  • Mathematics Education Philosophy Bullets
  • Research ArticlesSample Websites
  • Resume
  • ESOL Accommodations
  • Four-Step Problem Solving Process
summary
Summary

Putting together this PowerPoint presentation of everything that I have done for the course really shows me how much I have learned. I still stand by my earlier prediction that I would earn an A- for this class. To be very honest, I learned more than I expected to learn from taking this course. I found the textbook to be very helpful and to have practical ideas for the classroom. I really liked doing the weekly Problem Solving because I have always enjoyed the challenges of math. I worked very hard on the portfolio. Even though I know that it isn’t perfect, I’m proud of the effort that went into its creation.

  • Table of Contents
chapter reflections
Chapter One

Chapter Two

Chapter Three

Chapter Four

Chapter Five

Chapter Six

Table of Contents

Chapter Seven

Chapter Eight

Chapter Nine

Chapter Ten

Chapter Eleven

Chapter Twelve

Chapter Reflections
chapter 1 reflection
Chapter 1 Reflection
  • Chapter One Summary and Reflection  The background information about the “Traditional Approach,” 

“New Math,” and “Standards-Based Classrooms” was more helpful than I expected.  I was surprised to realize how much my own mathematics background fits into these molds.  In school I was told to memorize definitions and properties and all lessons and homework were directly from the textbook.  This learning style suited me very well and I prefer to work independently, so I did not miss the benefits of cooperative learning.  I agree with the text when it says that teachers struggle to get through the textbook by the end of the school year and cover numerous topics instead of pacing the curriculum for skills mastery.  If students master a topic one year, it should not be necessary to review that topic year after year.

  • Chapter Reflections
chapter 2 reflection
Chapter 2 Reflection
  • Chapter Two Summary and Reflection I have learned about multiple intelligences and learning styles in other workshops.  I still don’t understand how they relate to math and how I am supposed to incorporate this into my lesson plans. Even if I test the students to find out what category they fall under, I am not sure how to apply this information to best suit these students. To me it seems that math is so rigid that it does not allow for variety to accommodate different learning styles. When I took my gifted certifications courses, it seemed that other subject areas could use this information more easily than mathematics.
  • Chapter Reflections
chapter 3 reflection
Chapter 3 Reflection
  • Chapter Three Summary and Reflection My school had plenty of brand new manipulatives available and in the past two years I used one set in one lesson for Algebra Tiles.  It was a mess and the experience confused the students more than before the lesson.  I still think that manipulatives take longer to teach and am not sure how to incorporate them into lessons.  I also agree that some manipulatives put off older students because they appear elementary and it’s not cool for them to play with.  I was surprised by the data supporting the use of calculators as early as 5th grade.  I, as well as other math teachers, feel that calculators are a crutch that allow students to test well but prevent the learning of basic math skills and concepts.  
  • Chapter Reflections
chapter 4 reflection
Chapter 4 Reflection
  • Chapter Five Summary and Reflection

The book says that “the study of shape is motivating and enjoyable to many students, as contrasted to the study of abstract postulates and theorems prevalent in all too many geometry classrooms.” I agree that Geometry can be a fun subject when you consider all of the real world applications that you can bring in as examples and the use of technology to enhance lessons. Although Geometry has a lot of vocabulary, it seems easier for students to grasp the concepts when there is a concrete visual for them to reference. As the previous notes pointed out and the textbook reviews, Algebra and Geometry are interconnected with each other. Algebra is used to solve Geometry problems and Geometry is often used in Algebra examples. I am not surprised that 40-50% of students fail college-preparatory algebra. Although the text says “teachers should introduce and build upon algebra concepts in the earlier grades,” it gives no insight on how to accomplish this.

  • Chapter Reflections
chapter 5 reflection
Chapter 5 Reflection
  • Chapter Five Summary and Reflection

The book says that “the study of shape is motivating and enjoyable to many students, as contrasted to the study of abstract postulates and theorems prevalent in all too many geometry classrooms.” I agree that Geometry can be a fun subject when you consider all of the real world applications that you can bring in as examples and the use of technology to enhance lessons. Although Geometry has a lot of vocabulary, it seems easier for students to grasp the concepts when there is a concrete visual for them to reference. As the previous notes pointed out and the textbook reviews, Algebra and Geometry are interconnected with each other. Algebra is used to solve Geometry problems and Geometry is often used in Algebra examples. I am not surprised that 40-50% of students fail college-preparatory algebra. Although the text says “teachers should introduce and build upon algebra concepts in the earlier grades,” it gives no insight on how to accomplish this.

  • Chapter Reflections
chapter 6 reflection
Chapter 6 Reflection
  • Chapter Six Summary and Reflection

     The textbook discusses lesson planning strategies for daily lesson plans, unit lesson plans, and semester lesson plans.  I agree that it is important to use a calendar to approximate the test days for each unit based on the amount of material that needs to be covered during the year.  I also agree that you must consider early release days, standardized testing days, the day before a vacation break, etc. when outlining the lessons.  I have found this strategy useful when lesson planning, however it is discouraging when student comprehension does not progress with the preplanned schedule.  I am not yet sure how to adapt to factor in unknown time set-backs, such as when school is cancelled due to weather or unexpected assemblies or students do not understand the material.     The method the textbook recommends for daily lesson plans is in my opinion quite daunting.  Perhaps I am highlighting my inexperience of not coming from an education background, but I honestly don't know when I would find the time to write such detailed lesson plans for every section of every chapter.  It was difficult enough handling the paperwork and documentation for attendance, homework, quizzes, and tests.  I understand that once you have this in place, each year will take less time to modify.  However, it has been my experience that each year you can be teaching a different grade level with a different text, and all of the work may not be utilized the next school year.

  • Chapter Reflections
chapter 7 reflection
Chapter 7 Reflection
  • Chapter Seven Summary and Reflection This has been the most useful chapter so far.  I really liked the concrete examples of questions to ask to elicit student participation.  Some things I have heard before, like the three to five second wait-time and not giving praise for correct answers.  Other ideas I will try in my classroom, like pair-share before answering and handing out overhead transparencies and pens for students to write solutions out.  The textbook’s Do’s and Don’ts on page 250 and Examples of Questions on page 253 were specific and helpful.  The section on Communication Through Writing was enlightening.  I had heard of math journals but didn’t know how they would work.  I would consider using the Think-Talk-Write, teacher provided prompts, and student-written problem activities.  I really enjoyed reading this chapter because it spelled out what the teacher should do and why.
  • Chapter Reflections
chapter 8 reflection
Chapter 8 Reflection
  • Chapter Eight Summary and Reflection

I have experienced the problem where checking and going over homework has taken over half the period and I realize that it is a vicious cycle. I like the idea of students going over homework in small groups. The problem I see with this is motivating students to speak up and ask questions and help each other. I will try the method of selecting review questions and having multiple students work the answers on the board. I try to stress that review day is not a cram session but students should actually be prepared to take the test that day and review is the final opportunity to ask questions since they already studied. Chapter 8 touched on two points that I agree with regarding testing. First, “easily scored tests are less of a burden to the teacher.” If tests are to be returned in a timely manner, then I cannot grade 125 open ended tests overnight and make individual comments for each student. Second, “objectivity always is a part of grading.” I am the first to admit that I have caught myself giving more partial credit points to a student that I like than a student that I like less with the same incorrect answer. I then have to go back and re-grade to be fair to everyone.

  • Chapter Reflections
chapter 9 reflection
Chapter 9 Reflection
  • Chapter Nine Summary and Reflection

I completely understand what the authors are saying about the detriment of tracking. However, I sympathize with the teachers who have low level classes. One-on-one time is spent disciplining and writing referrals instead of tutoring and advancing the students. I dreaded my worst class last year. I even tried to get a student transferred to another class because she was a very hard worker but also ESOL and could eventually make it to advanced math but had no chance in that class. The guidance department never got around to changing her schedule, big surprise. I agree that tracking needs to end in high school. My experience with middle school students supports the observation that some students will mature and be capable of handling more challenging math later on. Even my “gifted” students struggled in Algebra because they did not have the discipline and study habits developed. I tried to talk to them about college and careers and the importance of learning these skills early, but at 11 only a few had any interest in college.

  • Chapter Reflections
chapter 10 reflection
Chapter 10 Reflection
  • Chapter Ten Summary and Reflection

I loved the plumber analogy! The performance tasks discussed in this chapter with the 4-point rubrics seem similar to FCAT short and extended response questions. I wish that my school would have a staff development for scoring these questions. They always give us any booklets published by the state, however, I think it is fair to say that most of those get recycled and not read. I have had a problem with identifying anchor papers with projects that I have done in the past. Going back to what I said in Chapter 8, it is very difficult to be objective. The information about Advanced Placement Tests was interesting. I guess the AP Exam is equivalent to the final exam in a college course, however I’ve never been in a college course that grades the final in scores from 1 to 5.

  • Chapter Reflections
chapter 11 reflection
Chapter 11 Reflection
  • Chapter Eleven Summary and Reflection This chapter discusses ways to communicate with parents.  This is perhaps the one area that we have received training and workshops on in our school because administration feels that it is so important.  I particularly liked Figure 11.2 on page 424.  I think that this is a great way to demonstrate how to help your student without knowing the answer!  I always cringe when parents tell me that they were never good at math and can’t help their child with homework or studying, especially when they do so in front of the child.  This series of questioning is also good for the teacher, a group project, and for the student to self-evaluate.  I really enjoyed the activities in this chapter.  More than others, these seem to be ones that I might use in my classroom.  “Math on the Job” and “Career Poster” involve parents and the community and broaden student’s awareness of mathematics.  I have done activities like these in the past but not as structured.  This is a more cohesive way of doing the project and I will be happy to type it up.
  • Chapter Reflections
chapter 12 reflection
Chapter 12 Reflection
  • Chapter Twelve Summary and Reflection

I found the ideas for self-evaluation most helpful. I suppose I would be considered an emergency credentialed teacher, since my background is not education or mathematics. After two years teaching, I have not found evaluation by a supervisor to be useful in the least. I do agree that you need to keep an open mind, ask colleagues for advice/help, and listen to that advice when it is given. I have found that by the third time I teach a lesson, I am probably more effective…I can anticipate where students will have questions and go over pertinent problems. I should do a better job of making these notes in my lesson plans because it is unlikely I will remember a year later. I would like to participate in more workshops but that is becoming difficult to do. The information on National Board Certification was very interesting. I tried to find the free online professional development mentioned at the end, but couldn’t find the correct link under the Web Destinations.

  • Chapter Reflections
problem solving
Week 1

Week 2

Week 3

Week 4

Week 5

Week 7

Table of Contents

Week 8

Week 9

Week 10

Week 11

Week 14

Problem Solving
problem solving week 1
Problem Solving Week 1
  • 1. I have two coins for a total of 35 cents. One is not a dime. What coin values do I have? A quarter and a dime.  

One is not a dime, but the other is.

  • 2. Add one line and one sign to make a true equation: 99 = 8 9 + 9 = 18     or     9 * 9 = 81I am assuming the number one counts as a line?
  • Problem Solving
problem solving week 2
Problem Solving Week 2
  • The Famous Goat ProblemFirst: The unknown is the area in meters squared that the goat has to graze. The data includes the dimensions of the barn and the length of the rope.

Second: If the goat is tied to the corner of the barn, he can walk in a circle. The radius, r, is the length of the rope. We must use the formula for the area of a circle, A = Л · r ². The barn represents one fourth of the circle that the goat may graze in. This area must be subtracted from the area of the circle to account for the area the goat cannot walk in.

Third: a. Find the area of the circle with radius 8 m. A = Л · 8 · 8 = 201.0619298

Take away one fourth of the circle for the barn. 201.0619298 · 0.75 = 150.7964474 m²

The shape that is formed is a circle with one 90 degree wedge taken out.

b. Find the area of the circle with radius 16 m. A = Л · 16 · 16 = 804.2477193

Take away one fourth of the circle for the barn. 804.2477193 · 0.75 = 603.1857895

The goat may also graze two meters past the barn and around the corner for 90 degrees on two sides. Find the area of the circle with radius 2 m. A = Л · 2 · 2 = 12.56637061

Take away three fourths of the circle for the barn and the area of grass already accounted for in the previous calculations. 12.56637061 · 0.25 = 3.141592654

Multiply this area times two for both sides of the barn. 3.141592654 · 2 = 6.283185307

Add the two areas together. 603.1857895 + 6.283185307 = 609.4689748 m²

  • Problem Solving
problem solving week 21
Problem Solving Week 2

c. Find the area of the circle with radius 24 m. A = Л · 24 · 24 = 1809.557368

Take away one fourth of the circle for the barn. 1809.557368 · 0.75 = 1357.168026

The goat may also graze four meters past the barn and around the corner for 90 degrees on one side. Find the area of the circle with radius 4 m. A = Л · 4 · 4 = 50.26548246

Take away three fourths of the circle for the barn and the area of grass already accounted for in the previous calculations. 50.26548246 · 0.25 = 12.56637061

The goat may also graze ten meters past the barn and around the corner for 90 degrees on one side. Find the area of the circle with radius 10 m. A = Л · 10 · 10 = 314.1592654

Take away three fourths of the circle for the barn and the area of grass already accounted for in the previous calculations. 314.1592654 · 0.25 = 78.53981634

Add the three areas together. 1357.168026 + 12.56637061 + 78.53981634 = 1448.274213 m²

  • Problem Solving
problem solving week 22
Problem Solving Week 2

Fourth: You can check your work by verifying the calculations for area. Instead of multiplying the area of the circle by the decimal equivalent of 75%, you could use division and addition or subtraction to derive the same result.

I would use ESOL strategy 5. Encourage drawings to translate and visualize word problems. It is beneficial for the students to see the shape of the barn and the relationship of the rope to the barn as the goat moves around at the end of the rope. I would also use ESOL strategy 16. Use technology and computers in pairs with ESOL and non-ESOL students. Students need to be using the pi button to get the most accurate answer when dealing with circles.

  • Pi: The symbol for pi is a Greek letter that stands for perimeter. It is the ratio for the circumference of a circle to its diameter. For every circle, the ratio will be the irrational number 3.14159265358979323846…. The value of pi continues on infinitely, however students typically use 3.14 for pi.
  • Problem Solving
problem solving week 3
Problem Solving Week 3
  • Japanese train problemThe passenger put the sword in a box diagonally.  The box would have the maximum length of 36 inches, and a width of at least 22 inches.  That would give the box a diagonal of approximately 42 inches, using the formula for the Pythagorean Theorem, (a x a) + (b x b) = (c x c).
  • Geometry and Measurement are related because geometry leads to measurement and requires measurement to understand its concepts.  

When you study the figures in geometry, i.e. circles, triangles, rectangles, prisms, cylinders, you classify them by shape and size.  Measuring a figure involves measuring the lengths of its sides and the degrees of its angles.  Measuring a figure's dimensions allows you to compare two figures based on area, surface area, and/or volume. 

  • Problem Solving
problem solving week 31
Problem Solving Week 3
  • Prior to the metric system, the Europeans used many different systems for weights and measures.  As people bartered and traded, this lead to confusion as there was no standard.  The global economy necessitated the creation of the metric system, or International System of Units, by the French in 1791.  Only Britain and the United States have not officially adopted the metric system.  The metric system is based on three fundamental metric units; meter for distance, liter for volume, and gram for weight.  The metric system uses decimals because it deals with powers of ten of the base unit.  By adding a common prefix, the unit is changed by one decimal place.  The common prefixes are kilo-, hecto-, deka-, deci-, centi-, milli-.
  • Problem Solving
problem solving week 4
Problem Solving Week 4
  • Choosing a Telephone Plan In a college dormitory, each student has a choice of two phone companies. Company A charges $7.46 per month plus 13 cents a call; Company B charges $6.17 per month plus 17 cents per call. A) About how many calls do you make per month? B) For each company, write an equation which represents the cost in a given month in terms of phone calls. C) Graph each equation you wrote in part B. Be sure to label the graph. D) Which plan is best for different types of users?

First, the unknown is the cost per month for two calling plans.

A) I make x number of calls per month.

Second, the more calls I make per month means the more I spend on the calling plan.

B) Company A = 0.13 x + 7.46 or y = 0.13 x + 7.46

Company B = 0.17 x + 6.17 or y = 0.17 x + 6.17

Third, create a chart showing how much it will cost for each company, starting with 1 call and increasing the number of calls. Plot the amounts on a line graph.

C) Graph created using the following website: http://nces.ed.gov/nceskids/createagraph/index.asp

  • Problem Solving
problem solving week 41
Problem Solving Week 4

Fourth, check the solution from the chart and graph in the equations from part B.

D) Company A is a better deal if you make 33 or more calls per month.

Company B is a better deal if you make 32 or fewer calls per month.

ESOL Strategies

3. Apply problems to daily life situations.

7. Encourage students to think aloud when solving word problems.

16. Use technology and computers in pairs with ESOL and non-ESOL students.

problem solving week 5
Problem Solving Week 5

8 1 6

3 5 7

4 9 2The famous Loh-Shu from 2800 B.C. It is the oldest known magic square of the world.

The story of 'Lo Shu' is as follows: In the ancient time of China, there was a huge flood. The people tried to offer some sacrifice to the 'river god' of one of the flooding rivers, the 'Lo' river, to calm his anger. However, every time a turtle came from the river and walked around the sacrifice. The river god didn't accept the sacrifice until one time, a child noticed the curious figure on the turtle shell. Hence they realized the correct amount of sacrifice to make (15). The word 'Shu' means books.

  • Problem Solving
problem solving week 7
Problem Solving Week 7
  • Firefighter: 29 rungs
  • I used a diagram to solve this problem. I drew a vertical line to represent the ladder and a line midway to represent the middle rung. I then had the firefighter move up and down, drawing new rungs when necessary. I ended up with 15 rungs, 14 above the starting middle rung and a corresponding 14 below, since you can’t have two middles. 14 + 14 + 1 = 29 rungs.
  • I also solved this problem algebraically and kept in mind a number line. Moving up would be a positive number and down a negative number. The starting point would be zero. X will be the number of rungs to get to the roof from the starting point.

0 + 3 – 5 + 7 + 9 = x

14 = x

  • 14 rungs to get to the roof, 14 rungs to get to the ground, plus the middle rung equals 29 rungs.
  • Problem Solving
problem solving week 71
Problem Solving Week 7
  • Logical Purchase
  • To be very honest, this one stumped me. I checked the answer on Blackboard and the answer makes sense now, however you would usually see commas between the digits! I did not notice the pattern of single digit = $1, double digits = $2, triple digits = $3.
  • Problem Solving
problem solving week 8
Problem Solving Week 8
  • Juan: $30
  • The first time I solved this problem I got the wrong answer. I used the equation 3/5 • x = 12 where x represents the money Juan started with; x = 20. When I checked the answer $20 back in the original problem, I realized that the 3/5 was taken away from x and leaving 12. I revised the equation to 2/5 • x = 12. If Juan spent 3/5 then he still has 2/5 OF (times) the total (x) OR (equals) $12. The first equation assumes that Juan spent $12, which is untrue.
  • To solve the equation 2/5 • x = 12, you must isolate x. First, multiply both sides by the reciprocal of 2/5, which is 5/2. To multiply fractions, 5/2 • 12/1, multiply the numerators 5 • 12 = 60 and the denominators 2 • 1 = 2 and simplify the resulting fraction 60/2 = 30/1 = 30.
  • For ESOL, 5 index cards represent the five parts of Juan’s money. Three of the five are spent. Two of the five he still has. Those two index cards represent the money he still has, which is $12 or $6 on each card. If you put $6 on each of the three cards he spent, he has five cards with $6 each, or a total of $30 spent and remaining.
  • Problem Solving
problem solving week 81
Problem Solving Week 8
  • Dancers: 60 dancers
  • This problem uses Least Common Multiples (LCM). I listed out the multiples of 4, 5, and 6 to find the smallest number that they have in common.

4, 8, 12, 16, 20…

5, 10, 15, 20…

6, 12, 18, 24, 30…

  • I advise my students to find the LCM of the larger numbers first. I see that 5 and 6 share 30, but 4 does not. Knowing this, the next LCM of 5 and 6 will be a multiply of the prior LCM. 30, 60… I check to see if 60 is a multiple of 4 by dividing 60 by 4, 60 ÷ 4 = 15. Bingo!
  • You can check this by continuing to list the multiples up to 60.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

6, 12, 18, 24, 30, 36, 42, 48, 54, 60

  • Problem Solving
problem solving week 9
Problem Solving Week 9

A.  The height of Building is approximately 32.34 meters. I 

researched how to solve this using the internet.  It has been a 

decade since I have studied trigonometry.  I drew a diagram to 

understand the relationship of the angel of the sun to the 

building to the shadow.  It formed a right triangle.  I knew that it

was dealing with sine, cosine, or tangent, but I couldn't 

remember which.  In my research, I came up with the following

formula:

Tangent = opposite/adjacent     

tan(57) = x/21 where x is the unknown building height

x = tan(57) * 21 = 32.33716424

  • Problem Solving
problem solving week 91
Problem Solving Week 9
  • B.  TrigonometryTrigonometry (from the Greek trigonon = three angles and metro = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of triangle is 90 degrees (right triangles).  Compliments of Wikipedia, the free encyclopedia; http://en.wikipedia.org/wiki/Trigonometry What can you do with trig? Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. 

Besides other fields of mathematics, trig is used in physics, engineering, and chemistry. Within mathematics, trig is used in primarily in calculus (which is perhaps its greatest application), linear algebra, and statistics. Since these fields are used throughout the natural and social sciences, trig is a very useful subject to know.  Compliments of David E. Joyce; http://aleph0.clarku.edu/~djoyce/java/trig/apps.html

  • Problem Solving
problem solving week 92
Problem Solving Week 9
  • C.  Astrolabe An astrolabe is an instrument used to “show how the sky 

looks at a specific place at a given time.”  It was created between 150 B.C. and 400 A.D. and typically made out of brass.  Astrolabes were 

used to tell time, predict sunrise and sunset, and solve other 

astronomical problems.  (http://www.astrolabes.org/)

  • Problem Solving
problem solving week 10
Problem Solving Week 10
  • Problem Solving: Half a Job
  • It takes Ms. Eng 2 days to do the job.
  • Mr. Muddle should paint 2 walls the first day to do half the job.
  • No, Mr. Muddle should have painted the other half the second day, meaning two walls.
  • The next day, there will be ½ of one wall left to be painted.
  • Tomorrow, Mr. Muddle will paint ¼ of one wall. There is still ¼ of one wall left to do.
  • Mr. Muddle will never finish painting the wall if he continues to only do “half the job.” When you divide something into two, you will result in two parts. In this instance, one half painted, one half not. No matter how small the section of wall, it can always be divided into two mathematically.
  • Practically speaking, Mr. Muddle will eventually paint the entire wall. At some point, the section of wall to be divided into halves will be so small that he will not be able to paint only half with a paint brush.
  • Problem Solving
problem solving week 101
Problem Solving Week 10
  • ESOL:
  • 3. Apply problems to daily life situations.
  • 5. Encourage drawings to translate and visualize word problems.
  • First, I would display a box with 2 walls painted for Day 1. Then I would show a box with 3 walls painted for Day 2. For the remaining blank wall, I would give each student a piece of paper to represent the wall. They would use a ruler and different colored markers to “paint” half of the remaining wall for the following days.
  • This problem relates to Calculus because there is an infinite number of times Mr. Muddle could divide the job in half to paint only half.
  • Problem Solving
problem solving week 102
Problem Solving Week 10
  • History of Calculus
  • Calculus is a central branch of mathematics. The word stems from the nascent development of mathematics: the early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, and the Latin word for "pebble" is "calculus."
  • Calculus is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus. Compliments of Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Calculus
  • Problem Solving
problem solving week 11
Problem Solving Week 11
  • A Small Increase
  • Problem Solving
problem solving week 111
Problem Solving Week 11
  • A large increase
  • Graphs were created using the website http://nces.ed.gov/nceskids/createagraph/default.aspx.
  • ESOL 16 Use technology and computers in pairs with ESOL and non-ESOL students
  • Problem Solving
problem solving week 112
Problem Solving Week 11
  • The sum of Holly’s scores is 522.
  • First, students must understand how to find the measure of central tendency mean.
  • Use a simpler problem: If Holly takes two tests and her mean score is 88, then she could have scored a 90 and 86 or 95 and 81 or 88 and 88. All three pairs have a mean of 88. All three also have a sum of 176 or twice the mean because there are two tests. So, for a mean of 87 and 6 tests, it would be six times the mean or 522.
  • Algebraically: ( a + b + c + d + e + f ) / 6 = 87 therefore ( a + b + c + d + e + f ) = 87 • 6 = 522
  • ESOL 3 Apply problems to daily life situations
  • ESOL 8 Have students give oral explanations of their thinking, leading to solutions
  • Problem Solving
problem solving week 14
Problem Solving Week 14
  • a. Makenzie could wear 24 different outfits.
  • This problem deals with finding the number of outcomes for three events. You can create a tree diagram to map out the different outfit options. You can also use the counting principle as a shortcut and multiple 4 • 3 • 2 = 24.

Red Shirt

Jeans 1 Jeans 2 Jeans 3

Sneakers Loafers Sneakers Loafers Sneakers Loafers

  • If there are 6 outcomes for a red shirt, then there would be 6 outcomes for the other three for a total of 24 outcomes.
  • ESOL 5 Encourage drawings to translate and visualize word problems.
  • Problem Solving
problem solving week 141
b. The sum of eight was rolled the most often. The sum of two was rolled the least often.

The chances are not the same for rolling any sum from 2 through 12. The reason has to do with probability. There is only one combination of dice that will give you a sum of two; 1 + 1. However, there are three combinations of dice that will give you a sum of eight; 2 + 6, 3 + 5, 4 + 4.

Problem Solving

2 0

3 1

4 1111

5 1

6 111

7 1111111

8 11111111

9 111

10 111

11 1111

11

ESOL 4 Use manipulatives to make problems concrete instead of abstract.

Problem Solving Week 14
classroom brochure
Classroom Brochure

Dear Parents/Guardians, 2006/2007 School Year

Welcome to a new school year at Glades Middle School! This year your son/daughter will be continuing the journey to understanding mathematics. The class will be integrating technology through the wireless laptop cart and graphing calculators, completing group projects for each unit, utilizing math manipulatives to enhance learning, practicing FCAT strategies weekly, and preparing for the county midterm and final.

It is crucial that your son/daughter comes to class well rested and prepared for class. Homework, notes, and study guides are essential for practicing and mastering mathematical concepts learned during class. Your child should be studying math DAILY. Mathematics is a cumulative subject and attendance is very important; each unit builds upon knowledge gained in the previous units. It is very important that your son/daughter does not get behind. Please encourage your son/daughter to ask questions and participate in class. It is through trial and error, discussion and practice, that they will truly be able to understand the math. I will update www.schoolnotes.com weekly so that you may know what your child is doing in class and any important dates.

Please review the syllabus below and sign and date the acknowledgement form. I hope that you will be involved in making this a successful school year. Please feel free to email me with any questions or concerns.

Mrs. Lindy Ruble

  • Table of Contents
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Classroom Brochure (con’t)

Algebra I Syllabus

Required Supplies: Pencil, Loose-Leaf Paper

Recommended Supplies: Red Pen, Scientific Calculator, Grid Paper, Folder or Binder, Index Cards

Grading

Homework: 10% 90 to 100% A

Projects: 15% 80 to 89% B

Quizzes: 20% 70 to 79% C

Tests: 30% 60 to 69% D

Midterm/ Final: 25% 0 to 59% F

Homework will be assigned and checked daily. No late homework will be allowed. It is important that you complete your homework prior to the next class period so that you may ask questions before we move on to the next topic.

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Classroom Brochure (con’t)

Details for the group projects will be given for each unit. You will be given sufficient time in class to complete your project if your group stays on task. You will earn an individual grade based on how much you contribute to the project. Class time will be given to utilize technology and manipulatives. You are not to touch the wireless computer cart or manipulatives unless you are given permission to do so. All class supplies are numbered, and you must check out the item that corresponds to your seat number. If there is a problem with an item that you check out, you must let me know immediately so that I can address the problem with the previous student. On the days that we work with the computers or manipulatives, you will receive a project grade based on your ability to stay on task.

Attendance and make-up work: Daily attendance is an important factor in academic success. Hall passes will not be written unless it is an emergency. It is a disturbance to the classroom for a student to come and go and that student will be missing the lesson in their absence. Students have two days to make up work from an excused absence. Students should check www.schoolnotes.com, the Absent Agenda at the Student Table, or a classmate's agenda to find out missing assignments. It is the student's responsibility to turn in make-up work and schedule a make-up quiz or test.

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Classroom Brochure (con’t)

Class Rules:

  • 1) BE ON TIME. Be in your assigned seat and quietly completing the warm-up when the bell rings.
  • 2) BE RESPECTFUL. Show respect for classmates, teachers, staff, guests, the school, and the classroom.
  • 3) BE RESPONSIBLE. Do your best! Come to class prepared with homework, pencil, paper, and your brain.
  • 4) BANNED ITEMS. No chewing gum or any other foreign object (i.e. straws), no eating, no drinking (except water), no cell phones.
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Classroom Brochure (con’t)

Consequences: Consequences will vary depending on the severity of the problem.

  • 1) Student Conference
  • 2) Writing Assignment
  • 3) Lunch Detention
  • 4) Phone Call Home
  • 5) Team Conference
  • 6) Parent Conference
  • 7) Administrative Referral
lesson plan
Lesson Plan
  • Date 10/31/06
  • Subject Pre-Algebra Grade Level 7 Length of Lesson Two 50 minute sessions
  • Solids on Dots: How to draw an isometric view
  • I. Instructional Objective(s)/Outcomes:
  • Specific Lesson Objectives: Students learn about isometric views of solids. The use of hands-on manipulatives, the Internet, and isometric dot paper will be incorporated.
  • Florida Sunshine State Standards:
  • MA.C.1.3.1
  • The student understands the basic properties of, and relationships pertaining to, regular and irregular geometric shapes in two- and three-dimensions.
  • MA.C.3.3.1
  • The student represents and applies geometric properties and relationships to solve real-world and mathematical problems.
  • Table of Contents
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Lesson Plan (con’t)
  • Goal 3 Standards:
  • Information Managers
  • 01 Students locate, comprehend, interpret, evaluate, maintain and apply information, concepts, and ideas found in literature, the arts, symbols, recordings, video and other graphic displays, and computer files in order to perform tasks and/or for enjoyment.
  • Responsible Workers
  • 05 Students display responsibility, self-esteem, self-management, integrity and honesty.
  • Cooperative Workers
  • 08 Students work cooperatively to successfully complete a project or activity.
  • NETS for Students:
  • 3.1 Students use technology tools to enhance learning, increase productivity, and promote creativity.
  • 6.1 Students use technology resources for solving problems and making informed decisions.
  • Lesson Plan
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Lesson Plan (con’t)
  • II. Subject Matter Content:
  • Introduce Vocabulary: Isometric View
  • Use computer, Unifix Math Linking Cubes, and isometric dot paper to understand 3-dimensional figures
  • Draw top, front, and right views of 3-dimensional solids
  • Draw 3-dimensional solids on isometric dot paper given top, front, and right views
  • Lesson Plan
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Lesson Plan (con’t)
  • III. Instructional Procedures:
  • Day 1
  • Lesson Initiating Activities:
  • Teacher will instruct students to draw a house or building on a piece of paper. Place overhead transparency “Front and Isometric Views” on overhead. After giving students time to study the four pictures, ask them to describe the similarities and differences between the buildings. Lead discussion in two-dimensional and three-dimensional figures and their uses. Was their drawing two- or three-dimensional? (7 minutes)
  • ESOL/ESE 5 Encourage drawings to translate and visualize word problems.
  • Lesson Plan
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Lesson Plan (con’t)
  • Core Activities:
  • 1. Introduce the vocabulary Isometric View, which allows you to see the top, front, and right side of an object because it is a corner view of the object. Discuss what information you can learn from the front view, the right side view, and the top view. (5 minutes)
  • 2. Pass around a model of the first figure from the Illuminations overhead constructed of Unifix cubes. Pass out the Unifix cubes, isometric dot paper, and graph paper. Explain that we will be using them to draw the isometric view of the figure and the front, right, and top views. Instruct students to study the overhead transparency “Illuminations Front-Right-Top Views” page 1 and construct their own Unifix model of the solid. Students should copy the images from the overhead onto their isometric dot paper and graph paper, referencing their model when necessary. Teacher will circulate. (10 minutes)
  • Lesson Plan
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Lesson Plan (con’t)
  • 3. Instruct students to create their own model out of Unifix cubes. Remind them that all blocks must be supported underneath by another block. Using their own model, students draw the isometric view, front, right, and top views. Teacher will circulate. (8 minutes)
  • 4. Students will trade models with a neighbor and draw the isometric view, front, right, and top views. Students will check each others work and peer correct. Teacher will circulate. (5 minutes)
  • 5. Students will trade drawings with a different neighbor and use views to construct the model out of Unifix cubes. Students will check each others work and peer correct. Teacher will circulate. (5 minutes)
  • ESOL/ESE 4 Use manipulatives to make problems concrete instead of abstract.
  • ESOL/ESE 9 Have students write original problems to be exchanged with classmates.
  • Lesson Plan
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Lesson Plan (con’t)
  • Closure Activities:
  • 1. Place “Illuminations” page 2 on the overhead. Students will attempt to draw the isometric view of figures 2 and 3. Students may use Unifix cubes to assist if necessary. (7 minutes)
  • 2. Re-discuss what information you can learn from the front view, the right side view, and the top view. Discuss if any one view tells you enough to construct the figure. (3 minutes)
  • Day 2
  • Lesson Initiating Activities:
  • 1. Review vocabulary, isometric view and three-dimensional shapes, and yesterday’s activities. (5 minutes)
  • 2. Pass out isometric dot paper and place “Illuminations” page 2 on the overhead. Students will attempt to draw the isometric view of figure 1. (5 minutes)
  • ESOL/ESE 10 Explain directions clearly and repeat key terms.
  • Lesson Plan
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Lesson Plan (con’t)
  • Core Activities:
  • 1. Students will check out a wireless laptop and go to the bookmarked page for the Isometric Drawing Tool. Students will read the Instructions. Teacher will point out that the solid must be built from the back corner forward, because you cannot lay a block behind another block. Teacher will circulate. After several minutes to explore the program, teacher will answer any questions about the program. (10 minutes)
  • 2. Students will create isometric views of solids. The front view should be red, the right view blue, and the top view green. Meanwhile, teacher will pass out graph paper. Students will copy down the isometric view, front, right, and top views on paper. They can do a self-check by using the program. Teacher will circulate. Students may ask help or share solids with neighbors. (20 minutes)
  • ESOL/ESE 16 Use technology and computers in pairs with ESOL and non-ESOL students.
  • Lesson Plan
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Lesson Plan (con’t)
  • Closure Activities:
  • Several students will be asked to plug in their laptops to the Promethian Projector and share their solids from the Isometric Drawing Tool. (10 minutes)
  • ESOL/ESE 17 Total Physical Response—actively involving students while doing math.
  • IV. Materials and Equipment:
  • Wireless Laptop Cart with “Isometric Drawing Tool” website bookmarked
  • Promethian Board and Projector
  • Class set of Unifix Math Linking Cubes
  • Isometric Dot Paper, two per student
  • Graph Paper, two per student
  • Overhead Projector and Pens
  • Overhead Transparencies of “Front and Isometric Views,” Isometric Dot Paper, Graph Paper, “Illuminations Front-Right-Top Views,” and blank
  • Class set of textbook, Prentice Hall Course 3 (Pre-Algebra)
  • Lesson Plan
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Lesson Plan (con’t)

Web-Links:

  • Isometric Drawing Tool

http://illuminations.nctm.org/ActivityDetail.aspx?ID=125

  • Isometric Dot Paper

http://www.incompetech.com/beta/hexGraphPaper/isoDots.pdf

  • Graph Paper

http://www.incompetech.com/beta/linedGraphPaper/plain.html

  • Illuminations Front-Right-Top Views

http://illuminations.nctm.org/lessons/isometric/Isometric-OVH-FRTViews.pdf

  • Lesson Plan
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Lesson Plan (con’t)
  • V. Assessment/Evaluation:
  • Teacher will assess comprehension as he or she circulates among students.
  • Isometric dot paper and graph paper can be collected and graded based on completion (since individual answers will vary).
  • Day 1 closure activity and Day 2 lesson initiating activity can be collected and graded.
  • Textbook homework can be collected and graded.
  • Workbook assignments can be collected and graded.
  • Checkpoint Quiz 1 p.485 can be graded.
  • VI. Follow-up Activities:
  • Isometric View Homework: p.479 #5, 6, 10, 11
  • Workbook Practice 9-2, Reteaching 9-2, and Enrichment 9-2
  • Isometric view and top view will lead into base plan drawings.
  • Lesson Plan
calculus textbook review
Calculus Textbook Review
  • Calculus by Calculator was probably on the cutting edge of mathematics when it was published in 1982. The book is divided into six chapters, and each chapter is divided into sections (i.e. 1.1, 1.2, 1.3). The instructional part of each section is in paragraph format. The vocabulary words are italicized, but otherwise un-delineated from the rest of the text. The definitions are given, but not necessarily in the same sentence as the word. Calculus by Calculator provides key by key instructions on how to perform exercises on a programmable calculator in parts called “illustrations,” which are very concise. It uses the term exercise for examples and problems for practice problems. There appears to be ample exercises and illustrations for students to reference.
  • Overall, it is my opinion that this book would be better for college students than high school students (and probably too dry for them as well). It completely lacks real world scenarios in exercises and problems, tie-in to real world applications and uses, and photographs to keep it interesting. The book has plenty of tables and graphs for the exercises, but they are straight mathematics without any problem-solving scenarios. It would be necessary to read this book with highlighter in hand to find and delineate the vocabulary words, whereas today’s math textbooks generally highlight and separate the words and definitions together. The paragraphs of text explaining the calculus is very dry, almost like reading an unimaginative professor’s lecture notes.
  • Table of Contents
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Calculus Textbook Review (con’t)
  • Would Calculus by Calculator teach you how to perform calculus? My opinion is yes. Would you enjoy this book and calculus? My opinion is no. Would this book motivate you to study mathematics and calculus in greater depth and inspire a new generation of mathematicians? Absolutely not.
  • Weir, M. D. (1982). Calculus by calculator. Englewood Cliffs, NJ: Prentice-Hall, Inc.
teacher observations
Teacher Observations

Clinical Observations/Teaching in Middle Schools Grade Sheet

CriteriaPossible Points/Received Points

  • Evidence of Completed Hours (Fill out Forms) 40
  • At least Two math teaching observations (Use Forms) 20
  • Interview with a teacher (Create or Use Forms) 10
  • Taught one math lesson--whole/small group 10

(Use the FAU Lesson Plan Format)

  • Hand in one Lesson Plan with teaching reflection 20

(Do an actual reflection of the lesson you taught and include)

Total Possible = 100

Total earned =

  • Table of Contents
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Teacher Observations (con’t)

Mathematics Textbook Lesson

  • 1. Randall I. Charles, 2004, Course 3 Mathematics, Prentice Hall
  • 2. Geometry and Measurement
  • 3. Objective: To draw solid figures from various perspectives.

Lesson Type: Direct Instruction

Manipulatives/models used to support learning: plastic or wooden cubes, three dimensional figures

Adaptations for diverse learners:

Below Level—Give students cubes and have them model the solid shown in the figure.

Advanced—Have students use isometric dot paper to draw a view of an object in the classroom.

  • 4. (see Lesson Plan above)
  • Teacher Observations
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Teacher Observations (con’t)

Reflection:

  • 1. It was pretty easy to develop the lesson plan from the textbook. The book does not include activities with manipulatives or technology. It lists the manipulatives as optional.
  • 2. I would also include computer technology to view three dimensional solids and an online manipulative to draw isometric views.
  • Teacher Observations
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Teacher Observations (con’t)

Classroom Manipulatives—Finding Them

Manipulative Available Used

Attribute Blocks ☺☺

Base Ten Blocks ☺

Calculators ☺☺

Geoboards ☺☺

Interlocking Cubes ☺☺

Meter Sticks ☺☺

Thermometer ☺

Pattern Blocks ☺☺

Tangrams ☺☺

  • Teacher Observations
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Teacher Observations (con’t)

Reflection:

  • Yes, I saw manipulatives being used during the visits.
  • The manipulatives were used by the teacher to demonstrate what to do and then by the students.
  • During my first observation, the students used calculators to find mean, median, and mode. During my second observation, the students used Algebra Tiles to solve one variable equations.
  • Teacher Observations
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Teacher Observations (con’t)

Reflection:

The classroom is small and the dry erase boards are fixed. The seating arrangement was primarily dictated by those factors. Students can work in pairs or small groups by rotating their desks.

  • Teacher Observations
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Teacher Observations (con’t)

Mathematics in the School

Observations:

  • There were no boards in the school dedicated to math. Most boards were for clubs, events, teams, or other subjects.
  • The math department chair (8th grade) and another 7th grade teacher had their rooms decorated with posters and student work.
  • Teacher Observations
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Teacher Observations (con’t)

Questions:

  • Glades Middle school hosts Back to School Night and Family Night for parents and students. Students may participate in county math competitions through the Math Club. Resource materials are stored in teacher classrooms and a list is kept by the department chair.
  • Math is given the same amount of time as most other subjects. Reading is the only subject that is given extra time at this school. Twenty extra minutes each day are devoted to FCAT reading. The same is not done for math.

Reflection:

Mathematics is important to this school only as far as FCAT is concerned. Most resources and priority are given to reading.

  • Teacher Observations
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Teacher Observations (con’t)

Observing Students

  • The teacher was talking about 75% of the time. She listened to the students’ questions carefully and rephrased what they were asking. She answered all questions that were asked. Eleven students were called on for answers. Three students asked questions during the lesson. No one dominated the conversation.
  • The teacher asked mainly close-ended questions. One example of a good question would be, “Explain how opposites and absolute value are similar and different.” The talk was only teacher to student. The teacher was going over her expectations for note-taking and homework, so she did a lot of talking and gave a lot of directions.
  • The discourse enhanced student learning because expectations were set forth.
  • Teacher Observations
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Teacher Observations (con’t)

Interviewing the Teacher 1

  • Topic: Integers and Algebraic Expressions
  • They should be familiar with order of operations, number lines, mean, variables—really all of it because this chapter is review.
  • Order of operations and equations are the fundamentals for Algebra.
  • In Algebra, they will be doing more complex problems that rely on these basics.
  • I introduce Algebra Tiles. A lot of students enjoy working with them because it’s something different.
  • Understanding the steps and properties. If they don’t get it now, they will be stuck for the rest of the year. Practice.

Reflection:

  • If you start using Algebra Tiles on these easier review topics, then students can benefit later when the material is more difficult.
  • Teacher Observations
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Teacher Observations (con’t)

Interviewing the Teacher 2

  • Children learn mathematics through practice and doing the math.
  • Lazy. Well, their priorities are elsewhere so you have to work harder to keep their attention.
  • Technology and activities. Anything that they perceive as fun and not work.
  • Well, I guess we spend most of the time going over the lesson. They get about 20 minutes to work on homework.
  • I think mathematics is necessary, but honestly, I don’t love it. It’s a challenge for the students.
  • Maybe they see it as a requirement to pass.
  • I talk to them about it and tell them it’s okay to be stressed out. I tell them that if they work hard, then they’ll do fine in my class.

Reflection:

  • I understood her answers and most of mine were similar. I try to get my students to enjoy math or at least not hate it anymore.
  • I think this teacher has the right idea about the activities. She may want to incorporate more hands-on and less practice in her lessons.
  • Teacher Observations
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Teacher Observations (con’t)

Interviewing the Teacher 3

  • I suppose it means that I have a job. No seriously, I think it means that you have to find what works for each student so that they can learn.
  • I expect all of my students to do their best. I know that doesn’t necessarily mean an A+ for everyone. I tell them that I want them to do their best.
  • For some of my students I have to make accommodations. I try to give them one-on-one help or seat them close to the front. We have ESE teachers that work with some of the students and peer tutors that can be assigned.

Reflection:

  • I agree with her responses. I think it is important for a teacher to communicate expectations.
  • If you do not believe that children can learn mathematics, then they won’t. You will give up on them and they will give up on themselves.
  • Teacher Observations
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Teacher Observations (con’t)

Observing the Teacher

Glades Middle 7th Grade/PreAlgebra 9/1/06

  • “Class Business” was handled while the students graded their homework.
  • Miss Tegeler went over the definitions of mean, median, and mode from the book while students took notes.
  • The class discussed the differences between the three and examples of when they are used in pairs and then as a whole. She called on students to share what they talked about.
  • Miss Tegeler responded to students during the discussion as a class. During homework time, students with questions raised their hands and came up to her desk for help.
  • Miss Tegeler’s body language was open. She made eye contact with students and walked around the classroom while they talked in pairs.
  • Miss Tegeler used the overhead projector and dry erase board.
  • I would suggest that she walk around every once in awhile when the students are doing their homework.
  • Teacher Observations
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Teacher Observations (con’t)

Observing the Teacher

Glades Middle 7th Grade/PreAlgebra 9/5/06

  • “Class Business” was handled while the students graded their homework.
  • Miss Tegeler went over the definitions of Commutative, Associative, and Distributive Properties from the book while students took notes.
  • Miss Tegeler called on students to rephrase the properties. She called on students to complete the steps to the example problems.
  • Miss Tegeler responded to students during notes and examples as a class. During homework time, students with questions raised their hands and came up to her desk for help.
  • Miss Tegeler’s body language was tense. She had to ask two boys to stop talking several times. She did not walk around the room.
  • Miss Tegeler had students change seats when the boys would not stop talking
  • Miss Tegeler used the overhead projector and dry erase board.
  • I would suggest that she ask why they are using each property for each problem.
  • Teacher Observations
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Teacher Observations (con’t)

Teaching a Lesson

Glades Middle 7th Grade/PreAlgebra 9/7/06

  • “Class Business” was handled while the students graded their homework.
  • I went over the steps for solving one step equations from the book while students took notes.
  • I called on students to name the operation and its inverse operation for the homework problems assigned. Students worked in pairs on practice problems and then I called on students to show their work on the front board.
  • As the students worked in pairs, I walked around and answered questions. During homework time, I walked around and helped students who raised their hands.
  • I tried to keep my body language positive. I smiled at students and made eye contact and tried to give them ample think time.
  • During homework time, the front office called for a student to pick up a handout. Miss Tegeler asked students who were finished with question 18 to raise their hand and then chose one to send to the office.
  • I used the overhead projector and the students used the dry erase board.
  • I think the lesson went well. I liked having the students work in pairs and also share on the board.
  • Teacher Observations
tessellation extra credit
Tessellation Extra Credit
  • Table of Contents
math autobiography
Math Autobiography
  • I am 26 years old.
  • I taught 8th grade PreAlgebra two years ago and 7th grade PreAlgebra and Algebra last year.
  • I have two dogs, two cats, two fish, but only one husband.
  • Table of Contents
final exam questions
Final Exam Questions
  • Final Exam Question 1
  • Final Exam Question 2
  • Final Exam Question 3
  • Final Exam Question 1 Answer
  • Final Exam Question 2 Answer
  • Final Exam Question 3 Answer
  • Table of Contents
final exam question 1
Final Exam Question 1

Counting Chicken Wings

  • At Annie's Home-Cooked Chicken Wings Restaurant, chicken wings are served by the bucket. The Biggest Bucket O' Wings is really big! Let's figure out how many wings are in it.
  • If they're removed two at a time, one wing will be left. If they're removed three at a time, two wings will remain. If they're removed four, five, or six at a time, then three, four, and five wings, respectively, will remain. If they're taken out seven at a time, no wings will be left over.
  • What's the smallest possible number of wings that could be in the bucket? How do you know?
  • Final Exam Questions
final exam question 2
Final Exam Question 2
  • Chapter Seven discusses writing in math journals.
  • If your department required this, how would you incorporate math journals into your lesson plans?
  • How would you grade the math journal?
  • Explain the pros and cons of requiring a math journal.
  • Final Exam Questions
final exam question 3
Final Exam Question 3
  • How would you approach teaching the concept of slope?
  • Final Exam Questions
final exam question 1 answer
Final Exam Question 1 Answer
  • 119 chicken wings
  • The number must be a multiple of seven, because it has a remainder of zero. The number must be an odd number, because it has a remainder of one when divided by two. The number must end in a nine, because it has a remainder of four when divided by five (and ending in four is an even number).
  • Looking at the multiples of seven, the first number that satisfies these requirements is 49. However, 49 divided by 3 is 16 R 1. The next multiple of seven is 119.
  • Final Exam Questions
final exam question 2 answer
Final Exam Question 2 Answer
  • Answers will vary. Sample answer: For each chapter, I would ask the students to preview the chapter and write about what they know already and what they are looking forward to learning. For each activity and project, I would ask students to write about what they liked about the activity, what they learned, and what they would change. For each test, I would ask the students to write on review day about how they felt about the chapter, if they feel prepared, and what they would need to be better prepared. For each test, I would ask the students to write the day after about how they felt about the test and what they felt was the most important thing they learned.
  • I would grade the math journals on a quarterly basis for a completion grade. I would try to read and write comments in the journals after each test to develop feedback before the next chapter gets underway.
  • I think the math journal can be a great avenue for feedback from students. It also documents students’ progress throughout the year and what they feel they have learned. The journal may provide information if the student is struggling or if a parent teacher conference is called. Some students may not feel comfortable writing in the journal in the beginning. I believe the journal will only be helpful if it is read by the teacher. It will be time consuming to read and comment in all of the journals.
  • Final Exam Questions
final exam question 3 answer
Final Exam Question 3 Answer
  • Answers will vary. Sample answer: I would introduce the concept of slope with the Chapter 3 Project in the textbook. It involves designing a game where the player rolls a marble down a ramp toward a target area. The player adjusts the ramp higher or lower to reach the target. After the students have played their “games,” I would lead a discussion about what happened when the ramp was adjusted. I would have the students graph their ramps on a coordinate plane and talk about the line and the rate of change for the marble.
  • Final Exam Questions
mathematics education philosophy bullets
Mathematics Education Philosophy Bullets
  • Show all of your work.
  • Don’t skip steps.
  • Always check your answer.
  • Punch the calculator keys carefully.
  • If you can’t get it the first time, take a break and tackle it again later.
  • Write neatly.
  • Table of Contents
websites
http://www.col-ed.org/cur/math.html

http://dimacs.rutgers.edu/%7Ejudyann/LP/lessons/

http://www.eduplace.com/

http://www.enc.org/

http://www.explorelearning.com/

http://www.gamequarium.com/prealgebra.html

http://hotmath.com/

http://www.iit.edu/~smile/mathinde.html

http://illuminations.nctm.org/

http://www.learner.org/

Table of Contents

http://www.marcopolo-education.org/home.aspx

http://www.math.com/

http://www.math.nmsu.edu/~history/

http://mathforum.org/

http://mathforum.org/ncsm/

http://mathforum.org/sum95/sinclair/alg1.html

http://nces.ed.gov/practitioners/teachers.asp

http://www.nctm.org/

http://www.puzzlemaker.com/

http://www.wtamu.edu/academic/anns/mps/math/mathlab/index.htm

Websites
resume
Resume

Education

  • Bachelor of Arts with Honors  Political Science  3.50 cumulative GPA

University of Kansas Lawrence, Kansas  December 2002

Florida Teaching Certifications

  • Middle Grades Math 5-9  Subject Area Certification

Florida Teacher Certification Examinations  April 2004

  • ESOL Certification

The School Board of Broward County, Florida  May 2006

  • Gifted Education Endorsed

The School Board of Broward County, Florida  July 2006

  • Table of Contents
resume con t
Resume (con’t)
  • Classroom Work Experience
  • Teacher Broward County, Florida
  • 7th Grade GEM and Advanced Math 2005-2006 School Year
  • 8th Grade Pre-Algebra 2004-2005 School Year
  •  implement the Broward County curriculum map to achieve Sunshine State Standards
  •  challenge and assist students to accomplish comprehensive learning gains
  •  integrate technology, projects, and math labs to motivate learning and broaden experience
  •  communicate and work with parents and students for a successful school year
  •  participate in staff development workshops, department collaborations, and team meetings to facilitate an effective learning environment
  • Math Club Coach Glades Middle School
  • 6th, 7th, and 8th grades 2005-2006 School Year
  •  coordinated and supervised Math Club meetings and annual county competitions
    •  recruited, motivated, and trained Math Club participants
  • FCAT Camp Glades Middle School
  • 7th Grade Mathematics 2005-2006 School Year
  •  mentored and coached struggling students in FCAT skills and strategies
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Education Training

Gifted Education Endorsement Training Series

The School Board of Broward County, Florida  July 2006

ESOL Strategies for Content Area Teachers

The School Board of Broward County, Florida  May 2006

8-Step Instructional Focus

Glades Middle School  May 2006

Secondary Mathematics Strategies

STAR  November 2005

Urban Teaching Strategies

STAR  September 2005

Great Exploration in Mathematics (GEM) Training

The School Board of Broward County, Florida  June 2005

New Educator Support System

Glades Middle School  May 2005

Child Abuse Study

The School Board of Broward County, Florida  April 2005

Reading for the Content Areas

The School Board of Broward County, Florida  March 2005

Digital Teacher Academy

The School Board of Broward County, Florida  December, 2004

New Teacher Orientation

The School Board of Broward County, Florida  August 2004

New Teacher Academy

The School Board of Broward County, Florida  July 2004

A Day in the Life of a Substitute  Substitute Teacher Training

The School Board of Broward County, Florida  April—May 2004

Substitute Teacher Orientation

The School Board of Broward County, Florida  March 2004

Resume (con’t)
resume con t2
Resume (con’t)

Education Coursework

  • MAE 4360  Teaching Middle and Secondary School Mathematics

Florida Atlantic University  Fall 2006

  • EDG 4930  Methods for Classroom Management

Florida Atlantic University  Fall 2005

  • MAE 4350  Principles and Methods: K—9 School Math

Florida Atlantic University  Fall 2004

  • RED 4308  Reading Level 1: Birth—Grade 3

Florida Atlantic University  Fall 2004

  • SCE 4350  Principles and Methods of Science: Elementary and Middle School

Florida Atlantic University  Summer 2004

  • LAE 4353  Language Arts and Literature: Birth—Grade 8

Florida Atlantic University  Summer 2004

esol accommodations
ESOL Accommodations
  • Teach vocabulary using realia and demonstration.
  • Relate math problems and vocabulary to prior knowledge and background.
  • Apply problems to daily life situations.
  • Use manipulatives to make problems concrete instead of abstract.
  • Encourage drawings to translate and visualize word problems.
  • Rewrite word problems in simple English terms.
  • Table of Contents
esol accommodations con t
ESOL Accommodations (con’t)
  • Encourage children to think aloud when solving word problems.
  • Have students give oral explanations of their thinking leading to solutions.
  • Have students write original word problems to be exchanged with classmates.
  • Explain directions clearly and repeat key terms.
  • Encourage students to follow the four-step problem solving process.
  • Realize that not all math notations are necessarily universal.
  • ESOL Accommodations
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ESOL Accommodations (con’t)
  • Group students heterogeneously during cooperatively learning.
  • Be sure that all concepts are taught and understood concretely using manipulatives.
  • Teach math by incorporating cultural and historical aspects for ESOL students.
  • Use technology and computers in pairs with ESOL and non-ESOL students.
  • Total Physical Response—actively involve students while doing math.
  • ESOL Accommodations
four step problem solving process
Four-Step Problem Solving Process
  • First. You have to understandthe problem.
  • Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
  • Third. Carry out your plan.
  • Fourth. Examinethe solution obtained.
  • Table of Contents