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Mathematics Portfolio
Prepared By: CONTACT _Con-3B8A7AF61 \c \s \l Krystal Rodney
CRIN E07
Elementary Math Curriculum and Instruction
Fall 2008
College of William and Mary
Profession Margie Mason
Table of Contents:
Page #
Overview
. 3
Literature Connections
. 5
Web Resources
8
Article Review
. 11
Problem Solving
.. 20
Lesson Planning
. 23
Reflections
30
Overview What Makes a Good Math Teacher?
A good math teacher must have many qualities. One must, of course, be able to do math, and compute mathematical problems fluently. But there are many other qualities that are necessary to become a successful math teacher. One must be able to plan well, create meaningful objectives, and using state standards. A math teacher must also be able to facilitate learning, and adjust instruction on the spot to accommodate students. A good math teacher must also accommodate students in terms of their diverse needs and backgrounds. The abilities to teach problem solving and use manipulatives are critical to successful math teaching. It is also necessary to be able to connect mathematics to core content and other subject areas. In this increasingly digital age, it is also important to incorporate technology into math instruction. Good math teachers must also be to include research - based techniques in order to increase student success. Most importantly, a good math teacher must be able to communicate effectively, so as to meet every student.
This portfolio consists of some of the work that I completed in my Elementary Math Curriculum and Instruction class in the fall of 2008. The work that I have included demonstrates my ability to be an effective mathematics instructor. The first piece of work that I included in this portfolio is called Literature Connections. This is a list of books that would be useful for teaching mathematical concepts. Web Resources is the next piece of work to be included. This is a list of websites that can be used in the classroom. During the course of the semester, I reviewed and critiqued recent research in the field of elementary math instruction. I have also included lesson plans and problem solving that I have done with my third grade classroom. As the last part of my portfolio, I have reflected on the work that I have done this semester.Literature Connections
A good teacher is able to create interdisciplinary connections across content areas. It is also important for a math teacher to use different teaching strategies to enhance student learning. In this assignment, I compiled a list of books that can be used when teaching mathematics. Along with a short summary of each book, I have included a list of ways that each book can be used in the classroom. These books are very entertaining, and would be great resources for teaching certain mathematical concepts, or as a fun way to practice math. This Literature Connections assignment opened my eyes to the amount of literature based math resources that are available. I truly enjoyed reading these books, and I will definitely use math literature in my future classroom. Using books is a great way to get students excited and interested in math.
Chicka Chicka 123
Authors: Bill Martin, Jr., Michael Sampson, & Lois Elhert.
ISBN: 0-689-85881-7
Description of content: This is very similar to Chicka Chicka Boom Boom, but for numbers. In this rhyming book, 101 numbers try to climb to the top of an apple tree. Even though there never seems to be a place for zero, he saves the day when bees bother the other numbers.
How you can use the source:
Help develop counting skills
Citation: Elhert, L., Martin Jr., B., & Sampson, M. (2004). Chicka Chicka 123. Simon & Schuster Books for Young Readers: New York City.
Arithmetickle: An even number of odd riddle-rhymes.
Author: J. Patrick Lewis
Illustrated by: Frank Remkiewicz
ISBN: 0-439-75535-2
Description of content: This is a book of addition and subtraction riddles.
How you can use this source:
Help students pick out the pertinent information in word problems
Help to develop problem solving strategies like drawing a picture.
Students can create their own math riddles after reading this book.
Citation: Lewis, J.P. (2002). Arithmetickle: An even number of odd riddle-rhymes. Scholastic, Inc.: New York City.
Less Than Zero
Author: Stuart Murphy
Illustrated by: Frank Remkiewicz
ISBN: 0-06-000126-7
Description of content: This story is about a penguin that wants to save up to buy an ice scooter. However, he buys other things with his savings, and has to borrow money from other penguins, which gives him a negative amount of clams. Throughout the story, he tries to get out of the hole and save enough money for his scooter.
How you can use this source:
Introduction to negative numbers
Drawing a number line, or a graph with negative numbers to keep track of Perrys clams
Citation: Murphy, S. (2003). Less than Zero. Harper Collins Publishers: New York City.
A Place for Zero: A Math Adventure
Author: Angeline Sparanga LoPresti
Illustrated by: Phyllis Hornung
ISBN: 1-57091-602-0
Description of content: This is a story about the number Zero. He lives in the land of Digitaria with other numbers. Their favorite game is Addemup, which he cant play because he has nothing to add. He goes on a journey to find his place in among the numbers. He meets people like Count Infinity, who help him learn how valuable he really is.
How you can use this source:
This can help students learn more about the concept of zero.
Can provide an introduction to multiplication.
Citation: LoPresti, A.S. (2003). A Place for Zero: A math adventure. Charlesbridge: Watertown, MA.
One Grain of Rice: A Mathematical Adventure.
Author: Demi
ISBN: 0-590-93998-X
Description of content: This is a story about a girl named Rani. She lives in India in a village ruled by a raja. The raja hoards all of the villages rice. As a reward for a good deed, Rani can choose a reward from the raja. She asks for 1 grain of rice, to be doubled every day for 30 days.
How you can use this source:
This can help students learn about multiplication by 2. You could also work backwards in the book, and talk about division by 2.
Citation: Demi (1997). One Grain of Rice: A mathematical folktale. Scholastic Press: New York City.
Web Resources
Students are becoming technologically savvy at a younger age. Many students spend lots of time playing video games, and using the computer. As a math teacher, it is important to use strategies that incorporate students interests and abilities. If students are not comfortable with technology, teachers can introduce technology into the classroom in a fun and non-threatening way.
In this assignment, I had the opportunity to collaborate with one of my classmates to create a list of websites. These websites can be used in many ways. We found websites that can be used to teach mathematical concepts, problem solving, and reinforce what it learned in the classroom using games. When compiling this group of websites, we explored each site. We then wrote short description of each site, and how it could be used in the classroom.
I decided to include this assignment in my portfolio because it shows my ability to use different resources in lessons. These resources can be incorporated in a lesson that introduces a topic, or provides practice and reinforcement for students.
The Futures Channel
Address: HYPERLINK "http://www.thefutureschennel.org/hands-on_math.php"http://www.thefutureschennel.org/hands-on_math.php
Description of contents:Under Teaching and Learning, click the Mathematics link. Under Activities, you will find links for Geometry, Measurement, Fractions, and more. There are even mathematics movies children can watch movies with activities. Most of the activities are simple and easy to for the students to do.
How you can use this source
You can give the students this address and they can work on problems in groups or even at home
It is a more interactive site than others I have seen
The Futures Channel. (2008). The Futures Channel. Retrieved from September 6, 2008, from HYPERLINK "http://www.thefutureschennel.org/hands-on_math.php"http://www.thefutureschennel.org/hands-on_math.php
Math Playground
Address: HYPERLINK "http://www.mathplayground.com"www.mathplayground.com
Description of contents:Students can practice math skills, play games, and have fun with math with this interactive, kid friendly web site. It is easy to navigate and has fun games for every level. It is colorful and bright and will hold the childs attention.
How you can use this source:
Have students go on to watch videos and play games
Another resource students can use at home to practice their math skills
Math Playground. (2008). Math Playground. Retrieved September 6, 2008, from www.mathplayground.com
Animal Math PageAddress: HYPERLINK "http://bingostreet.com/animal-math-bingo.html"http://bingostreet.com/animal-math-bingo.html
Description of contents:This is a fun site for the lower grades. It is a game children can play that has pictures of different animals. Children can pick from a number of levels and practice their multiplication and division skills. Children type in their name and the site is personalized for them!
How you can use this source:
This is a great site to have children practice with multiplication and division because it gives instant feedback
It is very easy and kid friendly, so children might revisit it time and time again
Animal Math Page. (2008). Animal Math Page. Retrieved September 6, 2008, from HYPERLINK "http://bingostreet.com/animal-math-bingo.html"http://bingostreet.com/animal-math-bingo.html
Math for Kids: A Medieval Adventure in Problem-Solving
Address: HYPERLINK "http://library.thinkquest.org/4471/" http://library.thinkquest.org/4471/
Description of contents: This website was designed for and by 4th graders. Students can solve word problems, or design their own word problems. Students can also learn how to solve word problems through multiple strategies listed on the site.
How can you use this source: Students can have a challenge by designing their own math word problems to post on the website.
ThinkQuest Jr. Team 4471. (1998). Math for Kids: A Medieval Adventure in Problem-Solving. Retrieved September 6, 2008, from HYPERLINK "http://library.thinkquest.org/4471/Default.htm" http://library.thinkquest.org/4471/Default.htm
Cool Math 4 Kids
Address: HYPERLINK "http://www.coolmath4kids.com/" http://www.coolmath4kids.com/
Description of Content: Students can learn math and solve problems on a colorful website. If you click on the teachers link at the top of the page, it will take you to strategies for teachers to use in their classrooms to teach a variety of subjects. One thing that struck us was Survivor Algebra, which can be used for middle school. Students are divided into groups and are taught a mini-lesson on algebra. Then they are given problems to solve within their group.
How you can use this source: Survivor Algebra would be a good way to allow for problem solving in the classroom. There are also other resources for teachers. Students can play math games and learn math (the games actually are challenging). There are also lessons on certain math subjects, and a math dictionary that students can use.
CoolMath.com, Inc. (2007) Cool Math 4 Kids. Retrieved September 6, 2008, from HYPERLINK "http://www.coolmath4kids.com/" http://www.coolmath4kids.com/
Article Review
In this article review, I read and critiqued four articles in the field of elementary math instruction. These articles were published after 2001. The articles cover teaching math in special education settings, incorporation of technology, National Council of Teachers of Mathematics (NCTM) standards, and the views of United States teachers on effective math teaching strategies. In the critiques of these articles, I addressed the articles connections to the NCTM standards, connection to the Virginia Standards of Learning, and how they can relate to my future experiences in teaching mathematics. This is very important to my development as a math teacher. I must be aware of current research that may improve my students success. It is also important to know the National and state standards, so that the lesson plans I create will be aligned with them. While it is always good to go beyond the standards if possible, the standards are a good starting point for the creation of quality lesson plans.
Article #1 Integrating Reform-Oriented Math Instruction in Special Education Settings
In this article, the effect of Enhanced Anchored Instruction on the performance of students with learning disabilities was explored. Enhanced Anchored Instruction (EAI) is rooted in problem-based learning. It allows students to do problem solving using multimedia and hands-on activities. The study sought to find out if this method was more effective for students with math learning disabilities (MLD), and what practices teachers used that provides positive results for students with MLD.
In the study, 4 math teachers were chosen. These teachers all had a background in special education. The teachers were randomly assigned to teach 100 middle school students. The teachers were also randomly assigned to teach one of two instructional sequences. All students took a pretest before the beginning of the study (the Iowa Basic Skills Test). Teachers assigned sequence A did problem solving with their classes, while teachers with sequence B worked with the typical curriculum (which emphasized very basic survival math skills). After a few weeks, students took a post-test (Kims Komet Problem Solving Test). After this, sequence B teachers did problem solving, while sequence A teachers went back to the normal curriculum. Students again took a post-test after a while.
The results of the study showed that students benefited from the use of EAI in the classroom. They also found that students problem solving skills deteriorated slightly after not being used for a while. However, the students were still able to use much of what they learned. Students improved in their problem solving skills, but had did not improve very much in computation.
I think that this article was very good. It seems like a legitimate study, and they documented the experiment very well. They also compared it to another study that they did earlier with EAI, and analyzed their findings. However, the study does not tell us whether they are in an urban or suburban setting. It also does not tell us about the type of population that we are dealing with. Multimedia problem solving might not be feasible in some areas where money is an issue.
This aligns very well with NCTM standards. NCTMs goal is to have problem solving be a primary form of math instruction in the classroom, and this type of instruction strives to do just that for all students. I think that it is also important for my future teaching. I would have never thought of using multimedia software to help learning disabled students with problem solving. However, considering that it seems to be successful, I think that I might use it.
Citation: Bottge, B.A., Rueda, E., LaRoque, P.T., Serlin, R.C., and Kwon, J. (2007). Integrating reform-oriented math instruction in special education settings. Learning Disabilities Research & Practice, 22(2), 96109.
Article #2 Beliefs about Using Technology in the Classroom: Interviews with Pre-service Elementary Teachers
This study explored the ability of web-based workshops to increase the confidence and competence of teachers when using instructional technology. It also explored the effect that these workshops had on teachers attitudes towards using mathematical instructional technology in the classroom. This was achieved through interviews preceding the workshops. Researchers used this information to design effective web-based workshops for teachers. The three main questions that the study sought to answer were if pre-service teachers perceive the importance of instructional technology in effective math instruction, if pre-service teachers feel more confident about using instructional technology after taking a web-based workshop, and how pre-service teachers feel about using instructional technology when teaching.
Students in this study were undergraduate students enrolled in an Elementary Mathematics methods course. Before the course, students were trained in web-based instruction. During 6 weeks of this course, they received instruction on geometry, statistics, and probability. Also during this time, students were introduced to and allowed to explore a few interactive math websites that might be helpful in the elementary classroom. After this, 10 of the students were chosen to participate in a 40-minute interview. The results of these interviews showed that math instructional technology (like virtual manipulatives) is very useful when teaching mathematics, and that many of the students felt confident about using it in the classroom.
I liked this article, because it introduced me to the idea of interesting and useful technology. I never thought about the possibility of virtual manipulatives, or computerized coin tossing programs. Now that I have heard of them, I think that I will definitely try to use them in my classroom to teach probability or geometry. It is also very important that teachers feel confident about using technology, and more importantly, that they know how to use it. Web-based workshops can be a good way to help do this. There were some drawbacks to this article, however. I dont think that the study was large enough. It does not clearly state how many students are in the class, so we dont know if 10 students might be considered a representative sample.
This article connects very well with the NCTM and SOL standards. This articles findings uphold the NCTM belief that technology is useful and necessary in the teaching of mathematics. The article explores instructional technology for geometry and probability/statistics. The article mentions virtual manipulatives, which would help in reaching VA geometry standards for grades K-6. The coin tossing program mentioned can help students reach VA probability standards from grades 3-6.
Citation: Lin, C. (2008). Beliefs about using technology in the classroom: Interviews with pre-service elementary teachers. Eurasia Journal of Mathematics, Science & Technology Education, 2008, 4(2), 135-142
Article #3 Perceptions and Applications of NCTM Standards by Special and General Education Teachers
In this study, 129 secondary general/special education teachers were chosen in a stratified random sample to determine teachers perceptions about the NCTM math standards. The study was done in the state of Maryland, and teachers were chosen from 24 school districts statewide. Teachers were specifically asked about NCTM standards related to students identified as Learning Disabled (LD) or Emotionally Disabled (ED).
Data for the survey was collected by mailing a survey to teachers. Out of the 286 surveys that were mailed, 129 were returned. Forty-eight percent of the teachers that participated were from urban school districts, 36% from rural districts, and 16% were from suburban school districts. Teachers were from both the middle school and high school levels.
Results of the study indicated that many of the special education teachers (55%) were not familiar with the NCTM standards, and that this was a barrier to creating activities aligned with the goals of NCTM. For teachers that did feel that they were familiar with the standards, confidence in their ability to follow NCTM standards increased. Many teachers also noted the lack of inadequate materials in the classroom to allow them to work towards NCTM goals. One of the major issues cited was the NCTM focus on learning math through problem solving.
This article was useful because it opened my eyes to something new. I did not even realize that there were NCTM standards for LD and ED students. I would not even know where to look for SOL standards on teaching LD/ED students. I am sure that there are some NCTM/SOL standards for elementary students. Before I teach, I must make sure that I become familiar with these standards. I am sure that it will be necessary in my career. It is important for every student to have access to quality education that reaches or exceeds NCTM standards. The goal of learning through problem solving can be useful even outside of the math classroom. It is probably more important for LD/ED students. To be independent in the world, it is necessary for LD/ED students to navigate tricky situations. Problem solving can be extremely helpful in this.
Citation: Maccini, P. & Gagnon, J.C. (2002). Perceptions and applications of NCTM standards by special and general education teachers. Exceptional Children, 68(3), 325-344.
Article #4 United States Teachers Views of Effective Mathematical Teaching and Learning
In this study, 11 teachers were interviewed to determine U.S. cultural beliefs about teaching and learning mathematics. Of all the teachers in this study, 6 of them had masters degrees. All of the teachers attend national and state conferences on a regular basis, and all of the teachers attend and provide in-service training in their respective schools.
Through the interviews, researchers found that all of the teachers think of mathematics as a necessary tool for life, a way to solve real problems, and as a different way of thinking. They also discussed other ideas in the interviews, such as the characteristics of an effective lesson. Through answers to these interview questions, researchers found that the teachers felt that an effective lesson features developmentally appropriate content that allows for student centered learning and exploring.
I dont believe that this was a very useful article. It is very difficult to believe that 11 teachers can accurately represent the views of the millions of teachers in this country. Also, many of these teachers were highly educated, and take their professional development very seriously. There are not many teachers that go to conferences and facilitate in-house professional development on a regular basis (at least once a year). These teachers are not part of the majority of teachers that work in our schools. We dont know where these teachers are from. Views about teaching can clearly change as you move from an urban to a suburban area, or from state to state.
This article somewhat aligns with NCTM standards. The teachers believe that students need math to deal with real life problems, and that they should be allowed to explore solutions, which matches well with NCTMs idea of problem solving in the math classroom. Since the Virginia Standards of Learning do not give specific requirements on how to teach, this article doesnt necessarily align with the SOLs.
One of the things that struck me in this article was the teachers view on memorization. Many of the teachers believed that while memorization should not be used as a method of instruction. However, there was some argument over whether rote memorization was important. Some teachers believed that it was. This has strong implications for my future career. I do not believe that memorization has much of a role in mathematics. I believe that it is important for any student to be able to work out mathematical problems, even if you can memorize them. That lets me know that they understand what they are doing, and in my opinion, provides a better foundation for future learning. However, I will have to make sure that I remember that other teachers do not believe this. I need to be aware of this in case o do have students that only memorize math.
Citation: Cai, J. &Wang, T. (2007). United States teachers views of effective mathematical teaching and learning. ZDM Mathematics Education, 39(4),315327.
Problem Solving:
I taught this problem to a class of 22 third grade students. These students had just finished learning about place value, and I decided to do this problem with them, so that they could have more practice with it. I have included this problem in my portfolio because it displays my ability to teach problem solving.
Problem solving is very important to the development of mathematical skill. Students must be able to figure out non-traditional problems. Exposing students to problem solving early allows them to become more proficient at it. Problem solving also gives students a challenge. I like doing problem solving, because it shows that math is not as difficult as they think. Students usually associate math with the memorization of rules and equations. It gives students a sense of satisfaction when they can figure out math by using other strategies, like drawing a picture, or acting out a problem. Problem solving can also be used to help students derive equations, and students usually remember them easily after doing this.
Topic: Place Value
Expected heuristic: Act it out
Problem: This mystery number has 4 digits. Every digit is an odd number. None of the digits is a 9. Every digit in the number is different. The smallest digit is in the thousands place. The greatest digit is in the ones place. The preceding describes two possible numbers. The mystery number is the greater of those two numbers. What is the mystery number?
Answer: 1537
Solution: Draw 4 lines to represent the 4 digits in the number. Write out all of the digits up to 9. Cross out 9, and all the even digits. Place a 1 in the thousands place, and the 7 in the ones place. Now we are left with a 5 and 3. Make the two numbers that can be made, then choose the larger one.
Citation: Adapted from: RHL School. (2007). Math Problem Solving. Retrieved December 4, 2008, from http://www.rhlschool.com/math.htm
What happened:
I read the problem to the students, and made sure that they understood any of the words that may have been too big for them. Then I let them work on the problem by themselves. I saw that most of the students came up with an answer after about 5 minutes, so went around the room and asked some of the students to tell me the answer that they came up with. After asking 3 students, one of the students gave me the correct answer. Then I went through the entire process that I did to solve the problem with the students (explained in the solution). When I got to the 2 numbers that could be made, I wrote them out on the board. The numbers were 1537 and 1357. I asked the students, What sentence in this problem will tell us which number we are going to choose? After asking about four students, one of the students was able to point out the correct sentence.
Reflections/Modifications/What I learned:
I really liked this problem. I changed the wording around just a little so that they could read it without many problems. A lot of the students would have gotten it if they had listened when I read it, and read the problem in its entirety. Most of the students missed the part of the problem that said that we were looking for the larger number. But when I went over the problem, I specifically asked them to tell me what part of the problem tells us which of the numbers we would choose. I am glad that I did this, because even some of the students who got the problem correct couldnt point out the sentence for me. Once one of the students pointed it out, it was like a light bulb went off in everyones head. This problem went really smoothly, and I am not sure that I can think of anything to change.
Lesson Planning
I created this lesson to teach second grade students about even and odd numbers. In this lesson plan, students play a game called Odd Bear Out! Through this game, students will be able to explore the difference between even and odd numbers. I decided to include this lesson plan because it shows my ability to incorporate the use of manipulatives in math lessons. This lesson also demonstrates students using manipulatives in a way that allows them to discover something new. This is important for the facilitation of student learning and the use of manipulatives.
Title: Odd Bear Out!
Grade: 2
Objective: Students will demonstrate differences between even and odd numbers using counting bears.
Related SOL: 2.5d The student will recognize even and odd numbers, using objects.
Materials: Counting Bears, Ziploc bags
Time: 1 Hour
Procedures:
Before class, put counting bears into Ziploc bags. Students will be put into groups of 2, and each group will get 1 bag. The first bag will get 10 bears, the second bag will get 11 bears, and so on.
Organize students into groups of two. (1 min)
Give each group a bag of bears. (1 min)
Have the students count the number of bears they have, and record the number. (3 mins)
Ask the students to put their bears into two equal piles. If there are any extra bears, students should put it/them aside and yell Odd Bear Out! Ask students to record the number of bears they had in each pile, and how many bears were left out.(5 mins)
Give each group of students 3 more bears, and repeat the game twice more. (20 minutes)
While students are playing the game, set up a chart on the board. The chart should look like this:
Number of BearsNumber in my equal pilesNumber of bears left out101214Fill in the number of total bears before the students finish the game. Do one table for even numbers and one for odd numbers. Ask students to come up to the board and write their answers in the appropriate rows. If there is an instance that more than one group has the same total. Choose one group to write on the board. (10 mins)
Ask students to list the similarities among the numbers in the two lists, and the differences between the lists. (10 mins)
Explain that odd numbers are even numbers plus 1. You can also explain that even numbers have a 0,2,4,6, or 8 in the ones place. Odd numbers have a 1,3,5,7, or 9 in the ones place. Explain that you can find if any number is even or odd by looking at the number in the ones place. (5 mins)
Evaluation:
Have students fill out an exit card with these problems on it. Students should write whether the number is even or odd.
9
22
95
44
77
108
233
556
Accommodations: Students are placed in groups of two. If necessary, students with motor disabilities can be placed with a responsible student that can move the bears. One student will move the bears, and the other will count the bears. The teacher can write the answers to the evaluation for any student who may not be able to write independently. The student will give the answers to the evaluation orally, and the teacher will write them down.
I taught this lesson on capacity to a class of third graders, consisting of 22 students. I decided to include this lesson in my portfolio because it shows my ability to plan and implement math instruction. It also shows my ability to use informal assessment to guide instruction on the spot. These qualities are very important for teaching mathematics.
After the lesson plan, I have included a critique of the lesson. It describes what happened when teaching the lesson, and what I would improve. Reflection is very important for teaching, in general. Improvement of specific lesson plans and of teaching strategies are important both for the growth of the teacher, and the education of present and future students.
In this lesson, students made Gallon Guys/Gals to help them remember how gallons, quarts, pints, and cups are interrelated. The students enjoyed making Gallon Guy, and renamed him Spongebob.
Title: Just how much does SpongeBob hold?
Grade: 3rd
Objective:
Students will differentiate among cups, pints, quarts, and gallons through the teacher demonstration.
Students will demonstrate the differences in size among cups, pints, quarts and gallons by making Gallon Guy/Gal.
SOL: 3.14
Time: 1 hour
Materials: 1 empty gallon sized bottle, 1 empty quart-sized bottles, 1 empty pint sized bottles, 1 8oz. cups (All bottles should be clear), 88 sheets of paper (assorted colors), glue, 22 paper plates.
Procedure:
Give each student 4 pieces of paper. Ask students to get their scissors and glue.
Show the students the gallon bottle, and ask them if they know what size it is. Tell students that it is a gallon, and ask if they know anything that we buy in gallons (milk, water, etc). This should be done throughout the lesson plan with all other bottle sizes.
Ask students to hold up one sheet of paper, and fold it in half (hamburger style). Tell them that the sheet of paper will always represent one gallon, and will also be the body of Gallon Guy/Girl. Also, tell students that each half of gallon guy is a half-gallon.
Ask students to hold up another sheet of paper, and ask them what it represents. Then ask students to fold the paper into 4 long strips, and cut them. Tell the students that each strip is an arm or leg for gallon guy, and represents 1 quart. Have each student write the word quart on each arm/leg. Write on the board that 1 gallon = 4 quarts. Ask students to put the strips together to make one sheet of paper.
Have the students hold up another sheet of paper, and ask them what the paper represents. Ask the students to fold the paper into 4 long strips, and ask them what the 4 long strips represent. Then, ask the students to fold and cut each strip in half (hamburger style). Tell the students that each new strip is a pint. Ask students if they can figure out how many pints are in a gallon/quart from the gallon guy. Students should write the word pint on each new strip, and put the strips back together to look like a full sheet of paper.
Have the students hold up another sheet of paper, and ask them what the paper represents. Ask the students to fold the paper into 4 long strips, and ask them what the 4 long strips represent. Ask the students to fold and cut each strip in half (hamburger style), and ask what that represents. Then, ask students to fold and cut each strip in half (hot dog style). Tell the students that each new strip is a cup. Ask students if they can figure out how many cups are in a pint/quart/gallon. Have the students write the word cup onto the strips, and put the strips together to make a full sheet of paper. Go through how many quarts/pints/cups are in a gallon.
Glue gallon guy together, and decorate if there is time.
Evaluation:
Give students this problem: 8 cups = how many pints? How many quarts? How many gallons?
Adaptations: The assessment should be read aloud to the students before they begin.
Capacity Lesson Plan Critique
I did my lesson plan on the topic of customary units of volume in a third grade classroom. We went over gallons, half gallons, quarts, pints, and cups. We started out by handing out 4 sheets of construction paper. One sheet was red, one was black, one was white, and one was yellow. I explained that each full sheet of paper represented one gallon. We folded the yellow paper in half to show a half-gallon. We folded the white paper into quarters (long strips) to represent quarts, then asked the students if they could tell how many quarts were in a gallon. Then we folded the black paper into eighths to make pints, and asked the students to tell from the paper how many pints were in a gallon. We then folded the red paper into 16ths to represent cups, and asked the students to tell how many cups were in a gallon. From the way that we folded the paper, we could go through the stages of folding that we did (quarts, pints, and cups). We went through this folding with the red paper to help students to visualize how many pints were in a quart, and how many cups were in a pint. While doing the folding, I also showed them gallon, half gallon, quart, pint, and cup containers.
After going through these, we cut the paper along the folding lines to create Gallon Guys, to help them remember how the units work. We finished our Gallon Guys just in enough time to get to centers, so I did the assessment the next week. The assessment question was: 8 cups = how many pints? How many quarts? How many gallons? I think the way I worded this question may have been a little confusing. I dont think that some students really understood what the question was asking, or how to answer it. So after I saw that some of the students were struggling, we went back and reviewed the assessment. Then we did some more examples, which I wasnt prepared for. Assessment data: 14 students answered the question correctly, 4 did not. (22 students in the class one student absent, 3 assessments not handed in). I noticed that some students were confused about how many gallons you could get out of 8 cups. I think that I may have presented the half-gallon as a separate unit, and not just half a gallon. This may have confused some students, because they put 0 for the amount of gallons you would get from 8 cups. Some students got the pints and quarts correct, but ended up with 16 gallons. My guess is that they confused cups and gallons.
I think that the lesson was good, but it could have been better. The assessment data might not be completely telling of how effective the lesson was. A few of the students were out of the classroom for most of the lesson. By the time they got back, we had finished going over all of the units, and were starting to make our Gallon Guys. Im not sure that those students really understand volume. I also did not anticipate that the students would be out of the room.
If I were to do this lesson again, I would make sure that while I was modeling the folding of the paper for the class, I would make some for the students that were out of the room, to help them out. I also think that before I would do my assessment, I would make sure that I would do some type of short review for those students. I think that I would also try to figure out a way to get the students to use their Gallon Guys more. It seemed that they were not using them. Im not really sure that I would use the Gallon Guy method again. It isnt a resource that would allow students to work through the units quickly when at the store, or on a test. I think that I would look for another way that they can figure out the units. Maybe I might draw a large gallon jar, and show them that they can divide in half to get the next smallest unit. The most important thing that I would probably do is create some extra problems just in case we get to the end of the lesson, and the students still dont understand. It would have been really helpful to have these problems readily available, because I think that having to think them up on the spot made me a little nervous.
Reflection
The elements of this portfolio serve to demonstrate my ability to teach math effectively. When completing the Web Resources and Literature Connections, I was able to think about ways to teach across content areas, and include technology in mathematics instruction. I was also able to inform myself about the resources that are available to teach math. This is very important to ensure that I continue to grow in my abilities. I was able to inform myself of new practices to use in the classroom through completing the article review. These articles helped my learn about incorporating technology, accommodating special populations, and become more familiar with the national and state standards concerning math. Through teaching problem solving, I was able to participate in one of the most important, effective, and integral methods of math instruction. Through lesson planning, I was able to incorporate student discovery and the use of manipulatives in the construction of standards-aligned lessons for second and third grade students. These activities have been very invaluable experiences in my development as an effective math teacher.
Throughout this semester, I have been able to learn many new and exciting ways to teach mathematics. I hope to use these new skills and ideas in my student teaching and future career.
This portfolio has allowed me to reflect on the successes and learning experiences that I have had this year. Through the work that I have included in this portfolio, I have been able to grow in my ability to teach math effectively, and believe that I will be a successful math teacher. I hope to continue this growth throughout my student teaching experience, and my career.
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