Kaicy's Article Reviews, 2006

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Keywords: Teaching Strategies
Ref: Kaicy1
Author(s): Alsup, Dr. John K.
Date: 2003
Journal or Publisher: Education
Volume, Issue, Pages: Vol. 123 Issue 3, p609
Reviewer: Kaicy
Date of Review: 02-15-06

This article reviews the concepts behind the teaching of pre elementary school teachers. It talks about good ways to set up and run your math classes according the NCTM Principles and Standards. The bulk of the information is on 7 classroom rules that if followed will yield a classroom that follows the NCTM Principles and Standards. The seven classroom principles cover the handling of a problem, and the steps though it, using key terms, "problem," "solved," "solution," "work list," and "progress report" the last two steps help the teacher, as a facilitator, and instructs the teacher not to solve open problems for the students. It sums up with "as a result [of these rules], they are better able to teach in classrooms envisioned by the NCTM and actualized by progressive reformers." The article is a bare bones reflection of one way to handle the NCTM classroom. I really like that there are examples included for a "good" problem to give the students. I love that it emphasizes that the students should work through the problems together, and if there isn't a consensus, to go back and figure out why. It is really important for the students to find their mistakes, with the teacher as a facilitator and not always the "answer giver," which is what this article emphasizes.

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Keywords: Problem Solving, Equity, Teaching Strategies
Ref: Kaicy2
Author(s): Fuchs, Lynn S.; Fuchs, Douglas
Date: 2005
Title: Enhancing Mathematical Problem Solving for Students with Disabilities
Journal or Publisher: : Journal of Special Education
Volume, Issue, Pages: Vol. 39 No.1 pp. 45-57
Reviewer: Kaicy
Date of Review: 02/20/06

This article is a little thick to read, but it contains some good ideas for approaches on higher mathematics for students with math disabilities. Included in the body of the article is an example of a problem used in instruction, an immediate-transfer problem, a near-transfer problem, and an example of a far-transfer problem. These are the steps Fuchs outlines as the fundamental basis that lead to the complex mathematical problem-solving skills. They conclude with five conclusions to enhance students with disabilities mathematical problem-solving skills, and highlight that students learn very well in small group, as opposed to the whole group, instruction.

I like that this article gives sample problems to illustrate their point on the transfer of skills. I wish it had a few more suggestions for in class suggestions rather than just spouting how it should be. I appreciated that the article didn't focus only on students with documented disabilities, but those that are seemly functional in other areas of instruction but struggle in math.

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Keywords: Algebra, Connections
Ref: Kaicy3
Author(s): Armstrong, Alayne C.
Date: 2005/2006
Title: An "Arithmetic" Thinker Tackles Algebra
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 11, No. 5 pp. 220-225
Reviewer: Kaicy
Date of Review: 02/22/05

The article chronicles one student in the introduction of algebra. She begins by categorizing students into the two groups Kieran has coined: "algebraic" and "arithmetic." She takes us through the three sessions with the student from the introduction of algebraic terms and equations to more advanced problems with split variables. By the final interview the student is connecting the language and knowledge from class to the interviews and vice versa.

This was an interesting glimpse into the mind of a 13-year-old girl who is classified "arithmetic." Over the entire article seems to be getting at the fact that students just need some time to digest the material, and to try it individually and as a group. They need to begin to make those connections from individual to class before we expect them to fully understand them.

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Keywords: Connections, Activities
Ref: Kaicy4
Author(s): Berkman, Robert
Date: 2006
Title: One, Some, or None: Finding Beauty in Ambiguity
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 11 No. 7 pp. 324-327
Reviewer: Kaicy
Date of Review: March 3, 2006

Though this article is not written with corporative learning, it demonstrates great skills on classroom corporative learning. The teacher is teaching the students about the ambiguity in math and that it is not only about finding the one right answer. He does this though having the students work together in groups and finding the answers, answer, or lack of an answer. The students have to work together to determine if there is one, some or none answers. When he brings the group together they work together using with they talked about in small groups to persuade each other to what they believe it's the right answer.

I enjoy the activity presented, about triangles; but he also gives other charts for the some, one, or none game. I can see it applicable, especially how it seems all student lead. He has them choose the cards they work together trying to convince each other of the answer they think is correct, then go on to work with the class to achieve one decision.

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Keywords: Teaching Strategies, Curriculum
Ref: Kaicy5
Author(s): Kenney, Joan M.; Metsisto, Diana; Tuttle, Cynthia L.; Heuer, Loretta; Hancewiz, Euthecia
Date: 2005
Title: Literacy Strategies for Improving Mathematics Instruction
Journal or Publisher:
Volume, Issue, Pages:
Reviewer: Kaicy
Date of Review: March 3, 2006

In this book a different author writes each chapter. The goal of this book is to introduce ways to include literacy in to your mathematics instruction. It covers teaching the literacy of the mathematics language as well as reading and writing in the classroom and how to incorporate graphic representation into this strategy. The book is filled with great Ideas and lesson plans that can be inserted into any curriculum.

I really like this book because it seems so daunting to include the new literacy requirement into the mathematics content area. It gives you great places to start and little seeds of ideas that can grow into great core ideas for literacy instruction in mathematics.

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Keywords: Geometry, Problem Solving, Representations
Ref: Kaicy6
Author(s): Reynolds, Anne; Cassel, Darlinda; Lillard, Eileen
Date: 2006
Title: A Mathematical Exploration of Grandpa's Quilt
Journal or Publisher: Teaching Children Mathematics
Volume, Issue, Pages: Vol. 12 No. 7 pp. 340-345
Reviewer: Kaicy
Date of Review: March 6, 2006

A problem is presented to a classroom: Grandpas quilt is too short, can you rearrange the quilt pieces to make it long enough to cover his feet during the winter? In groups the students tackle the problem from different angles. One group works with a table examining the multiplication properties starting with a 6x6 quilt. The students share with the class how they attempted to solve this problem. On the fourth day on this problem a student found it as a 9x4 quilt. The teacher can pose a different problem as a longer quilt with a diamond in the center.

The students were engaged in solving this problem because they could see the problem, some used the tables, some used graphs and grids to solve the problem, and some used the actual squares to solve the problems. They used different representation techniques outlined in both the PSSM and the State standards, applying real world knowledge and translated the 6x6=36 into whatXwhat=36, finding out that it was 9 and 4. This is a good problem for a younger group of students.

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Keywords: Manipulatives
Ref: Kaicy7
Author(s): Jawa Mariappan
Title: Prime and Composite Numbers, Grade Level - 6-7
Journal or Publisher: http://www.lessonplanspage.com/MathPrimeAndCompositeNumberTiles67.htm
Volume, Issue, Pages:
Reviewer: Kaicy
Date of Review: 03/08/06

This lesson plan successfully teaches students how to discover the difference between prime and composite numbers using manipulatives. The teacher takes the students through the number 4, and 6, and 9, and then 3 and 5, to show the difference between those with more than two factors and those with just 2. The teacher suggests letting the students find all primes between 2-20. A good lesson, and concept, that could be used in younger grades as well.

I really like that the students can see for them selves that if this rectangle is two by three, and total there are six, two and three are factors. I can see this as a way to teach greatest common factor or least common factor in a future lesson, because the students are already comfortable with the process. This also seems to give the students power over their learning, because they are discovering the factors themselves and not having a teacher tell them that the factors of 4 are 1, 2 and 4.

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Keywords: Curriculum, Activities, Standards
Ref: Kaicy8
Date: 1992
Title: Addenda Series Grades K-6
Journal or Publisher: Addenda Series Grades K-6
Volume, Issue, Pages: Fifth-Grade Book
Reviewer: Kaicy
Date of Review: 04-05-06

The grade level book outlines each of the four standard areas; Patterns, Number Sense and Operations, Making Sense of Data, and Geometry and Spatial Sense. Within each section there are specific instructions and class activity ideas to implement these standards into the classroom. Each task works under the "Get ready, Get Going, Keep going," slogan. This can help you and the students organize the tasks and delve deeper into the reasons behind what you are doing. There are work sheets and many different projects for each of the four areas. I see these books as a very good addition to a curriculum.

I really like that they have a specific focus on the standards, and can really help include those aspects into my teachings. I really like that it has worksheets and games and ideas that are easily adaptable to the classroom you have, and to differentiate so all the students are doing the same "type" of mathematics but they are each working at their ability level. I think the, "Get ready, Get Going, Keep going," mantra carried out through each topic in these books relates very well to the KWL reading strategies, and can be pulled easily across disciplines.

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Keywords: Curriculum, Teaching Strategies, Algebra
Ref: Kaicy9
Author(s): National Council of Teachers of Mathematics
Date: 2001
Title: Navigating through Algebra in Grades 3-5
Journal or Publisher: Navigations Series
Volume, Issue, Pages:
Reviewer: Kaicy
Date of Review: 4/12/06

The book is laid out to fit to the standards, and is written for the teacher. I feel this can be given to the most novice math teacher and they will be able to teach a decent lesson if they follow the Navigations text. There are solutions in the margins that show what real students have done in the past, and thinks to look for to correct. There are activities for third through fifth in this book, which could work well to differentiate in the classroom. You could expand for those in third who are advanced, and simplify for a fifth grader who is struggling in math.

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Keywords: Problem Solving, Activities,
Ref: Kaicy10
Author(s): Beaton, Tisha
Date: August 2004
Title: Harry Potter in the Mathematics Classroom
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10, NO. 1
Reviewer: Kaicy
Date of Review: 04/24/06

This lesson infused the literature the students were learning in their English class with the mathematics classroom. The students were reading Harry Potter and the Sorcerer's Stone so Beaton had a budgeting lesson in her class. Each student was assigned an amount of money, and given a list of required items to bring to their first year at Hogwarts, as well as optional items that could make their year easier. They worked alone and together to figure out what their individual budget could get them.

This is a great literacy link, and got the students thinking about a real world problem with out telling them, "you are now going to be thinking of a real world problem." She said the students never lost interest or got off task and were very self motivated to get the most for their money. I can see this working in a fifth grade classroom where you are the primary teacher, as well as up through junior high with collaboration from the language arts teachers. I see possibilities for an across content application for Harry Potter.

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Keywords: Algebra, Games, Manipulatives
Ref: Kaicy11
Author(s): Cheryl Tucker
Date: 2006
Title: Using Tiles and Games to Teach Algebra in Middle School
Journal or Publisher: MCTM Session
Volume, Issue, Pages:
Reviewer: Kaicy
Date of Review: 04/25/06

The main goal of this session was to demonstrate different ways you can incorporate and teach algebra into your curriculum. She used different manipulatives to help the students wrap their head around algebraic thoughts of what is missing. The first game she introduced was Some-Sum. It required some teacher preparation to go get tile spacers from the hardware store and make half look like minuses. The aim is to grab tiles from a cup or bowl, and let the students decide who wins; is it the person who gets the most or the person with the most after the pluses and minuses cancel. She said that she has never had a class not ask these questions. This can lead to discussion of negative numbers and cancellation.

The second game she introduced was the classic Rock Paper Scissors. After assigning each throw with appropriate pluses and minuses the students work in pairs and record the positive or negative score. Again the students are to work through who won and why. While they explore if the numbers cancel, the teacher can introduce value to the pluses and minuses at this point as well. She then covered how it is possible to work with multiplication and division using positive and negative numbers and the tiles from the previous games. It took the group a while before we actually understood, but basically you work from a completely neutral field, grouped pluses and minuses, and do the multiplying and dividing.

In addition to the games above she showed us a few other related games that are in the hand out that I brought to class. This was a very valuable session, and I am very glad that it was the first session that I attended because it gave me great ideas for my future math classroom. I can see myself using all or part of most of these games at any grade level k-9. She was an excellent presenter and worked with us to understand not only the game but also how to approach it with our students so they'll get the most out of the game.

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Keywords: Equity/Diversity, Standards,
Ref: Kaicy12
Author(s): Berry, Robert Q.
Date: 2004
Title: The Equity Principle Through the Voices of African American Males
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10 No. 2 pp. 100-103
Reviewer: Kaicy
Date of Review: 04/17/06

The article covers the views represented by the NCTM on equity, and how African American males view the equity in the classroom. It also covers which teachers the students liked growing up and what they liked about them. The article outlines the equity principle in the NCTM Principles and Standards, and provides areas for further reference.

This article was a good eye opener. I was not aware that these standards were being ignored in the classroom, whether they were aware of it or not. It gave me some Ideas of where to look for activities to engage my African American students and activities to incorporate technology. This article also gave me a good summary of the NCTM Principles and Standards listing of the equity principle. It helped me understand it more which will help me in my classroom in the future.

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Keywords: Teaching Strategies, Management
Ref: Kaicy13
Author(s): Herbel-eisenmann, Beth; Breyfogle, M. Lynn
Date: May 2004
Title: Questioning Our Patterns of Questioning
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 10 No. 9 484-489
Reviewer: Kaicy
Date of Review: 4/13/06

This article begins by questioning why we question our students. It follows a few classrooms through some questioning strategies. First it discusses the IRF strategy, where the students are asked a pointed question. Then it covers Funnelling and Focusing. Each of the latter has different ways to help the students focus their ideas and thoughts, so they are discovering the material rather than being told the answer outright. I like the actual student teacher exchanges that are included in this article. They really give me something to go by if I am teaching a class. I also like how straight forward this article is and doesn't beat around the bush. It states exactly what it intends to and sums up at the end after actually proving that point. This is an article that can help me plan and teach lessons in the future.

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Keywords: Teaching Strategies, Planning, Activities

Ref: Kaicy14
Author(s): Bonnie Hagelberger Date: 2006 Title: If I had only known then what I know now
Journal or Publisher: MCTM Session Volume, Issue, Pages: Reviewer: Kaicy Date of Review: 5/8/06

This session was an hour packed with information. She teaches a first grade class, and in this session discussed how, even during 'literacy time,' she could work mathematics into their daily lives. Her overarching principle was: to make the field of learning bigger to cement what they (the students) need to know. That included teaching and showing them things that were beyond most of their capabilities and also repetitive teaching because that can help the lowest students in the class. For the topics that may be over the student's heads she would only teach or show if the students asked or mentioned it first.

An Example: She works with basic subtraction principles. For example 3-2, she would demonstrate three apples take away two and you have one apple left. And, like addition, students would reverse the numbers 2-3. She used to tell the students no, you cant do that. But one student always would mention negative numbers. She realized that telling her students that they cant take 3 from 2 was incorrect. So now she shows her students on a number line that it is -1. She made a strict point that the students only be held accountable for the at-level achievement.

She gave many great ideas, including getting the crutches off the students desk such as the alphabet and number line, because they will always count on the line if they aren't held responsible for learning the 'head math.' She places a large number line in the room, so it is accessible but not mandatory in their mathematics ability. This was a great session for a beginning teacher like me, or a teacher looking for new ideas. She even explained beginning proofs for first graders so it is not such a shock later in school. Though this session was geared toward early elementary, it could be applied further up and even in the middle school. This was a very worthwhile session.

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Keywords: Activities, Problem Solving, Puzzles
Ref: Kaicy15
Author(s): Tammy Brooks
Date: 2006
Title: Estimation More than a Wild Guess
Journal or Publisher: MCTM Session
Volume, Issue, Pages:
Reviewer: Kaicy
Date of Review: 05/14/06

Tammy was a first time presenter at the conference and she was a little bit nervous. She pulled through very well having the listening audience participate throughout her session. She began developing this strategy for teaching estimation when her students were having problems guessing how many jellybeans were in a jar. Many had not basis for their guess, just a stab in the dark, and Tammy thought that was unacceptable. So first she implemented the Estimates of the Week. Each week the students would have one problem that they had to estimate. Many were applicable to real worlds, and all have to be countable.

After a few weeks of the Estimate of the Week she began implementing estimation into her daily curriculum. She did best guesses, where easily rounded problems were given, and the student’s best guess was applied. Her goal was to get students to see how estimation could help them in their daily lives. Tammy found that using estimation with many different operations and fractions, decimals, and percents the students became more confident and more comfortable with this mathematics.

Her program seems to breed success. I really like the games she showed us, like putting cars, bugs, or a picture, and having students estimate how many wheels, legs, or what ever. They were short little exercises that got the students minds thinking and working on estimation tactics. I really like the estimation of the week, because it can get the student estimating at home, and the rewards can be mathematical as well, what are the odds of winning? Estimation is such a vital tool; I was very inspired to see a teacher so dedicated to helping her students understand that fact. I can see myself using these games and tactics in my classrooms of the future.

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Keywords: Teaching Strategies, Problem Solving, Communication
Ref: Kaicy16
Author(s): Reeves, Charles; Reeves, Rosemarie
Date: March 2003
Title: Encouraging Students to Think About How They Think
Journal or Publisher: Mathematics Teaching in the Middle School.
Volume, Issue, Pages: Vol. 8, No. 7
Reviewer: Kaicy
Date of Review: 05/14/06

This article discusses Einstellung’s problem solving. The authors show how to prepare and conduct an Einstellung experiment, by giving students problems that are easily solved if one thinks ahead, or are difficult if one follows the step-by-step procedure. The article also gives an experiment you can conduct in your class by moving water from three different sized jugs to make a specified amount of water. Then covers how to handle discussion in the classroom to further the experiment, and enhance the student’s deeper thinking. The whole goal is to help student figure out how to ‘switch gears’ to more efficient methods of problem solving.

I like this process, helping the student’s find different ways to think about the same thing. It is important to have students expand their mind and be able to switch gears at any point because life isn’t always straightforward. The examples given were very good, and can be pulled right out of the article and placed into any classroom, that I really appreciate. There is also very good discussion on using this method as one teaches, and when to avoid over use of this method. This is only one way to help the students expand their thinking, not the only way, and that is something that we should all keep in mind.

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Keywords: Problem Solving, Probability, Discrete
Ref: Kaicy17
Author(s): Hylton-Lindsay, Althea
Date: February 2003
Title: Problem Solving, Patterns, Probability, Pascal, and Palindromes
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8 No. 6 p. 288-293
Reviewer: Kaicy
Date of Review: 05/14/06

This article covers many different ways to get to the same answer. The author is a teacher of teachers, and presents the article how I would expect her class to go: very methodical and to the point. It was very clear and had a lot of great ideas. It used only one problem and explored solving with a pattern, probability, Pascal’s triangle, and even palindromes. She says in her conclusion that her “goals is to encourage these future teachers to become confide3nt problems solvers so that they, in turn, can do the same for their students.” And she presents the material in such a way.

This was a great article to get ideas from. All of the ideas presented in this article could stand alone, but would benefit the students the most if they are coupled with a great curriculum. Because the students follow the same problem through many different solutions they not only gain more understanding of the problem but of each individual process, because the problem isn’t standing in the way. I also like that this article was written by a teacher who is teaching how to teach mathematics, because you have to teach something well you really have to know what works and what doesn’t work. This was a valuable article, and is very applicable to my future teaching.

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Keywords: Select one..., Keyword 2, Optional..., Keyword 3, Optional...
Ref: Kaicy18
Author(s): Steele, Marcee
Date: November 2002
Title: Strategies for Helping Students Who Have Learning Disabilities in Mathematics
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8 No. 3 p. 140-143
Reviewer: Kaicy
Date of Review: 05/14/06

This article covers very well the different disabilities student in our general education classroom may have. She does a very good job of relating each of the disabilities to their affect on mathematics learning, and then presents strategies to overcome some of the gaps. The author presents thirteen different teaching strategies the teacher can do to help the learning disabled students in the class. The article also makes the point that these modifications are helpful fro all students and the time should be put into lesson planning to accommodate for these students.

The different ways the disabilities can relate to mathematics comprehension was very insightful. Though I have studied about learning disabilities, I have rarely seen the specifics related to a subject matter before. This can prove to be very helpful to a beginning teacher who is unsure how to alter the lesson plans they have spent so long writing. The list provided for strategies is a nice place to start, and none of the accommodations would take much more time, and as the article said all of the students, special needs or not, will benefit form the adapted teaching. This is a brief yet information filled article that can be applied creatively to teaching in the future.

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Keywords: Algebra, Teaching Strategies, Equity
Ref: Kaicy19
Author(s): Allsopp, David; Lovin, Louann; Green, Gerald; Savage-Davis, Emma
Date: February 2003
Title: Why Students with Special Needs Have Difficulty Learning Mathematics and What Teachers Can Do to Help
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8 No. 6 p. 308-314
Reviewer: Kaicy
Date of Review: 05/15/06

This article clearly describes different disabilities and how each effect mathematics learning. It also covers how to change your current teaching strategies just a little bit to accommodate for these students that will inevitably be in our general education classroom. After describing different disabilities, there is a case study of one teacher and how she changed her algebra lesson plan to include all types of learning. In the end she used visual cues, auditory cues, and kinesthetic cues to include the most students.

The teacher featured in this article had a very good out look for teaching. She believes that all students are capable of learning, not only because of the standards, but because she truly does believe that. The way she incorporated the different styles of learning was very neat, and something I have thought of, but it was very nice to see in practice. The students also charted their progress on success graphs to show their understanding, and the students said that was and ego boos and was proof they are getting it. I again liked the link to mathematics comprehension and the specific disabilities because it gives me something more specific to look for, rather than just an under performing student. There are some good ideas in this article that I can see myself trying out in my future teaching.

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Keywords: Connections, Problem Solving, Standards
Ref: Kaicy20
Author(s): Koirala, Hari; Goodwin, Phillip
Date: October 2002
Title: Middle-Level Students Learn Mathematics Using the U.S. Map
Journal or Publisher: Mathematics Teaching in the Middle School
Volume, Issue, Pages: Vol. 8 No.2 p. 86-90
Reviewer: Kaicy
Date of Review: 05/15/06 This article outlined a multidisciplinary mini unit plan for a fifth or sixth grade classroom. The overall goal was to connect different aspects of mathematics to social studies and geography. This was achieved by presenting the students with a state chart, and using Connecticut as the unit of measure (the students are from CT) Estimate the size of the other states. The students estimated alone, and then with a peer, using only knowledge they could glean off each other and their own brains. The next few days presented the students with a United States Map and as for estimation again, and an almanac to get the actual ratio and size. The student’s journals showed increased interest because of the link to another class, especially among students who are not fond of math class.

This was an interesting mini unit. The things you would have to be aware of is if the students have learned basic knowledge of the united states, and general knowledge of their home state (or which ever state for a unit of measure). The article suggests that Rhode Island be used as a unit of measure if you live in a big state, and I think that is a good suggestion. Other wise the students will be dealing only with fractions and decimals, and though those concepts have been introduced (hopefully) the goal of the lesson is only decimal work. I also really like that it encompasses many different facets of mathematics, from decimals to ratios and more. This is a pretty good lesson, and I would be interested to try this in my middle school, or upper elementary classroom.