Tuesday, August 31, 2010

M2G1 - Geometry in Primary Grades (2)

M2G1. Students will describe and classify plane figures (triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes) according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute).

Well, it has been a long time since I wrote an entry here. I apologize for those who posted their comments for not responding. I will try to keep updating this blog a bit more frequently.

Last time, I started writing on the geometry standards, and I will continue the discussion of geometry in this entry. In M2G1, students are now expected to classify plane figures "according to the number of edges and vertices and the sizes of angles (right angle, obtuse, acute)." The GPS includes the following figures: triangles, square, rectangle, trapezoid, quadrilateral, pentagon, hexagon, and irregular polygonal shapes. Last time, I questioned the appropriatenes! s of the expectation that kindergarteners to distinguish squares and rectangles. In Grade 2, students are learning about different types of angles, right, acute and obtuse. Therefore, it is in Grade 2 when it is appropriate for students to learn that rectangles are quadrilaterals with 4 right angles, and squares are rectangles with all sides equal.

However, let's think about how students can understand right angles. When I ask my adults, including some teachers and teacher candidates, what right angles are, they almost always respond by saying "90-degree angles." Although it is true that right angles measure 90 degrees, measuring angles using "degree" as the unit is a Grade 4 standard. Thus, how are second grade students to understand what right angles are? A Japanese elementary math textbook by Hironaka and Sugiyama has an interesting approach to this topic. They define a right angle to be the angle you obtain when you fold a piece of paper as shown in th! e figures below:



Note that the piece of paper can be any shape to start with. The second fold is made in such a way that the first fold line will be folded onto itself. Although it might also be helpful to point out to children that the corners of note papers, index cards, etc. are right angles, we cannot always be sure that corners of any piece of paper are right angles.

Interestingly, this definition of a right angle is very much comparable to Euclid's definition of right angles in his book The Elements. He defines that the angles you obtain by equally dividing a straight angle are right angles. When the second fold is made so that the first fold line will be folded onto itself, we are indeed dividing the straight line (the first fold line) into two equal angles.

I want to end this entry by raising another issue with! the standard, however. This standard expects students to des! cribe an d classify trapezoid. However, in order to describe trapezoids, children need to concept of parallelism. The Grade 2 Geometry unit of Math Frameworks define trapezoids as "quadrilaterals with two parallel sides." Unfortunately, parallelism is a Grade 4 topic. Therefore, it is very strange that we should expect students in Grade 2 to describe and classify trapezoids.

To make the matter even worse, Grade 4 Geometry unit of Math Frameworks defines trapezoids as quadrilaterals "with only one pair of parallel sides." This definition is different from the Grade 2 definition, which does not say anything about the other two sides of quadrilaterals. In a recent publication, Zalman Usiskin and his collaborators document how these two definitions of trapezoids has existed in US mathematics textbooks. Therefore, the fact that the definitions are different isn't too surprising. However, it is rather unfortunate that a document that emphasizes coherence will not try to ! be consistent in their definition of a geometric figure.

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Creative Mathematics- Holidays Homework(Class 9 and 10)


Each student is required to work on any one of creative Maths activity work according to the following distribution:

Roll No. 1 to 10

  • Self composed poem on Mathematics : Do you like writing poems? If yes then try your hands on writing a Math Poem. You may choose any topic and start writing.

OR

(Click pictures of every step while making and send it through e mail to your respective Maths activity teacher. You can make a presentation or write on a word file along with pictures.)

Roll No. 11 to 20

  • ! Role play (Script writing explaining any Maths concept from chapters learnt till now)

Please note: there is no specific word limit. Be sure, it should not be vague and cater to the topic's need.

OR

(Click pictures of every step while making and send it through e mail to your respective Maths activity teacher. You can make a presentation or write on a word file along with pictures.)

Roll No. 21 to 30

  • Life sketch of a Mathematician (atleast 500 words)

OR

  • Making designs and patterns using geometrical shapes

(Click pictures of your designs and send it through e mail to your respective Maths activity teacher. Write a small brief on your explorations.)

Roll No. 31 to 40

  • Or igin of a Maths concept (e.g. origin of Real Number System , origin of coordinate geometry etc.)
  • OR

    • Making mathematical patterns using line segments .(Visit this link WIKI HOW? )

    (Click pictures of your designs and send it through e mail to your respective Maths activity teacher. Write a small brief on your explorations.)

    Roll No. 41 onwards

    • Utility of a Maths topic (e.g. application of Linear equations in two variables etc. )

    OR

    See Sample work by students http://mathematicsprojects.blogspot.com/2008/01/making-paper-snowflakes.html

    (Click pictures of ever! y step while making and send it through e mail to your respective Maths activity teacher. You can make a presentation or write on a word file along with pictures.)

    Please note:

    1. The work should be submitted online through e mail to your respective Maths activity teacher latest by 15. 06.2010 .

    2. Do mention your Name, Class/Section, Roll Number

    3. Original and innovative work will be highly appreciated.

    4. Click pictures if you are working on making a Fractal Card, a 3D Snowflake, designs and patterns using geometrical shapes, mathematical patterns using line segments or a paper snowflake.
    5. In case you choose the first one out of the two, then write it in your own words. If you find some relevant pictures, you may attach it with description. Please do not forget to mention the source of your information.

    6. For any query: E mail mathclass_khms@yahoo.co.in

      Class 9A students will e mail their work to Mrs Mamta Katyal mamtakatyal1970@yahoo.co.in

      Classes 9B and 9 G students will e mail their work to Mrs Roman Dhawan dhawanroman@gmail.com

      Classes 9C ,9D, 9E and 9H students will e mail their work to Mrs Sujata Manchanda samolina6@yahoo.com

      Class 9F students will e mail their work to Mrs Kaveri Ramachandran kaverikulachi@gmail.com

      Classes 10A, 10B, 10K and 10I students will e mail their work to Mrs Ankita mathematics_khms@yahoo.co.in

      Classess 10C, 10D, 10G and 10H students will e mail their work to Mrs Rashmi Kathuria mathclass_khms@yahoo.co.in

      Classes 10E, 10F and ! 10J students will e mail their work to Mrs Mamta Katyal mamtakatyal1970@yahoo.co.in

      Classes 9I, 9J and 9K students will e mail their work to Mr. Mohit Khanna mkmaths0706@yahoo.co.in


      DO YOUR ASSIGNMENTS IN YOUR MATHS NOTE BOOK. (DOWNLOAD THEM FROM SCHOOL'S WEBSITE)


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    Holy Frijole Mole!

    Got this recipe from Fairview Gardens, best darn CSA around. Using my green beans and fresh basil from the share I received this week.

    I just made it and oooooohhhhh baby! I have one great little lunch to take to work tomorrow -- scooping up this stuff with some FoodShouldTasteGood chips. O Happy Day!

    Recipes for Green Beans: Frijole Mole

    This recipe is from an inspirational book: Animal, Vegetable, Miracle by Barbara Kingsolver. You can eat this dip with crackers or in wraps. Make sure you steam the beans thoroughly.

    1. Steam green beans until tender.
    2. Saute onions over medium heat in oil until transparent.
    3. Combine beans, cooked onions, eggs, basil, and lemon juice in food processor and blend into coarse paste.
    4. Remove puree to a bowl and combine with enough mayo or yogurt to hold mixture together. (Note from Kelly: I used Trader Joe's White Bean Hummus. Very good if I do say so myself)
    5. Add salt and pepper to taste.
    (Last chime from Kelly: I cut this recipe in half - using only 1 egg - to make just enough for me. This made plenty. I'm not really into sharing....)

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    Tutorial - Revit and Calculus - Part 1
















    My Calculus 1 professor has given us the option of doing a final project instead of taking a final exam. Given the hatred I have for any type of testing I decided to start tackling the idea of a final project. One thing that has always fascinated me about Revit families is the ability to use formulas.

    The ability to create parametric fami! lies is already a major advantage but using formulas to drive some of these parameters opens up a whole new world. First, I would like to copy and paste the page in "Revit Help" that presents the correct syntax to use when conducting formulas within Revit:

    "Formulas support the following arithmetic operations: addition, subtraction, multiplication, division, exponentiation, logarithms, and square roots. Formulas also support the following trigonometric functions: sine, cosine, tangent, arcsine, arccosine, and arctangent.
    The valid formula abbreviations for arithmetic operations and trigonometric functions are

    • Addition— +
    • Subtraction— -
    • Multiplication—*
    • Division—/
    • Exponentiation—^: x^y, x raised to the power of y
    • Logarithm—log
    • Square root—sqrt: sqrt(16)
    • Sine—sin
    • Cosine—cos• Tangent—tan
    • Arcsine—asin 226; Arccosine—acos
    • Arctangent—atan
    • e raised to an x power—exp
    • Absolute Value—abs

    You can enter integers, decimals, and fractional values in formulas, using normal mathematical syntax, as shown in the examples below:

    • Length = Height + Width + sqrt(Height*Width)
    • Length = Wall 1 (11000mm)+ Wall 2 (15000mm)
    • Area = Length (500mm) * Width (300mm)
    • Volume = Length (500mm) * Width (300mm) * Height (800 mm)
    • Width = 100m * cos(angle)
    • x = 2*abs(a) + abs(b/2)
    • ArrayNum = Length/Spacing.

    Parameter names in formulas are case sensitive. For example, if a parameter name begins with a capital letter, such as Width, you must enter it in the formula with an initial capital letter. If you enter it in a formula using lower-case letters instead, for example, width * 2, the software will not recognize ! the formula."


    Now, my goal is to create some sort of element, family, or project that will be driven solely by calculus, trigonometry, and basic mathematics. The purpose is to prove the use of these subjects within my field of study (architecture). Therefore, how would architecture and calculus relate?


    Topics Covered:
    • Creating a Conceptual Mass.
    • Create From with Spline and Profile.
    • Edit and Create formulas within Families.
    • Drive formulas with parameters.
    • Add Profile.
    • Use CALCULUS IN REVIT!
    Here is a great video to compliment my tutorial: Greg Lynn at TED:



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    Christian Gladiators? Athletics as a metaphor for Christian life


    Image : http://www.flickr.com


    When Paul went to Corinth, in the middle of his second missionary journey, Acts 18:2-3 reports that he joined Aquila and Priscilla, manufacture of tents. This fits well with what Paul writes to himself, at the same time. For example, in 1 Thessalonians. 1:9 says, "But remember, brothers, our toil and hardship, we have worked day and night to avoid becoming a burden to anyone while he was preaching the gospel of God for you." Even in 2 Thess. 3:7-8, Paul: "Wenot idle when we were with you, even eat without paying. Instead, we worked day and night, with difficulty, so it would not be a burden to be one of you. "

    Paul in these two States still at Corinth. Shortly after Corinth, left, towards the end of the third missionary journey, Paul in his apostolic right, which supported intellectually benefit (1 Co! r. 9). The question is rhetorical irony, "OrThere are only I and Barnabas who must work for a living? "(1 Cor. 9: 6).

    By Jerome Murphy-O'Connor:

    View of the trade the first time in a tent-maker seems particularly appropriate for a department that focuses on the city, but there was a tendency among the craftsmen of that title, though not actually covered a much broader and more ... the same purpose as a craftsman of today, sometimes described as a carpenter. Paul was in allChance, leather work, hand in producing the large number of items contained in this material: "Can [sandal] has, in turn, would gourds for water and wine, crockery saddles, shields, etc. shops and footpaths are were also made of leather, and a ready market in Corinth (St. Paul, we Corinth: Texts and Archeology, 168).

    One reason for this is true is that the Games of the Isthmus took place in nearby Isthmia. After the Olympics among the four major Panhellen! icGames, Isthmian Games were two times more likely than others! , is hel d every two years. Time Paul went to Corinth, the Isthmian Games were 500 years. They were not even in the century of its tradition of welcoming Corinth was abandoned almost completely disrupted (146-44 BC).

    At the time of Paul to Corinth, 50 CE, are the games have been brought from Corinth to Isthmia. Another cesarean games simultaneously with another event in every location in the isthmusGames. The Commission presented its own site of action. Groups of people from all over the Roman Empire, met Isthmia, either to participate or attend events. According to Casio, a contemporary of Paul (in his speeches, 8.12), containing the basic sporting breeds Isthmian Games, wrestling, diving, boxing, javelin throw and threw it on the disc.

    One time or another in the history of the Games, including the new phenomena of horse racing, racing, poetryReading, theater, singing, announcing, playing the lyre and the flute, and a painting competition. Yacht Race, near the Saroni! c Gulf, has a function, not the Games of Olympia, Delphi, Nemea, O. Demonstrations were planned for women, like men, and even for children. Large amounts of money in hand, not only for players who have won and lost, but that gives the winner.

    Isthmia excavations began in 1883 with Paul Monceaux. RenewedSB 1930 by Jenkins and H. Megawati. These initial efforts yielded only meager results. Oscar Broner, however, that the site of excavation 1959-1967 discovered the temple of Poseidon, porticoes, the sanctuary of Palaemon, two stages, much earlier than others, and a Hellenistic settlement near "Rashi". Assistant Broner, Elizabeth Gebhard outdoor theater. From 1967 to 1976, Clemente excavated Roman baths and other buildings. Ms. Gebhard againExcavated in 1980 and 1989 in the central chapel and a prehistoric settlement "Rashi".

    Archaeologists were unable to find permanent housing for the crowd of participants in the Games as a track in the firs! t century AD They were built only in the second century. With ! the opti on of dealing with several miles of walking per day to reflect events or shopping and to enter a tent, hundreds if not thousands, witnessed what you prefer. In other words, this city was theBest places in the Mediterranean world of Paul to open the tent-making shop. Small shops like yours (with lines of 10 feet, 10 meters), the squares in cities throughout the Hellenistic empire.

    Games of Paul, while living in Corinth? We have no idea, for sure. The games began with a sacrifice to Poseidon, the patron of the local deities. In addition, many sporting events were conducted in the most simple men and women were likelyonly poor clothing. One might expect that this nerve to offend the scruples / Judeo-Christian. However, Murphy-O'Connor said:

    It is difficult to decide whether Paul himself took part in the games. Jewish Palestinian resistance against these glasses is well documented ... but we think that the same attitude that has prevailed in the di! aspora. The wire was free, I had an all-in wrestling competition (see Probis Omnis, 26), we can be sure that many Hellenized Jews did not hesitateParticipation in the Games. Jews had special reserved seats in the theater of Miletus in western Asia Minor .... (17).

    We do not know for sure is that Paul uses the familiarity with the games as a source of images in their teaching. A review of his speeches and letters, in roughly chronological order, presents a series of allusions to sports competition. (I want the fat and suggestions for a more literal translation.)

    Delivered before arrival in Corinth, in a sermon13h25 to Antioch in Pisidia (Acts), Paul "(race)" (Drôme greek, after "rollerdrome" and "Racetrack") as a metaphor for God's purpose for the life of John the Baptist: "And while John ended his career, he continued: "Who do you think I am? I'm not him. "

    Years later, Paul us! ed the same pictures again, their objectives in life. Older Ep! hesians (Acts 20:24) was rejected, said Paul"But I think my life is worthless for me, if I can finish the race and only fill the job that I received the Lord Jesus, to testify the gospel of the grace of God."

    In Galatians 2:2, Paul describes as a next visit to Jerusalem, to write together, "I. .. first to preach the Gospel, are among the nations. But I did it in private, that seemed to be transported by a fear that walking or running, he had run in vain. "Later inthe same book (5.7), commented: "You did a good race. Who cut for you and obeying the truth?"

    These metaphors Paul employs, before arriving in Corinth. The longer wheelbase, however, occurs in the first Corinthians 9:24-27. Shortly after the founding of the church at Corinth, Paul urges the Corinthians:

    Do not you know that running in a race all the runners, but only one receives the prize? Run, so that price. AnyoneParticipate in games goe! s into strict training. They do it to get a crown that will not last, but we do it for a crown, the eternally preserved. I can not, like a man running aimlessly, not knowing who fights like a man in the air. No, I beat my body and my slave so that after preaching to others I am not disqualified.

    In previous centuries, of course, (was in greek: Stefano), the crown as a prize at Isthmia, fromThe branches of pines, like the back of the coins and find contemporary sculpture Isthmia in the sample. The crown of pine branches is a symbol of the Games of the isthmus, there was no evidence that the plant than others, Selinon (a plant similar to celery or parsley was) in the first century BC and a votive size of gains Crowns shows isthmic Selinon used in a variety of plants, including pine y. Goes particularly well with the phrase "crownno less important, or more literally, "crown perish." At the moment the isthmus that athlete! s have received their crown of grass, as it had dried.

    ! In seve ral letters of Paul, he uses the word "fight" or "competence" (the agon greek, that "torture" and torment. ") In Rome. 15:30, for example," Please, my brothers through our Lord Jesus Christ, the love of the mind, in my struggle with prayer to God for me to come with me. "Similar steps are presentedPaul wrote in his letters from prison (see Eph. 6:12, Col. 1:29, 2:1, 4:12, Phil 1:30) in which he wrote after (edition 1 Tim was 4.: 10, 6.12).

    In one of these letters in the same prison (Phil 3:13-14), Paul Racing photos on his experience: "One thing I do: forgetting what lies behind and strain forward to what you end the sentence to which I go God in Jesus Christ in heaven. "

    The word translated "reward"(In brabeion greek) is used by a greek at least three words to describe the prize to the winner of the competition. The context indicates that Paul refers to forget his su! ccesses, not the mistakes of the past. Contrary to what many preachers use this verse does not say: "Do not let your past failures discouraged by their earnings." Says the opposite: "Do not trust your" bottom line "benefits." Every race is a completely new business, and all runnersincluding the captain, must rise again. "

    When Paul is back in prison shortly before his execution, he wrote in his latest letter (2 Tim. 4:7-8):

    I have fought the good fight (dying), which is the rate (Drôme), I concluded kept the faith. What I have to get the crown (Stefano), the righteousness which the Lord has given me that day when the just judge, Not only has given, but all that the love of her appearance.

    As in modern times, has the honor to submit the transfer higher premiums, said Paul expected Jesus, his crown will be awarded by his victory in the Christian race.

    Although! this may reduce some principles, some "rules":
    !
    D espite the victory of Christ on the cross and his desire for forgiveness, having continued to live the Christian life to a struggle between good andMal. This is a fight with the devil, where the stakes are high and the risk of loss is real (Eph. 6:12).

    God wants us to win this competition, and all terms of our success. But we must be prepared to submit to the discipline and establishing a rigorous training, if we expect (with a gain of 1 Cor. 9:24-25).

    God is the price you want to be with us (Acts 20:24). The boundaries of behavior that has staked its moral is, we movebeyond the limits, if you commit sins or "sins." Within this moral line, but we must ask ourselves the same freedom of our judgments themselves, the best way to "run our race" (2 Tim. 4:7).

    Death is the goal, and life with Christ in eternal prize (Philippians 3:13-14, 2 Tim. 4:8).

    In the sense of the word, who are already winners, as soon a! s you start the race. In the words of Paul, who are champions of the Super, "Him who loved us" (Romans 8:37). But we still have to runthe race and to avoid being disqualified (1 Cor too. 9:26-27).

    When you are in your career, Christian? Are behind the scenes? Perhaps you have doubled the last corner and stared at the finish line ahead of me. Or maybe you're still in the stands watching people in the race.

    Wherever you are, the challenge of God to enter the race, all I have to run and cross the finish line victorious. Allows you to equip and train you. But it is necessaryYour role: to take seriously their Christian life, to learn all about the "rules" to listen and obey their coaches. Then, run!

    Want to go further?

    Here are some useful sources:

    1962 Oscar Bronner. "The Crown Victoria del Istmo. American Journal of Archeology. 66:259 et seq. (See also Broner writings of many others in Isthmia.) !

    1967 Pfitzner, Victor C. And the reason Paul Agon: The! images of the traditional sport Pauline literature. Leiden: EJ Brill. (Ph.D.Thesis, Faculty of Evangelical Theology in Münster, Westphalia, Germany)

    1973 Elizabeth Gebhard. The theater at Isthmia. Chicago: University of Chicago.

    1983 Jerome Murphy-O'Connor. St. Paul's Corinth: Texts and Archeology. Wilmington, DE: Michael Glaser.


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    More Damn Vegan Pecan Pie

    Yo! I've moved to a new domain:


    It has pages of information, in addition to normal posts! Oh my gosh!
    Please update your bookmarks.

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    Vegan Pecan Pie - adapted via Todd x on the PPK/Millenium Cookbook (thanks for the update!)


    Oops, I did it again? I made another one of Toddx's vegan p! ecan pies. And quoted a bad song.

    This time with a chocolate graham cracker crust with a chocolate maple ganache on top. I brought it to a Vegan Thanksgiving themed potluck with some Roasted Garlic mashed potatoes and went home empty handed and incredibly full.

    The slightly adapted recipe for the pie is available here on the Try Vegan PDX website for download. I opted for some chocolate-ness because I was leaving the optional booze out.

    Smovely Inspiration.

    Okay, back to being anti-holiday girl. Pie good.

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