Type I – Mathematical Investigation Lacsap’s Fractions The focus of this investigation is surrounding Lascap’s Fractions. They are a group of numbers set up in a certain pattern. A similar mathematical example to Lacsap’s Fractions is Pascal’s Triangle. Pascal’s Triangle represents the coefficients of the binomial expansion of quadratic equations. It is arranged in such a way that the number underneath the two numbers above it‚ is the sum. Ex. 1 1 1 1 2 1 1
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What’s So Hard About Fractions? Fractions as we know them today‚ the symbols and the algorithms for performing operations‚ have developed over thousands of years‚ beginning with ancient Egyptians. Through research of the origins‚ the development of fractions to appearing symbolically as we know them today‚ and of the developments of how we operate with them today and then connecting that knowledge with the observations of contemporary math education experts and personal interviews and observation
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Lacsap’s Fractions Laurie Scott SL Math Internal Assessment Mr. Winningham 9/5/12 Instructions: In this task you will consider a set of numbers that are presented in a symmetrical pattern. Pascal’s Triangle |n=0 |1 | |1 |0 | |2 |3 | |3 |6 | |4 |10
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Iva Rhiana C. Santiago 4218 “Man is like a fraction whose numerator is what he is and whose denominator is what he thinks. The greater the denominator‚ the lesser the fraction.” –Lev Tolstoy We should take note that in a fraction‚ as the denominator becomes larger‚ the value of the fraction becomes lesser. Man is also like a fraction as what Lev Tolstoy said in his quotation. Life is full of choices‚ full of situations. Where sometimes all our way to run away is by pretending. Pretending is one
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Basic Concepts on Fraction Fraction – is defined as a part of a whole. In some other books‚ it is defined as a number written in the form ab ‚ where “a” and “b” are numbers and “b” is not equal to zero. Basic Parts of a Fraction * Numerator – the number above tells how many parts are taken. * Denominator – the number below tells how many equal parts the whole is divided. * Fraction bar – line that separates the two numbers. It also indicates division. There are several kinds
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Adding & subtracting fractions 1. Where in life is this useful? a) Cooking: [pic] b) Measurements (construction‚ remodeling‚ etc): [pic] c) Time: [pic] d) Money: [pic] 2. Fractions with the same (“common”) denominators Example: (without converting back & forth from mixed numbers): [pic] [pic] 3. Fractions with different denominators In order to add (or subtract) fractions with different denominators
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Portfolio #1 This portfolio surrounds the mathematical ideals of the LACSAP’s Fractions‚ and creating the task of answering certain questions about a specific symmetrical pattern. Through a work entirely of my own and without any unauthorized outside assistance‚ I answers all of the questions in this portfolio along with showcasing all my work‚ aided by the use of technology and patterns discovered by me. The symmetrical pattern provided possesses only 5 vertical rows‚ with number of elements
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Lacsap’s Fractions The aim if this IA is to investigate Lacsap’s Fractions and to come up with a general statement for finding the terms. When I noticed that Lacsap was Pascal spelt backwards I decided to look for a connection with Pascal’s triangle. Pascal’s triangle is used to show the numbers of ‘n’ choose ‘r’(nCr). The row number represents the value of ‘and the column number represents the ‘r’ value. Eg. Row 3‚ colomn 2 = 3C2 =
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| Math SL Portfolio-Lacsap’s Fractions | Type 1: Investigation Portfolio Greenwood High (An International School) | | | | | Table of Contents: Introduction……………………………………………………………………………………………………..……..…...Page 2 Patterns in Numerator………………………………………………………………………………….………………Page 2 and Page 3 Plotting Graph of Row Number and Numerator……………………………………………………………Page 4 to Page 7 Finding Denominator………………………………………………….………………………………………..………Page 8 to Page 9 Finding Further Rows……………………………………………………………………
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Lesson Plan Grade Level Content Standard: Number Sense 2.1 Solve problems involving addition‚ subtraction‚ multiplication‚ and division of positive fractions and explain why a particular operation was used for a given situation. Standard Based Objective: When given division problems with fractions‚ students will use the rules for dividing fractions to solve problems with 80% accuracy as measure by student work samples by the end of the week. Materials Paper Pencils White Board Yellow and Pink
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