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 |
|5 |15 |
|6 |21 |

Table 1: Relationship between Row Number and Numerator of Figure 2 [pic]
Figure 3: Graph of the relationship between Row Number and Numerator of Figure 2

In order to find the sixth and seventh rows, a pattern for determining the denominator must be found:

First it is helpful to determine a relationship between the numerator and denominator of the first term in each row:

|Row Number ( n ) |Difference of Numerator and |
| |Denominator (1st term) |
|1 |0 |
|2 |1 |
|3 |2 |
|4 |3 |
|5 |4 |

Table 2: Relationship between Row Number and the difference of the Numerator and Denominator of the 1st term in Figure 2

This data shows that the difference increases by 1 as the row number increases. The data also shows that the difference between the row number and the difference of the numerator and denominator is also 1. From this a statement for the denominator of the first term in each row can be derived:

...Lacsap’sFractions
The aim if this IA is to investigate Lacsap’sFractions 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...

...In Lacsap’sFractions, En(r) refers to the (r+1)th term in the nth row. The numerator and denominator are found separately, therefore to find the general statement, two different equations, one for the numerator and one for the denominator, must be found. Let M=numerator and let D=denominator so that En(r) = M/D.
To find the numerator for any number of Lacsap’sFractions, an equation must be made that uses the row number...

...Lacsap’sFractionsIBMathSL
Internal Assessment Paper 1Lacsap’sFractions
Lacsap is Pascal spelled backward. Therefore, Pascal’s Triangle can be used practically especially with this diagram.
(Diagram 1)
This diagram is of Pascal’s Triangle and shows the relationship of the row number, n, and the diagonal columns, r. This is evident in...

...Choe
March 25 2011
MathIBSL
Internal Assessment – LASCAP’S Fraction
The goal of this task is to consider a set of fractions which are presented in a symmetrical, recurring sequence, and to find a general statement for the pattern.
The presented pattern is:
Row 111
Row 2...

...MathSL I.A:
Lacsap'sFractions
Introduction
In my internal assessment, type1, I was given Lacsap'sFractions task. To do my calculations I used a TI-84 graphic calculator. To type the I.A I used Apple's Pages, Microsoft Excel 2011 and Microsoft Word 2011.
Lacsap'sFractions
To find the numerator of the sixth row I looked at...

...Exploration of Lacsap’sFractions
The following will be an investigation of Lacsap’sFractions, that is, a set of numbers that are presented in a symmetrical pattern. It is an interesting point that ‘Lacsap’ is ‘Pascal’ backwards, which hints that the triangle below will be similar to “Pascal’s Triangle”.
11111...

...SLTYPE1-LACSAP’SFRACTIONS
* INTRODUCTION
This investigation is going to do research patterns relates to the Lacsap’sFractions. For its external structure, Lacsap’sFraction is analogous to Pascal’s Triangle. Lacsap’sFraction presents the way of generating and organizing the binomial coefficients. Within this investigation, the...

...MathSL Portfolio – Tips and Reminders Checklist
Notation and Terminology
Check for the following:
• I did not use calculator notation. (I didn’t include things like ‘x^2’ for or Sn for Sn)
• I used appropriate mathematical vocabulary.
Communication
Check for the following:
• The reader will not need to refer to the list of questions in order to understand my work.
• My responses are not numbered.
• I have an introduction, conclusion,...

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