Ib Sl Math Type 1 Ia - Lacsap's Fraction
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 |
|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: Denominator (1) = Numerator (1) - (n-1) (n = row number)
Example:
- When n = 5 Denominator (1) = 15 - (5 – 1) = 15 - 4 = 11
Now for the
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: Denominator (1) = Numerator (1) - (n-1) (n = row number)
Example:
- When n = 5 Denominator (1) = 15 - (5 – 1) = 15 - 4 = 11
Now for the