Tasks | Early Adolescence | Exploring Pascal's Triangle

Tasks - Year 10

Exploring Pascal's Triangle   by Peter Cazalet, Collie SHS
(Could be modified for Years 9 & 8)

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understanding Graphs Represent Variation
Number	Understand Numbers Calculate Reason about Number Patterns
Brief Description:	Exploring Pascal's Triangle and finding patterns (rules) that will allow predictions.
Expected Outcomes:	Understand how the triangle is generated, find patterns in the "diagonals" that allow us to determine future terms in rows.
Context:	Use with class of Year 10 students. 20 Casio CFX 9850 Graphics Calculators.
Learning Activities/ Experience:	Students will be given the first few rows of Pascal's Triangle and asked to extend the triangle, explaining how they did it. Pose the question What are the first four terms of the 100th row of the triangle? Students will use difference patterns to establish the nature of the function rule. That is: Constant Linear Quadratic Cubic The students can then use the Stat Menu on their graphics calculator to enter the data and find the function rule. These function rules can then be used to solve the problem. Note: The Casio will find the Quartic regression line so students could predict the fifth term of the 100th row and check their theory by considering earlier values in the table.
Resources:	Learning Technologies: Graphics Calculators.
Practical Frameworks/ Templates/ Worksheets:	Consider the array of number below: 1 1   1 1     2     1 1     3     3     1 1    4     6     4     1 Complete the next 5 rows of the array. What is the first four terms of the 100th row of this array? Explain how you arrived at your answers in part 2. Based on your work in parts 1 to 3, what is the fifth term in the 100th row? Explain how you arrived at this answer.