Pascal's Triangle Exploration
Explore the patterns and properties of Pascal's Triangle with this engaging worksheet for Grade 6 students.
Includes
Standards
Topics
Pascal's Triangle Exploration
Name:
Date:
Score:
Follow the instructions for each section to complete the worksheet. Pay close attention to the patterns in Pascal's Triangle.
Pascal's Triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal. Below is the beginning of Pascal's Triangle.
Row 0: 1
Row 1: 1 1
Row 2: 1 2 1
Row 3: 1 3 3 1
Row 4: 1 4 6 4 1
Fill in the missing numbers to complete the next two rows of Pascal's Triangle.
Row 0: 1
Row 1: 1 1
Row 2: 1 2 1
Row 3: 1 3 3 1
Row 4: 1 4 6 4 1
Row 5: 1 1
Row 6: 1 1
1. What is the sum of the numbers in Row 3 of Pascal's Triangle?
4
6
8
16
2. What pattern do you notice about the numbers along the second diagonal (the numbers 1, 2, 3, 4, ...)?
They are even numbers.
They are odd numbers.
They are counting numbers.
They are prime numbers.
1. Describe in your own words how each number in Pascal's Triangle is found from the numbers above it.
2. What is the sum of the numbers in Row 0, Row 1, and Row 2? What pattern do you notice about these sums?
1. Every row of Pascal's Triangle starts and ends with the number 1.
True
False
2. The numbers in Pascal's Triangle are always increasing as you move from left to right within a row.
True
False
Related Worksheets
Balancing Equations Worksheet
Understand and solve one-variable equations by maintaining balance on both sides of the equals sign.
Understanding Algebraic Expressions
A Grade 6 math worksheet on identifying and understanding the parts of algebraic expressions, including terms, coefficients, variables, and constants.
Grade 6 Math: Inequality Word Problems
This worksheet helps 6th-grade students practice solving word problems involving inequalities, including writing and graphing inequalities.
Naming Polynomials Worksheet
A Grade 6 math worksheet focused on identifying and naming polynomials based on their degree and number of terms.
Translating Equations Worksheet
Grade 6 math worksheet on translating word problems into algebraic equations and vice versa.
Exploring Linear Relationships
This worksheet helps sixth-grade students understand and identify linear relationships through tables, graphs, and equations.
Isolating Variables Worksheet
Practice isolating variables in equations with this Grade 6 math worksheet.
Understanding Unlike Terms
This worksheet helps Grade 6 students identify and combine unlike terms in algebraic expressions.