Interactive
CK-12 Foundation

Pascal's Triangle: Pyramid Blocks

For Students 9th - 12th Standards
Build a pyramid of sums. An interactive presents the first five rows of Pascal's Triangle as a pyramid. Pupils match missing entries in the pyramid and continue the pattern to determine entries of other rows. The learners use the entries...
Lesson Plan
Curated OER

Patterns in Pascal's Triangle

For Teachers 7th - 9th
Learners examine the patterns that exist in Pascal's Triangle. They explore multiples and factors. Sudents use an applet to create and color the multiples in Pascal's Triangle.
Worksheet
Curated OER

Coalitions and Pascal's Triangle

For Students Higher Ed
In this coalitions worksheet, students answer 5 questions involving Pascal's triangle, coalitions, combinations, and the Banzhaf power index.
Lesson Plan
Alabama Learning Exchange

Binomial Expansion—Shortcut Please

For Teachers 9th - 12th Standards
There has got to be a better way; you just have to find it! Given a general binomial to expand with increasing powers, pupils realize that there must be a better way than multiple multiplications. Classmates look for patterns and use...
Handout
Curated OER

Series Review Sheet

For Students 9th - 12th Standards
Save an infinite amount of time and enjoy this pre-made series formula guide. Arithmetic and geometric formulas are all included as well as Pascal's Triangle and examples of how the Binomial Theorem expands. 
Worksheet
Curated OER

nCr: Combinations

For Students 9th - 12th
In this probability learning exercise, learners utilize factorials or Pascal's Triangle to calculate the combination given in the form of nCr. There are 4 questions.
Lesson Plan
Curated OER

Students use fundamental counting principle to compute combinations and permutations

For Teachers 9th - 10th
Students define Pascal's triangle and special notations used to represent nth elements. In this geometry lesson plan, students solve problems using permutations and combinations. They compare the formula for permutation to that of...
Activity
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Curated OER

Mathematical Treasure Hunt

For Teachers 3rd - 8th Standards
The hunt is on! Young mathematicians follow clues and complete a series of ten math puzzles as they try to crack Dr. Integer's code and find the location of his hidden treasure.
Worksheet
Curated OER

Probability and Patterns with Pascal

For Students 6th - 10th
In this Pascal worksheet, students solve word problems dealing with probability and patterns based on Pascal's triangle theory. Students complete 10 problems total.
Lesson Plan
Curated OER

Exploring Pascal's Triangle and Other Recursive Patterns

For Teachers 3rd - 5th
Students explore patterns in everyday life and in the mathematic world. They create various concrete examples of patterns and verbally describe these patterns to a fellow student.
Lesson Plan
Curated OER

I Am Golden

For Teachers 6th - 8th
Young scholars become familiar with patterns, the Fibonacci Sequence, and the Golden Ratio. They see how many places these occur. They have practical applications for using the calculator and making charts to extend patterns.
Lesson Plan
Curated OER

Building Shapes From Numbers

For Teachers 5th - 8th
Students experience how to illustrate some of the many connections between number and geometry. Through this 2-3 day focus on square numbers and triangular numbers, students make connections among mathematical topics.
Handout
National Council of Teachers of Mathematics

The Math Forum: Pascal's Triangle and Combinations

For Students 9th - 10th Standards
This page gives a description of how to use Pascal's Triangle to determine the total number of possible combinations for a sample set. Also provides a helpful example.
Activity
National Council of Teachers of Mathematics

The Math Forum: Exploring Pascal's Triangle

For Students K - 1st
Every grade level can learn from Pascal's Triangle, and this site helps make it possible. There are explanations, examples, exercises and printable worksheets available.
Lesson Plan
National Council of Teachers of Mathematics

The Math Forum: Exploring Pascal's Triangle

For Teachers 3rd - 5th
Contains lessons and activities on Pascal's Triangle at three levels: elementary, intermediate, and advanced.
Activity
National Council of Teachers of Mathematics

The Math Forum: Pascal's Triangle and the Ice Cream Cones

For Students 9th - 10th
Dr. Math explains how Pascal's triangle can be used to determine the possible combinations of ice cream cones that can be made with different numbers of flavors. His response also includes an explanation using combination functions.
Activity
National Council of Teachers of Mathematics

The Math Forum: Ask Dr. Math: Pascal's Triangle and Binomial Expansions

For Students 9th - 10th
This Math Forum author shows how combinations can be used to identify the pattern in Pascal's Triangle.
Activity
Texas Instruments

Texas Instruments: The Binomial Formula: Its Expansion Using Pascal's

For Teachers 9th - 10th Standards
This set of questions pertains to the binomial formula and Pascal's triangle. Students will find terms of an expansion and investigate combinations. Questions are short answer, true/false, and multiple-choice; solutions are included.
Unit Plan
Math Is Fun

Math Is Fun: Combinations and Permutations

For Students 9th - 10th Standards
Combinations and permutations are explained clearly, with lots of examples. Includes practice questions.
Activity
Texas Instruments

Texas Instruments: Numb3 Rs: Right or Wrong

For Teachers 9th - 10th Standards
Based off of the hit television show NUMB3RS, this lesson helps students draw a connection between binomial expansions, probabilities, combinations, and Pascal's Triangle. The lesson is framed in the context of randomly guessing a number...
eBook
Mathigon

Mathigon: Combinatorics: World of Math

For Students 6th - 8th
This lesson focuses on Combinatorics, a branch of mathematics which is about counting. It includes 5 sections: Factorials, Permutations, Combinations, Combinatorics and Pascal's Triangle, and Combinatorics and Probability with examples...
Activity
Texas Instruments

Texas Instruments: Using the Ti 83/84 to Explore the Binomial Theorem

For Teachers 9th - 10th
This lesson will introduce students to the binomial theorem through a variety of activities. Pascal's triangle and probabilities will be explored through problem solving. The binomial theorem, combinations formula, and the binomial...
Activity
Texas Instruments

Texas Instruments: Probably Not!

For Teachers 6th - 8th Standards
Students learn to find the theoretical probability of different female/male combinations in a family of kittens. Students will investigate empirical and theoretical probabilities and make a connection to Pascal's triangle and binomial...