Presentation is loading. Please wait.

Presentation is loading. Please wait.

Patterns, Patterns, and more Patterns!

Published byAubrey Pearson Modified over 5 years ago

Similar presentations

Presentation on theme: "Patterns, Patterns, and more Patterns!"— Presentation transcript:

1 Patterns, Patterns, and more Patterns!
Pascal’s Triangle Patterns, Patterns, and more Patterns!

2 It all starts with 1 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

3 And continues with the counting numbers (the Naturals)
28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 And continues with the counting numbers (the Naturals)

4 … and the Triangular Numbers
28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 … and the Triangular Numbers

5 Rows add to powers of 2 4 1 3 2 6 7 5 9 8 1 = 2 = 4 = 22 8 = 23 16= 24
28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 1 = 2 = 4 = 22 8 = 23 16= 24 32= 25 64= 26 128= 27

6 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 Even Numbers

7 Numbers Divisible by 3 28 84 36 210 330 462 70 126 252 4 1 3 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

8 Numbers Divisible by 5 28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

9 Numbers Divisible by 6 28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432

10 28 84 36 210 330 462 70 126 252 4 1 3 31 2 20 6 10 15 35 21 7 5 120 220 45 165 55 11 9 364 66 286 78 91 455 105 13 14 3003 6435 5005 1001 1365 495 1287 715 2002 12 924 1716 8 56 792 3432 Numbers Divisible by 7

11 And so it goes, on, and on, and on …

Download ppt "Patterns, Patterns, and more Patterns!"

Similar presentations

Triangular Pyramids. Surface Area Step 1: Find the area of the base of the pyramid. Step 2: Find the area of the 3 congruent triangles. Step 3: Add them.

Triangular Pyramids. Surface Area Step 1: Find the area of the base of the pyramid. Step 2: Find the area of the 3 congruent triangles. Step 3: Add them.
Volume of Triangular Prism. Volume of a Triangular Prism Length Volume of a prism = Area x length Area of triangle = ½ x base x height.

Volume of Triangular Prism. Volume of a Triangular Prism Length Volume of a prism = Area x length Area of triangle = ½ x base x height.
It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.

It’s a triangle. A triangle of numbers! Pascal did not create it…. The Chinese did. Blaise Pascal discovered all of the unique patterns in it.
What percentage of the numbers in Pascal’s Triangle are even? 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1.

What percentage of the numbers in Pascal’s Triangle are even?
PASCAL’S TRIANGLE. * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.

PASCAL’S TRIANGLE. * ABOUT THE MAN * CONSTRUCTING THE TRIANGLE * PATTERNS IN THE TRIANGLE * PROBABILITY AND THE TRIANGLE.
PowerPoint Created By Nicholas Albanese

PowerPoint Created By Nicholas Albanese
Why and when did Pascal make the triangle? What are some patterns in Pascal’s triangle(what is so important about what’s in Pascal’s triangle?) What does.

Why and when did Pascal make the triangle? What are some patterns in Pascal’s triangle(what is so important about what’s in Pascal’s triangle?) What does.
Notes 9.2 – The Binomial Theorem. I. Alternate Notation A.) Permutations – None B.) Combinations -

Notes 9.2 – The Binomial Theorem. I. Alternate Notation A.) Permutations – None B.) Combinations -
What does Factorial mean? For example, what is 5 factorial (5!)?

What does Factorial mean? For example, what is 5 factorial (5!)?
1-1 Numbers and Patterns Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective:

1-1 Numbers and Patterns Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes Objective:
The student will identify and extend geometric and arithmetic sequences.

The student will identify and extend geometric and arithmetic sequences.
Warm up 1. Write the expression in expanded form, then find the sum. 2. Express the series using sigma notation.

Warm up 1. Write the expression in expanded form, then find the sum. 2. Express the series using sigma notation.
5-7: The Binomial Theorem

5-7: The Binomial Theorem
Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.

Pascal’s Triangle and the Binomial Theorem Chapter 5.2 – Probability Distributions and Predictions Mathematics of Data Management (Nelson) MDM 4U.
Course 2 1-1 Numbers and Patterns 1-1 Numbers and Patterns Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Course Numbers and Patterns 1-1 Numbers and Patterns Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
9.5 The Binomial Theorem Let’s look at the expansion of (x + y)n

9.5 The Binomial Theorem Let’s look at the expansion of (x + y)n
Binomial Theorem & Binomial Expansion

Binomial Theorem & Binomial Expansion
Math 409/409G History of Mathematics

Math 409/409G History of Mathematics
Numeracy Resources for KS2

Numeracy Resources for KS2
2-6 Binomial Theorem Factorials

2-6 Binomial Theorem Factorials

Similar presentations

Ads by Google