https://www.khanacademy.org/math/class-6-ncf/x04ca845a9a148c80:patterns-in-mathematics-india/x04ca845a9a148c80:patterns-in-shapes-india/v/patterns-in-shapes 2025-12-05T09:40:41.786169848Z Patterns in Shapes In this video, we will discuss some interesting shape patterns (and fractals). Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Patterns in Shapes In this video, we will discuss some interesting shape patterns (and fractals). https://cdn.kastatic.org/ka-youtube-converted/D1KWce8Sbkg.mp4/D1KWce8Sbkg.mp4 310 Patterns https://www.khanacademy.org/college-careers-more/bjc/x4c51c62a:2022-challenge/x4c51c62a:2022-challenge-popular-vote-regional-champions/v/josefina-chile-math-s-america-region-champion-semifinalist-2022-breakthrough-junior-challenge 2023-04-06T04:51:06.745361174Z Fibonacci Numbers FIBONACCI NUMBERS Learn more at https://breakthroughjuniorchallenge.org. The Breakthrough Junior Challenge is an annual competition for students, ages 13-18, to share their passion for math and science with the world! Each student submits a video that explains a challenging and important concept or theory in mathematics, life sciences, or physics. The winner receives a $250,000 college scholarship. The winning student's teacher and school also benefit: $50,000 for the teacher and a state-of-the-art $100,000 science lab for the school. Khan Academy video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Fibonacci Numbers FIBONACCI NUMBERS Learn more at https://breakthroughjuniorchallenge.org. The Breakthrough Junior Challenge is an annual competition for students, ages 13-18, to share their passion for math and science with the world! Each student submits a video that explains a challenging and important concept or theory in mathematics, life sciences, or physics. The winner receives a $250,000 college scholarship. The winning student's teacher and school also benefit: $50,000 for the teacher and a state-of-the-art $100,000 science lab for the school. https://cdn.kastatic.org/ka-youtube-converted/GzM_zfDHajM.mp4/GzM_zfDHajM.mp4 90 Patterns https://www.khanacademy.org/math/geometry-home/geometry-lines/the-golden-ratio/v/the-golden-ratio 2021-05-19T21:46:39Z The golden ratio An introduction to one of the most amazing ideas/numbers in mathematics Sal Khan video https://cdn.kastatic.org/googleusercontent/GwSojXAXUfg0D-XhaZ6UH0WwM5_8M0AFiFfl-Rmi9RmFvy548bowPsHBhvRDreZ8IS5vohjpxP4f6PTSvKnrUelR The golden ratio An introduction to one of the most amazing ideas/numbers in mathematics https://cdn.kastatic.org/ka-youtube-converted/5zosU6XTgSY.mp4/5zosU6XTgSY.mp4 882 Patterns https://www.khanacademy.org/math/ka-math-class-11/x0419e5b3b578592a:sequences-and-series-ncert-new/x0419e5b3b578592a:series/v/worked-example-fibonacci-sequence 2025-03-01T15:52:37.13987578Z Worked example - Fibonacci sequence Given the recursion formula for Fibonacci sequence, how do we generate the list of first few numbers. We first try playing with the recursion formula but then quickly realise the pattern. Every term is equal to the sum of the previous two. The question asks us to find the ratio of consecutive terms which means we briefly get to say hello to the golden ratio! Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Worked example - Fibonacci sequence Given the recursion formula for Fibonacci sequence, how do we generate the list of first few numbers. We first try playing with the recursion formula but then quickly realise the pattern. Every term is equal to the sum of the previous two. The question asks us to find the ratio of consecutive terms which means we briefly get to say hello to the golden ratio! https://cdn.kastatic.org/ka-youtube-converted/KaF0rEG8ySM.mp4/KaF0rEG8ySM.mp4 346 Patterns https://www.khanacademy.org/math/cc-third-grade-math/arithmetic-patterns-and-problem-solving/imp-patterns-in-arithmetic/v/recognizing-number-pattern-examples 2022-10-06T09:25:13.606060383Z Recognizing number patterns Sal explores whole number patterns and their rules, including patterns in tables. video https://cdn.kastatic.org/ka_thumbnails_cache/f119d8e4-6e03-4e4b-9812-b4fd0e3ff846_1280_720_base.png Recognizing number patterns Sal explores whole number patterns and their rules, including patterns in tables. https://cdn.kastatic.org/ka-youtube-converted/skDNVst7Glw.mp4/skDNVst7Glw.mp4 149 Patterns https://www.khanacademy.org/math/class-6-ncf/x04ca845a9a148c80:patterns-in-mathematics-india/x04ca845a9a148c80:patterns-in-numbers-india/v/recognizing-number-patterns-indian-accent 2025-05-29T05:05:30.332110463Z Recognizing number patterns Recognizing number patterns (Indian Accent) Aakash Bagga video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Recognizing number patterns Recognizing number patterns (Indian Accent) https://cdn.kastatic.org/ka-youtube-converted/6sJLCiWtQAc.mp4/6sJLCiWtQAc.mp4 147 Patterns https://www.khanacademy.org/math/algebra-1-eureka-squared-aligned/x15446f63b23e2a07:quadratic-functions/x15446f63b23e2a07:arithmetic-and-geometric-sequences/v/recursive-arithmetic-sequence 2025-08-28T00:00:48.862639845Z Recursive formula for arithmetic sequence Find the recursive formula for an arithmetic sequence by using the common difference and solving for the designated initial term. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/1cbbc9b2-bf5f-45b9-ba0a-64d6fdb0400a_1280_720_base.png Recursive formula for arithmetic sequence Find the recursive formula for an arithmetic sequence by using the common difference and solving for the designated initial term. https://cdn.kastatic.org/ka-youtube-converted/ddRPUzAXAG4.mp4/ddRPUzAXAG4.mp4 189 Patterns https://www.khanacademy.org/math/cc-fourth-grade-math/imp-factors-multiples-and-patterns/imp-math-patterns/e/patterns-with-shapes 2026-04-08T00:54:09.631945657Z Patterns with shapes Practice identifying features of a pattern with shapes. Kami Soltesz exercise https://www.khanacademy.org/math/cc-fourth-grade-math/imp-factors-multiples-and-patterns/imp-math-patterns/e/math-patterns 2025-03-06T09:22:25.497672024Z Patterns with numbers Generate terms in a pattern when given a rule.  Identify features of a pattern that are not explicit to the rule itself. Tomer Gal exercise https://www.khanacademy.org/math/cc-fifth-grade-math/imp-algebraic-thinking/imp-number-patterns/e/visualizing-and-interpreting-relationships-between-patterns 2026-03-06T17:10:44.240025138Z Relationships between 2 patterns Generate patterns using given rules. Identify relationships between terms. Graph ordered pairs consisting of corresponding terms from the patterns. lisa exercise