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Unraveling Math Patterns: From Numbers to Friends

Discover fascinating math patterns and solve the challenge of friends telling friends about a product using a strategic approach. Explore multiplication patterns, tables, and power functions in a fun and engaging way.

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Unraveling Math Patterns: From Numbers to Friends

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  1. PATTERNS

  2. Math is recognizing patterns. If you can figure out the pattern, you can figure out the math behind it.

  3. Examples of patterns:

  4. 1 X 8 + 1 = 9 12 X 8 + 2 = 98 123 X 8 + 3 = 987 1234 X 8 + 4 = 9876 12345 X 8 + 5 = 98765 123456 X 8 + 6 = 987654 1234567 X 8 + 7 = 9876543 12345678 X 8 + 8 = 98765432 123456789 X 8 + 9 = 987654321

  5. 1 X 9 + 2 = 11 12 X 9 + 3 = 111 123 X 9 + 4 = 1111 1234 X 9 + 5 = 11111 12345 X 9 + 6 = 111111 123456 X 9 + 7 = 1111111 1234567 X 9 + 8 = 11111111 12345678 X 9 + 9 = 111111111 123456789 X 9 + 10 = 1111111111

  6. 9 X 9 + 7 = 88 98 X 9 + 6 = 888 987 X 9 + 5 = 8888 9876 X 9 + 4 = 88888 98765 X 9 + 3 = 888888 987654 X 9 + 2 = 8888888 9876543 x 9 + 1 = 88888888 98765432 x 9 + 0 = 888888888

  7. 1 X 1 = 1 11 x 11 = 121 111 x 111 = 12321 1111 x 1111 = 1234321 11111 x 11111 = 123454321 111111 x 111111 = 12345654321 1111111 x 1111111 = 1234567654321 11111111 x 11111111 = 123456787654321 111111111 x 1111111111 = 12345678987654321

  8. Find the pattern: An old TV commercial had the phrase in it: “Tell two friends, and they tell two friends, and they tell two friends, and so on, and so on.” Suppose that you started telling your two friends about this product. If your friends told their friends about it at the rate of one set of friends per day, on what day would 64 friends be told about this product.

  9. One method What if you drew a picture of what this would look like?

  10. (YOU) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

  11. 1 Now, add each row. 1 1 1 1 1 1 1 1 1 1 1 1 1 1

  12. 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1

  13. 1 1 2 1 4 1 1 1 1 1 1 1 1 1 1 1 1

  14. 1 1 2 1 4 1 1 1 1 8 1 1 1 1 1 1 1 1

  15. Each row represents the DAY. We could keep drawing the “tree” until we found the answer. 1 1 2 1 4 1 1 1 1 8 1 1 1 1 1 1 1 1

  16. That would take a lot of room!!!!!!! There must be another way.

  17. Second method Make a table for the first couple of times friends are told about the product.

  18. Second method Make a table for the first couple of times friends are told about the product.

  19. Second method Make a table for the first couple of times friends are told about the product.

  20. Second method Make a table for the first couple of times friends are told about the product.

  21. Second method Make a table for the first couple of times friends are told about the product.

  22. Let’s see if we can figure out the pattern.

  23. Let’s see if we can figure out the pattern. How can we determine the # of Friends Told of Product without writing every day out????

  24. How can we get from 1 to 2??

  25. If we raise 2 by the power of the day number, we get the # of Friends Told of Product

  26. If we raise 2 by the power of the day number, we get the # of Friends Told of Product So on what day will 36 friends be told? Extend the table.

  27. If we raise 2 by the power of the day number, we get the # of Friends Told of Product So on what day will 36 friends be told? Extend the table.

  28. If we raise 2 by the power of the day number, we get the # of Friends Told of Product So on what day will 36 friends be told? Extend the table.

  29. On day 6, 64 friends will be told

  30. Can you find the pattern?? 11 X 11 = 121 11 X 12 = 132 11 X 13 = 143 11 X 14 = 154 11 X 15 = 165 Use your pattern to find the following:

  31. 11 X 21 = 11 X 32 = 11 X 45 =

  32. 11 X 21 = 231 11 X 32 = 11 X 45 =

  33. 11 X 21 = 231 11 X 32 = 352 11 X 45 =

  34. 11 X 21 = 231 11 X 32 = 352 11 X 45 = 495

  35. Life Lesson You are always asked to give it your best. So what percent is your best???? How can you achieve 100% (your best) all the time??

  36. Life Lesson Suppose that you assigned each letter a number following the pattern: A = 1, B = 2, C = 3, . . .

  37. Life Lesson H A R D W O R K 8 + 1 + 18 + 4 + 23 + 15 + 18 + 11 = 98% K N O W L E D G E 11 + 14 + 15 + 23 + 12 + 5 + 4 + 7 + 5 = 96% Not quite there. What will get you to the top??

  38. Life Lesson A T T I T U D E 1 + 20 + 20 + 9 + 20 + 21 + 4 + 5 = 100%

  39. Assignment 1-8: 1 – 5, 7, 8

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