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Patterns and sequences

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Patterns and sequences

  1. 1. Patterns and Sequences<br />A Prelude to Sequences and Series<br />Math 2B Lecture <br />4th Quarter SY 2010-2011<br />
  2. 2. Source: http://www.icoachmath.com/SiteMap/Pattern.html<br />Patterns – are sets of objects in which all the members are related with each other by a specific rule.<br />Visual Patterns – are patterns that consist of elements that can be perceived through the sense of sight.<br />
  3. 3. Source: http://ellie-earlychildhoodmathematics.blogspot.com/2010/10/algebra.html<br />Patterns can be shapes, designs or groups of numbers that repeat. Patterns can be seen when investigating items that are around them in their everyday environment.<br /> The core of a pattern is the shortest string of elements that repeats. Patterns can also be extended. <br />
  4. 4. Patterns possess the following characteristics:<br />Change – a change that is observable and predictable, gradual or uniform.<br />Elements – patterns can have elements such as colors, shapes, numbers, images, and even words.<br />Repetition – a pattern has repetition if its core is repeated over and over. <br />Succession - a pattern has succession if the elements form a predictable increase or decrease. <br />
  5. 5. Visual Patterns can be observed according to changes in the following:<br />Direction<br />Perspective<br />Order<br />Size<br />Quantity<br />
  6. 6. Source: http://www.learner.org/teacherslab/math/patterns/logic.html<br />To produce and extend patterns, we need to:<br />sort and classify objects by different properties;<br />order objects by size or other numerical property (seriation);<br />Identify and recognize the core of the pattern<br />describe the change that generates the pattern.<br />
  7. 7. Visual Pattern Tests<br />Identify the characteristic manifested in each pattern and name the next figure.<br />Are you ready?<br />
  8. 8. What is the next figure?<br />The next figure is .<br />The core is .<br />There is repetition in the pattern.<br />
  9. 9. What is the next figure?<br />The next figure is .<br />There is a change in quantity.<br />
  10. 10. The next figure is .<br />The change in the pattern is rotation.<br />What is the next figure?<br />
  11. 11. ?<br />A<br />
  12. 12. ?<br />C<br />
  13. 13. ?<br />C<br />
  14. 14. Sequences<br />Sequences are patterns whose elements are numbers. The elements in a sequence are called terms.<br />Each sequence follows a certain rule. Observing the rule is important to predict and identify the next term.<br />
  15. 15. Sequences can be finite or infinite. A finite sequence contains a countable number of terms, while an infinite sequence is usually represented by a sequence whose end has three dots (…) or an ellipsis.<br />
  16. 16. 4, 7, 10, 13, 16 is a/an sequence.<br />-5, -4, -3, -2, -1, … is a/an sequence.<br />finite<br />infinite<br />
  17. 17. Identify the next term in each sequence.<br />4, 5, 6, 7, 8, ___<br />9, 16, 23, 30, ___<br />9<br />37<br />These are called Increasing Sequences. <br />
  18. 18. Identify the next term in each sequence.<br />12, 10, 8, 6, 4, ___<br />4.5, 2, -0.5, -3, ___<br />2<br />-5.5<br />These are called Decreasing Sequences. <br />
  19. 19. Identify the next term in each sequence.<br />0, 1 , 0, 1, 0, ___<br />1<br />This is called an Alternating Sequence. <br />
  20. 20. Identify the next term in each sequence.<br />3, 6, 9, 12, 15, ___<br />9, 18, 27, 36, ___<br />18<br />45<br />These are called Multiples Sequences. <br />
  21. 21. Identify the next term in each sequence.<br />1, 4, 9, 16, 25, ___<br />36<br />This is called a Perfect Square Sequence. <br />
  22. 22. Identify the next term in each sequence.<br />1, 8, 27, 64, 125, ___<br />216<br />This is called a Perfect Cube Sequence. <br />
  23. 23. Identify the next term in each sequence.<br />4<br />10, 2, 8, 6, 6, 10, ___<br /><ul><li>10,8, 6 </li></ul>form a sequence.<br /><ul><li> 2, 6, 10</li></ul>form a sequence.<br />
  24. 24. Identify the next term in each sequence.<br />1, 4 , 9, 16, ___<br />25<br />These numbers are called Square numbers. <br />
  25. 25. Identify the next term in each sequence.<br />1, 3, 6, 10, ___<br />15<br />These numbers are called Triangular numbers. <br />
  26. 26. Identify the next term in each sequence.<br />2, 6, 12, 20, ___<br />30<br />These numbers are called Rectangular numbers. <br />
  27. 27. Identify the next term in each sequence.<br />1, 1, 2, 3, 5, ___<br />8<br />This sequence is called a Fibonacci sequence.<br />
  28. 28. Improving Pattern Skills<br />Visual discrimination is an important factor for success in predicting patterns. Here are some figures that will help you train your eye to look at a given figure.<br />
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  33. 33. Read the following statement.<br />The<br /> quick <br />brown fox<br />jumps over the <br />the lazy dog twice.<br />
  34. 34. Name the color. Do not read the word.<br />White<br />Black<br />Blue<br />Violet<br />Red<br />Yellow<br />Brown<br />Green<br />Orange<br />
  35. 35. The End<br />

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