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Patterns, Relationships, and Algebraic Thinking (part 2)

TAKS Obj. 2 and 6: Make generalizations from patterns or sets of examples and non-examples (4.16A). Patterns, Relationships, and Algebraic Thinking (part 2). Generalizations.

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Patterns, Relationships, and Algebraic Thinking (part 2)

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  1. TAKS Obj. 2 and 6: Make generalizations from patterns or sets of examples and non-examples (4.16A) Patterns, Relationships, and Algebraic Thinking (part 2)

  2. Generalizations • Generalizations about numbers and patterns make mathematicians more accurate in their predictions and more efficient in their work with specific problems • Definition: To infer or form (a general principle, opinion, conclusion, etc.) from only a few facts and examples

  3. Example of Generalizations • An alien drops into our classroom. He notices that all the boys in the class are wearing red shirts. He makes the generalization that “All Human Boys Wear Red Shirts” This may not be true, but based on all the examples of boys that he has seen, he made the generalization.

  4. Examples of Generalizations • Because every male in my family LOVES sports, I could say that “Boys like sports.” This is a generalization, based on the examples that I have seen.

  5. Generalizations • Let’s try one with numbers. • These are sigors: 2, 14, 6, 24, 10, 4 • What generalization can we make about sigors?

  6. Examples, Non-Examples • These are plats: • These are not plats: • What generalization can you make about plats?

  7. Examples, Non-examples Kareem created a table to record how he sorted various symbols into two groups. Kareem’s Symbols Which statement about how Kareem sorted the symbols is true? A The symbols in Group B have two pairs of perpendicular sides. B The symbols in Group A have acute angles. C The symbols in Group B are quadrilaterals. D The symbols in Group A have a line of symmetry.

  8. Examples, Non-examples Jennifer says that the letters H, M, O, and A are examples of letters that have a vertical line of symmetry and the letters C and B are examples of letters that do not have a vertical line of symmetry. Jolene says they all have a horizontal line of symmetry. Who is correct? Explain your thinking. H M O A C B

  9. Let’s try some on our own!

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