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Classification and Patterning EDN 322 Classification and Patterning… Fundamental to learning about the real world; involve the creation of relationships; are easily integrated; can be viewed as a form of problem solving and provide students with the opportunity to develop logical reasoning abilities; provide the basis for building early number concepts; facilitate algebraic thinking; are fun! Classification Making decisions about certain attributes of objects and sorting them based on that classification. Difference Trains Each car in a train is different from the car it follows in a specified number of ways. Find the difference pattern in this train… Can you continue the train? One-difference train: Two-difference train: Thin Blue Venn Diagram Attribute Blocks Rectangle T T T T T T T T T Color – Red, Yellow, Blue Guess my Rule T T T Shape – Triangle, Square Thickness – Thick, Thin Size – Small, Large Large Triangle T T T T T Guess my Rule T T T T T Thick T T Quadrilaterals Venn Diagram Quadrilaterals Regular Polygon Quadrilaterals Trapezoids Parallelograms Quadrilaterals Trapezoids Parallelograms Venn Diagram Quadrilateral Parallelograms Seriation Seriation is the ability to place objects in order according to a given or chosen criterion Possible criteria include: - length - width - height - weight - diameter - tone Prerequisite to more abstract ordering of numbers and a foundation for math reasoning Types of patterns Repeating Patterns Growing Patterns or Sequences Number Patterns 2, 4, 8 NEXT Other Repeating Patterns Fill in the missing part: ____ ____ ____ Examples of Patterns Number of Boys Number of Hands Number of Girls Number of Triangles 1 2 2 4 3 6 4 8 3 1 6 2 9 12 3 4 10 20 B 2XB 45 ? N N3 Calculator Patterns Choose a number between 0 and 9 and add a constant repeatedly to that number. Remember to use the automatic constant feature. For example, to start with 7 and add 4 repeatedly, you press 7 + 4 = = = . . . • What digits appear in the ones place? • How long is the pattern before it repeats? • Are all patterns the same length? • Are there shorter ones? • Can you find one that is length 6? Why not? • How does this change when the start number changes? • How does it change when the skip number changes? Calculator Patterns Repeat the preceding exploration, but this time use multiplication instead of addition. What do you notice? For multiplication, the first factor is generally the one stored. Therefore to start with 4, for example, and repeatedly multiply by 7, press 7 x 4 = = = . . . In this exploration the calculator will “overload” relatively quickly. Since you are only interested in the values of the ones digit, how can you continue the pattern? Calculator Patterns Pick any one-digit number and multiply by 9, then 99, then 999, then 9999. What do you observe? Try other numbers such as 2, then 22, then 222,…