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Gaining A Deeper Understanding of Place Value

Gaining A Deeper Understanding of Place Value. Dianna J. Spence Gregg Velatini North Georgia College & State University. Clarification. The exercises we introduce today are FOR YOU ( not for your students! )

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Gaining A Deeper Understanding of Place Value

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  1. Gaining A Deeper Understanding of Place Value Dianna J. Spence Gregg Velatini North Georgia College & State University

  2. Clarification • The exercises we introduce today are FOR YOU (not for your students!) • We do not expect (or recommend) that you use these Base 6 activities with your elementary students. • You may choose to do similar Base 10 activities with your students.

  3. Why? • “If not for our students, why do them?” • To strengthen your own… • …understanding of number systems • …awareness of students’ perspectives & challenges • “Why not just show us these activities in Base 10?” • Because you know too much! • Helpful (as a teacher) to experience lack of familiarity and limitations similar to those of your students

  4. Learning a Number System • Suppose our hands looked like this… • Imagine learning to count on your fingers

  5. Finger Counting ONE TWO 1 2 FOUR 4 THREE 3 “TEN” FIVE SIX 5 10

  6. Help is on the way! • Base Six Blocks unit rod

  7. Counting with Blocks 1 2 3 4 = 5 11 12 10 14 13 15 21 20

  8. Representing 2-Digit Numbers • Build these numbers with your blocks *All numbers below are written in Base 6 24 40 51 35 55

  9. What comes next? • What is the next number after 45? • What is the next number after 55? 50 100

  10. Base Six Blocks Revisited unit rod flat 1 10 100 cube 1000 “giant rod” 10000

  11. Representing 3-Digit Numbers • Build these numbers with your blocks *All numbers below are written in Base 6 204 134 120 325 152

  12. Identifying Numbers • Write the number represented in each picture (answers should be in Base 6).

  13. Modeling Simple Addition 23 +12 35

  14. Modeling Addition with Trades 23 +15 42

  15. More Addition with Trades 42 +34 120

  16. Practice: Addition 32 +33 21 +15 30 +43 105 40 113 102 +45 214 +54 151 312

  17. Modeling Simple Subtraction 45 -24 21

  18. Modeling Subtraction with Trades 41 -24 13

  19. Practice: Subtraction 52 -33 21 -15 50 -43 15 2 3 103 -45 200 -54 14 102

  20. Modeling Simple Multiplication 2 ×4 12

  21. Modeling 2-Digit Multiplication 12 ×11 132 Notice Partial Products: 100 (flat) 20 (rods at top) 10 (rods at right) 2 (units)

  22. 2-Digit Multiplication w/ Trades 14 ×21 334

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