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January 29, 2009

This homework note discusses the concept of number bases, specifically base 5, base 2, and base 16. It includes explanations, examples, and problems for students to practice.

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January 29, 2009

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  1. January 29, 2009 "I never failed once. I invented the light bulb. It just happened to be a 2,000-step process." -Thomas Edison (after he was asked about his 2,000 “failed” attempts!)

  2. January 29, 2009 • Another homework note • Section 2.3 (cont’d) – bases • Exploration 2.9 – more bases

  3. Homework note Since you will be teaching math, it’s vital that you write math correctly. What’s wrong with this: Ex: Add 5 and 7, then divide the result by 4. 5 + 7 = 12/4

  4. 2.3 (cont’d) Our class Alphabitia system is a “base 5” system. Typical notation for base 5: instead of A, B, C, D, A0, AA, etc., write 15, 25, 35, 45, 105, 115, etc.

  5. 2.3 (cont’d) • When you see “3215”, say “three-two-one base 5” • Let’s count in base 5: 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104,…

  6. 2.3 (cont’d) Ex: Explain your thought process for these. • Convert 1235 into our usual (base 10) numbers. b) Convert 16710 into base 5.

  7. 2.3 (cont’d)

  8. 2.3 (cont’d) As you explore various bases, think about how they are similar to base 10. Can you see why some children have trouble learning the base 10 system?

  9. Exploration 2.9 • You will learn and practice with base 6, base 2 and base 16. Base 2: • Important in computer science • Also known as “Binary” numbers Base 16: • Important in computer science, too! • Also known as “Hexadecimal” numbers

  10. Exploration 2.9 Base 6: just another base that can be used (I can’t see any particular reason why 6 was chosen here…)

  11. Exploration 2.9 • Read the introduction (pg 43). • Do Part 1 #1a. • Do Part 1 #2 (try this by yourself first, then discuss with your table) Repeat for Base 2 and Base 16 (typos in base 16 section) Questions?

  12. Exploration 2.9 Work on Part 3: #2 & 3 and Part 4: #1, 2 & 4 (these are due on Tuesday)

  13. Homework • Read textbook pgs 109 – 118 • Do the textbook problems listed online • Exploration 2.9 Part 3: #2 & 3 Part 4: #1, 2, 4

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