1. Week 3 Exploration 3.2 Do problem 1 on your own When you are done, work on problem 2 in your groups Let’s share what we did!

2. 39+57=?? Mental Arithmetic Strategies 39  40, 57  60, 40+60 =100, 100-3=96 39  40, 57  56, 40+56=96 30+50+9+7=80+16=97 For some reason we lost our work 

3. Agenda Exploration 3.2 (Mental Arithmetic) New way to organize/distinguish homework assignments. (Remember, only work from textbook needs 4 pt. explanations.) Something that makes your instructor (and should make you) very very very very upset. Working in other bases (Exploration 2.9). Homework (what to turn in from Exploration 2.9 will be posted on the web.)

4. Another Way to Think About Strategy & Justify Strategy: Answers student who says, “I don’t know what to do!” or “I don’t know how to start!” but doesn’t give away the solution/answer. Justify: Answers the student who asks “Why?” and convinces them your work makes sense and gives the correct answer.

5. Very Very Upsetting (and Wrong!) 1 + 2 + 3 = 6 / 3 = 2 Meaning of “=“ : Correct: 1 + 2 + 3 = 6 and 6 / 3 = 2

6. So, let’s count in base 6 Digits allowed: 0, 1, 2, 3, 4, 5 There is no such thing as 6 When we read a number such as 213 6, we don’t typically say “two hundred thirteen.” We say instead “two-one- three base 6.”

7. Count! In base 6 1, 2, 3, 4, 5, … 10, 11, 12, 13, 14, 15, … 20, 21, 22, 23, 24, 25, … 30, 31, 32, 33, 34, 35, … 40, 41, 42, 43, 44, 45, … 50, 51, 52, 53, 54, 55, … 100, 101, 102, 103, 104, 105, … 110

9. In base 6, write the first five place values. 1296, 216, 36, 6, 1 6 4 6 3 6 2 6 1 6 0 Illustrate these with manipulatives cube flat long unit

10. Count! In base 16 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, … 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f, … 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f, …

11. In base 16, write the first five place values. 65,536, 4096, 256, 16, 1 16 4 16 3 16 2 16 1 16 0