Welcome to Math 302A Attendance: Number Sense Game

1. Welcome to Math 302AAttendance: Number Sense Game Use a given operation to get from a starting number to within 1 of the goal. Example: Start: 100, Goal: 50, Operation: Multiplication (please use decimals: eg. 0.5 = five tenths) Solution:

2. Syllabus • Purchase your book from the bookstore – it comes bundled and includes manipulatives. Class Notes packet will be available at the Bookstore ~ Jan. 26 (needed in Feb.) • Plan on bringing “Explorations” every day • Attendance is required • 3 Exams (40%) plus the Final Exam (25%) • Quizzes/Projects/Explorations/Other (25%)

3. Homework (10%) • Homework will be collected weekly (posted on website – check it frequently www.math.arizona.edu/~cblackburn/courses) • Problems on the homework list to turn in will be indicated in red and bold and is due at the beginning of class. • All types of problems are examinable – collected or not • Do not expect homework exercises (or exam problems) to be “just like…”

4. Help Sessions (currently scheduled)in Math East Lobby • M: None Scheduled • T: 12:00 – 3:00 • W: 9:00 – 11:00, 1:00-2:00 • Th: 10:00 – 11:00, 12:00 – 1:00, 2:00 – 3:00 • Fri: None Scheduled

5. Instructor Office Hoursin MATH 303 • I will have 3 scheduled office hours • One of those hours will be in the Math East Lobby • Scheduled office hours will be announced as soon as available, until then, by drop-in or appointment.

6. Agenda • Observations About Number Sense Game • Initial Questions – Why are we here? • A Holiday Cleaning Problem • Problem Solving Strategies • A New Way of Looking at Mathematics • Assign Homework

7. Number Sense Observations • If it took more than one step to get close enough to the goal, were they mistakes? • Making a mistake (or getting a wrong answer) is not a bad thing. The real mistake is if you don’t learn something from it. • I have not failed. I’ve just found 10,000 ways that won’t work. ~ Edison

8. Which is More Valuable?(As a Teacher) • Getting to the (right) answer immediately or • Turning “wrong answers” into learning experiences • Wrong answers are (unfortunately) often more abundant than right ones so the skill is in tricking the wrong ones into giving up the right one.

9. When you think about the fact that you will be teaching elementary school mathematics are you: • Filled with warm fuzzy feelings and excitement? • Indifferent? • Filled with dread and anxiety?

10. Do you want your student’s experience with and attitudes toward mathematics to be: • Filled with warm fuzzy feelings and excitement? • Indifferent? • Filled with dread and anxiety?

11. This is a Mathematics Course • This is a course in mathematics NOT in methods. • Translation: In this course we are looking at elementary school mathematics from a sophisticated viewpoint. • Note: I did NOT say we are looking at elementary mathematics!

12. Assumptions and Goals of this Course • Assumption: You have mastered the skills required to solve elementary school level mathematics problems. • Goal: Understand the mechanics behind the skills and develop your number sense and problem solving skills.

13. Timed Discussion:Holiday Problem • 4 bedroom house + garage • Holiday decorations are up • Seasonal decorations stored in the garage • You’ve had company for the last 2 weeks • In your groups, come up with a plan of how to put your house back in order in 24 hours.

14. Did you have a hard time coming up with a plan? • Because of the time pressure? (If this were a math problem – do you think you might have trouble?) • Because why would you come up with a plan? You would just “do it” and get it done.

15. Share Strategies

16. Problem Solving Strategies • Understand the problem and what kind of answer you are looking for. • Draw a picture! • Often more than one approach can reach the “right answer” (clean house). • Develop a plan to answer the question and write it down. • Break the problem down into smaller, more manageable ones (clean one room at a time). Anticipate what “smaller problems” you could answer that will solve the “big problem” together.

17. Grading Most homework problems will be graded on a 4 point scale. • +1 you show the (organized) work you did to arrive at the correct answer • +2 you can explain (coherently) the strategy you used to find your solution / justify your solution • +1 you extend your thinking

18. Why Come up with a plan? Every time you practice by planning a strategic approach to a problem you are training your mind to make your future problem solving more efficient. This skill is indispensible when you are faced with harder, complex, new problems.

19. Extending your thinking • Subtleties • Company implies linens to clean • Given information • (missing) Details about the garage • Filtering and using what you are given • Extension • Will this strategy work even if the situation changes? Or was the solution a convenient (numerical) coincidence (2+2 = 2*2)?

20. Extension continued: • Could there be a more efficient strategy? • Why is your strategy appropriate (or not?) in this situation? • Could there be another way of understanding/interpreting the question?

21. Extension continued: • Did your strategy to solve the problem allow you to recognize or identify any patterns or relationships? • If your problem did not lend itself to a visual representation explain why. Can you create an example that can be represented in a picture? • Ask other relevant questions that push beyond the scope of the “problem at hand”.

22. Homework For class Friday: • in textbook, Read Sections 1.2, 1.3, 1.4 • in explorations, Read Preface • Due Friday:in textbook, p. 26-29 3, 14