MATH 381 – Summer 2011

1. MATH 381 – Summer 2011

2. First week materials • Syllabus • Problem of the Week • The Learning Environment • My Expectations • Assignments • In-class • Exams • Books • Questions

3. Getting to Know You • Create a tri-fold paper with your first and last name. • You may decorate as you wish • Place in front of you – task time -5 minutes • Short introduction of self 1-2 minutes each • Possible things to include • Info about you • Why teaching? • Feelings about math • If math phobic, when it happened • Your expectations of class

4. Standards based math • 1989 NCTM envisioned STANDARDS based math • Underscored by cooperative learning • Concept teaching • Exploration • Problem solving • How does this differ from the way you learned math, if any? • Important tools for teachers • Knowledge of math • Knowledge of how students learn

5. Math strands – content • 5 strands of math • Numbers and operations • Algebra • Geometry • Measurement • Data analysis & probability • Overlapping information • Our course of study • Not equally weighted • Goals for each strand • http://k12.wa.us/Mathematics/Standards/WAMathStandardsGradesK-8.pdf

6. Math strands - process • How students acquire and use mathematical knowledge • Problem solving • Reasoning and proof • Communication • Connections • Representation • These direct the method of doing math

7. Six principles for high quality math education • Combine into 6 tables. Await direction • Equity • Curriculum • Teaching • Learning • Assessment • Technology • BREAK INTO GRADE LEVEL PREFERENCES K-1, 2-3, 4-5, 6-8 • Turn to pg 501 – Appendix A-2

8. Math is an action verb • Create 8-10 action verbs you think apply to today's math • Write them on the paper supplied and post them on the wall. • Be prepared to communicate your reasons for selecting these verbs

9. Math basics • Students must experience that math makes sense. • Students must come to believe that they are capable of making sense of math • Teachers must stop teaching by telling and start letting students make sense of their own learning. • Teachers must believe in their students.

10. Time to practice – activity 1 • Activity 1- Start and Jump Numbers: Searching for Patterns • Start with the number 4 (your start number) and add 5 consistently (your jump number). Write the start number at the top of your list, then each consecutive number after adding the jump number until your list extends to about 130-140. • Examine the list of numbers and find as many patterns as you can. Write down the patterns to share with the whole class. • Now keep the same start number and add a new jump number larger than 5 but smaller than 12, BUT NOT 10. What new patterns did you find? How do these numbers differ from the last pattern with start number 4 and jump number 5? • Finally, choose a new start number (make it a prime number less than 20) and a prime jump number. Find as many patterns as possible. (Review prime numbers?)

11. Some patterns

12. Time to practice – activity 2 • Activity 2: Two Machines – One Job • Robert’s Recycling started when Robert bought a used paper shredding machine. Business was good, so Robert bought a second shredding machine. • The old machine could shred a truckload of paper in 4 hours. The new machine can shred the same truckload in only 2 hours. • How long will it take to shred a truckload of paper if Robert runs both shredders at the same time? • Show your work in words, numbers and/or pictures and be prepared to share your findings. • DO NOT use an algebraic equation to solve, but you can use one to check your answer

13. Time to practice – activity 3 • Activity 3: One Up One Down Try a grade 1-3 activity and then the accompanying grades 4-7 activity. • Grades 1-3 – When you add 7 to itself (7 + 7) you get 14. When you reduce the first number by 1 (7 becomes 6) and increase the second number by 1 (7 becomes 8), what happens. • Try this with multiple numbers and see what happens. Is the pattern always the same or does it change? • Now try adding a number to itself and subtract 2 from the first number and add 2 to the second number. What happens? Why? • Grades 4-7 – What happens when you change the addition process to multiplication? Take a number and multiply it by itself. The reduce the first number by 1 and increase the second number by 1? • Is the answer the same? Why or why not? • Try it with a variety of other numbers and see if you can find a pattern. • Then multiply the same number, and then add two to the first number and subtract two to the second number and multiply the resulting numbers. • What happens? Why? What pattern appears, if any?

14. Time to practice – activity 4 • Activity 4 – The Best Chance of Purple • Four students are spinning to get purple with two spinners, either by spinning first red and then blue, or first blue and then red. See the spinners below for division of color. The students may choose to spin each spinner once or one of the spinners twice. • Sally chooses to spin twice on spinner A; • Jose chooses to spin twice on spinner B; • Gloria chooses to spin first on spinner A and then spinner B; and • Hakeem chooses to spin first on spinner B and then on Spinner A. • Who has the best chance of spinning “purple?” Show your work and be able to explain your proof. Spinner A Spinner B

15. Kathy Richardson video • Kathy Richardson is a math guru, • Her work with primary students specifically is used in many school districts in Washington • She has many books, videos and professional development techniques available • We will watch “Thinking with Numbers”