MATH 381 – SUMMER 2011

FIRST WEEK MATERIALS Syllabus Problem of the Week The Learning Environment My Expectations

Assignments In-class Exams

Books Questions

GETTING TO KNOW YOU1. Create a tri-fold paper with your first and

last name.2. You may decorate as you wish3. Place in front of you – task time -5 minutes4. Short introduction of self 1-2 minutes each

A. Possible things to include1. Info about you2. Why teaching?3. Feelings about math4. If math phobic, when it happened5. Your expectations of class

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

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/WA

MathStandardsGradesK-8.pdf

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

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

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

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.

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?)

Some patternsStart #

Jump #

Sum Digit +

4 5 9 99 5 14 514 5 19 119 45 24 624 5 29 118 4 24 734 5 39 3

4 9 13 413 9 22 422 9 31 431 9 40 440 9 49 4

5 13 18 918 13 31 431 13 44 844 13 57 357 13 70 770 13 83 283 13 96 696 13 109 1

7 11 18 918 11 29 229 11 40 440 11 51 651 11 62 862 11 73 173 11 84 384 11 95 5

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

TIME TO PRACTICE – ACTIVITY 3 Activity 3: One Up One DownTry 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?

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

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”