Welcome to Math 302A Chris Mikel Section 004: T/Th 11:00 - 12:15 Math East 141

On Index Card… First and Last Name. Put the name you prefer to go by. Class standing: FR, SO, JR, SR Last math class: what, where, when? Other College Level Math Classes On the back, write a few sentences about your experiences with and feelings about math.

As soon as possible: Send an email message to me to schedule a 15-minute get acquainted appointment. Include the times you are available to meet with me in your message and I will get back to you with an appointment time.

Help Sessions in Math East Lobby W: 10-11 Th: 10-11, 1-3

Principles and Standards of School Mathematics (NCTM, 2000) Website: http://www.nctm.org/standards/ Five process standards: problem solving reasoning and proof communication connections representations

Exploration 1.1 With 23 people in class, including yourself, if each person shakes hands once with every other person, how many handshakes will there be?

General Solution How many handshakes will there be in a group of n people, if everyone shakes each other person’s hand once?

How to Solve a Problem Read--understand EVERY ASPECT of the problem. What is given, what is to be found, what can be assumed, what should not be assumed, all vocabulary, what the final answer should look like, etc. Plan--ways to get at the final answer Find the answer. Check and extend.

Pigs and Chickens A farmer’s daughter likes working math problems so he gives her this problem to work on: We have pigs and chickens in our barnyard. I count 24 heads and 80 feet. How many pigs and how many chickens are out there?

Using random trial and error

Guess-check-revise Organized trial and error.

Make a diagram Use pictures to clarify and help solve the problem.

Organizing the information in a table

Use algebra There are 24 animals total: p + c = 24 p represents the number of pigs and c represents the number of chickens. There are 48 feet. Each pig has 4 feet and each chicken has 2 feet, so 4p + 2c = 80

Things to Remember Explain what you did. Explain why you did it. Be sure you check to see that the answer does really answer the question asked. Check to make sure you have not made arithmetic errors.

Problem Solving Strategies Guess and check • Work backwards Solve a simpler problem • Draw a picture Solve a similar problem • Make a table Draw a diagram • Make a graph Find a pattern • Write an equation Find a counter-example • Estimate Solve by induction • Act it out Organized List (Proof by exhaustion) Other?

Homework for Tuesday, January 19th Read course policy information. Read Section 1.1 in the textbook and write your answers in your notebook. Write up your solution of the Handshake problem (#3 and #5) How many handshakes will there be in a group of 23 people? How many handshakes will there be in a group of n people?

Exploration 1.7 This problem explores both representations and connections. Insert whole numbers in the circles so that they add up to the numbers in the squares between. 10 7 13

Exploration 1.7 This problem explores both representations and connections. Read this together as a class. Model the first one. 10 5 8 2 7 13

More Patterns Try to figure out the next number in the sequence--explain how you got it in words that a 3rd grader would understand. 1, 3, 6, 10, … 1, 4, 9, 16, … 2, 4, 8, 16, … 1, 1, 2, 3, 5, 8, …

Exploration 1.4 Problem 1 Darts We will start this in class, and you will finish it for homework. The purpose of this exploration is to focus on having a solution strategy, instead of trying random things. Instead, we will try to think of strategies that work for solving different problems.

Homework Due Thursday 1/21 Do the Problem Solving Strategies handout. Read Textbook sections 1.2, 1.3, 1.4 Do Textbook problems pp. 26 - 29: 3, 5,14, 21a, 22d,f, 25, 30c, 39. Complete and write up Exploration 1.4: Problem 1 Darts, parts 1-4

Four 4s Use four 4s and the arithmetic operations (+, -, x, /) plus grouping symbols to create each of the counting numbers from 0 to 10. Use exactly four 4s for each number.