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5-Minute Check on Activity 1-1 Problem Solving Techniques: 1. What do we need to get from the information given to us about a problem? All relevant information on the problem 2. What was the problem from yesterday? Do we have time to get the new book before class starts? 3. What did we do to help solve the problem? We drew a graph (model) with a time-line. Click the mouse button or press the Space Bar to display the answers. Activity 1 - 2 The Handshake Objectives • Organize information • Develop problem-solving strategies – Draw a picture – Recognize a pattern – Do a simpler problem • Communicate problem-solving ides Vocabulary • Arithmetic sequence – a list of numbers in which consecutive numbers share a common difference • Geometric sequence – a list of numbers in which consecutive numbers share a common ratio • Fibonacci sequence – a list of numbers in which consecutive numbers are added to get the next number • Inductive reasoning – arrives at a general conclusion form specific examples • Deductive reasoning – uses laws and properties to prove/disprove conjectures 4 Steps in Problem Solving 1. Understand the problem (determine what’s involved) 2. Devise a plan (look for connections to obtain the idea of a solution) 3. Carry out the plan 4. Look back at the completed solution (review and discuss it) from George Polya’s book, How to Solve It Problem Solving Summary • Problem Solving Strategies – – – – – Discussing the problem Organizing information Drawing a picture Recognizing patterns Doing a simpler problem • Four-step process – – – – Understand the problem Devise a plan Carry out the plan Look back at the completed solution Description This mathematics course involves working with other students in the class, so form a group of 3, 4, or 5 students. Introduce yourself to every other student in your group with a firm handshake. Share some information about yourself with the other members of your group. Handshakes Table Number of students in group Number of handshakes 1 2 3 3 6 4 10 5 15 6 21 7 2 students: AB 3 students: A B, A C, and B C 4 students: A B, A C, A D, B C, B D, and C D Handshakes Describe a rule for determining the number of handshakes in a group of A. seven students Start adding 1 less than 7 and 2 less than 7 until you get down to 1: 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes B. students in our class Start adding 1 less than x and 2 less than x until you get down to 1: C. n students Start adding 1 less than n and 2 less than n until you get down to 1: The Classroom • Square tables in a classroom could be arranged in various clusters • Figure out the number of students at each cluster Classroom Table Number of tables in cluster 1 2 3 4 5 6 7 Number of students 4 6 8 10 12 14 16 A 1 table: A, B, C, D B 1 D C 2 tables: 3 tables: B A, B, C, D and E, F A, B, C, D, E, F and H, G B A E H 1 2 3 C F G D A E 1 2 C F D Class Room Seating Describe the pattern that connects the number of square tables in a cluster and the total number of students that can be seated. Write a rule in sentences that will determine the total number of students that can site in a cluster of a given number of square tables, n. Pattern: add a table, add two students Rule: Starting with 4 students at one table, with every table you add, you add two more students. Math: 4 + 2(n – 1) Class Room Seating 24 students are in a science course at MSHS a. How many tables must be put together to seat a group of 6 students? 2 b. How many clusters of tables are needed for that class? 24 6 = 4 How would we use square table clusters in our class? Summary and Homework • Summary – Problem Solving Strategies • • • • • Discussing the problem Organizing information Drawing a picture Recognizing patterns Doing a simpler problem – Four-step process • • • • Understand the problem Devise a plan Carry out the plan Look back at the completed solution • Homework – pg 6-9; 1-7, 9