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Effective Problem Solving Strategies for Math: Organizing Data and Analyzing Patterns

This guide provides an overview of essential problem-solving strategies in math, including making organized lists and tables, using tree diagrams, and experimenting to find solutions. It covers practical in-class practices and engaging exercises that enhance the understanding of data organization and analysis. Explore how to tackle problems involving point totals from dart throws and solving riddles about animal counts in a barnyard using logical reasoning. Utilize these techniques to develop skills that aid in comprehensive data understanding and problem-solving effectiveness.

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Effective Problem Solving Strategies for Math: Organizing Data and Analyzing Patterns

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  1. Turn in homework for credit • Attendance 4 min • Week 2 information updates 1 min • $15 class fee, room parent • Week 2 homework review 15 min • Organized List 20 min • Make a Table • In-Class Practice 10 min Agenda – Week 3

  2. Drawing a picture or diagram • Making an organized list • Making a table • Solving a simpler related problem • Finding a pattern • Guessing and checking • Experimenting • Acting out the problem • Working backwards • Writing an equation 2. Problem Solving Strategies (Plan) • Today’s Topics • Tree Diagram • Organized list • Make a table

  3. Making an Organized List When a problem requires you to generate a large amount of data, a list may help you account for all possibilities and avoid repetitions. Bull’s Eye! Three darts are thrown at the target shown below. Assume that each of the darts lands within one of the rings or within the bull’s eye. How many different point totals are possible? 3 4 9 Answer: 10

  4. Tree Diagram Review Words, Words, Words! How many different three-letter “code words” can you make using the letters P, Q, and R if repetition of a letter is not permitted? Use Tree Diagram PQR PRQ QPR QRP RPQ RQP Answer: 6

  5. In-Class Practice Problem: Suppose that four darts are thrown at the target with point values of 3, 5, and 7. How many different point totals are possible if each lands on this target? 3 5 7 Answer: 9

  6. In-Class Practice Problem: A domino has two square spaces on its face. Each of the two square spaces is marked with 1, 2, 3, 4, 5, or 6 dots, or it is left blank. A complete set of dominoes consists of one domino for each of the possible combinations of these markings. How many dominoes are in a complete set? 0,0 0,1 1,1 0,2 1,2 2,2 0,3 1,3 2,3 3,3 0,4 1,4 2,4 3,4 4,4 0,5 1,5 2,5 3,5, 4,5 5,5 0,6 1,6 2,6 3,6 4,6 5,6 6,6 Answer: 28

  7. When a problem involves data that has more than one characteristic, an effective strategy is to organize the data into a table. Displays data so it is easily located and understood, and missing data becomes obvious. An invaluable aid in detecting significant patterns. Making a Table

  8. Take a Chance! Suppose that you roll two number cubes, each of which has faces numbered from 1 through 6. What is the probability of rolling a sum of 8 in the uppermost faces? Making a Table Answer: 5 out of 36

  9. Barnyard Brainstorming: I know that there are 18 animals in the barnyard. Some are chickens and the rest are cows. I counted 50 legs in all. How many of the animals are chicken and how many are cows? Observe the pattern: each time we exchange one cow for one chicken, there are 2 few legs. So, to reduce 72 to 50, we would exchange 72-50=22/2=11 cows for chickens. Thus, there will be 18-11=7 cows and 11 chickens. Making a Table Answer: 7 cows and 11 chickens are in the barnyard

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