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Agenda – Week 5

Turn in homework for credit Attendance 5 min Week 4 homework review 15 min Finding a Pattern 20 min In-Class Practice 10 min. Agenda – Week 5. Drawing a picture or diagram Making an organized list Making a table Solving a simpler related problem Finding a pattern

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Agenda – Week 5

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  1. Turn in homework for credit Attendance 5 min Week 4 homework review 15 min Finding a Pattern 20 min In-Class Practice 10 min Agenda – Week 5

  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 • Solving simpler… • Finding a pattern

  3. Finding a Pattern Most frequently used problem solving strategies. Many times, it is used in conjunction with other problem solving strategies.

  4. Odds and Ends Problem: What is the sum of the following series of numbers? 1 + 3 + 5 + … + 97 + 99 Consider the sums of a few simpler series: Pattern:The sum of each of the odd number series beginning with 1 is equal to the square of the number terms in the series. There are 50 odd numbers, so 502 = 2500 Answer: 2500

  5. Connect the Dots Problem: Fifteen points are placed on a circle. How many straight line segments can be drawn by joining all the points in pairs? Pattern: The total number of line segments determined by 15 points is the sum of the counting numbers 1, 2, 3, …14 shown on the table. So, 0 + 1 + 2 + 3 + … + 14 = 105 segments.

  6. In-Class Practice Problem: If 12 + 22 + 32 + … + 92 + 102 = 385, what is the sum of 22 + 42 + 62 + … + 182 + 202 ? Solution: Series A 12 + 22 + 32 + … + 92 + 102 = 385 Series B 22 + 42 + 62 + … + 182 + 202 = ? Evaluate each term: Series A 1 + 4 + 9 + 16 + … + 81 + 100 = 385 Series B 4 + 16 + 36 + 64 + … + 324 + 400 = ? Series B = 4 x Series A = 4 x 385 = 1540

  7. In-Class Practice Problem: What is the units digit of the product when one hundred 7s are multiplied? Solution: 7 = 7 7 x 7 = 49 7 x 7 x 7 = 343 7 x 7 x 7 x 7 = 2401 7 x 7 x 7 x 7 x 7 = 16,807 7 x 7 x 7 x 7 x 7 x 7 = 117,649 The units digit repeats in cycle of four: 7, 9, 3, 1, 7, 9, 3, 1, … 100/4=25, so when one hundred 7s are multiplied, the unit digit is 1.

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