1.  Turn in homework for credit  Attendance5 min  Week 4 homework review15 min  Finding a Pattern20 min  In-Class Practice10 min

2. DDrawing a picture or diagram MMaking an organized list MMaking a table SSolving a simpler related problem FFinding a pattern GGuessing and checking EExperimenting AActing out the problem WWorking backwards WWriting an equation 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 50 2 = 2500 Answer: 2500 SERIESSUM 11 1 + 34 1 + 3 + 59 1 + 3 + 5 + 716 1 + 3 + 5 + 7 + 925

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. Number of points on circle123456…15 Number of new segments012345…14 Total number of segments01361015…?

6. In-Class Practice Problem: If 1 2 + 2 2 + 3 2 + … + 9 2 + 10 2 = 385, what is the sum of 2 2 + 4 2 + 6 2 + … + 18 2 + 20 2 ? Solution: Series A 1 2 + 2 2 + 3 2 + … + 9 2 + 10 2 = 385 Series B 2 2 + 4 2 + 6 2 + … + 18 2 + 20 2 = ? Evaluate each term: Series A1 + 4 + 9 + 16 + … + 81 + 100 = 385 Series B4 + 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.