Turn in homework for credit Attendance 5

min Week 4 homework review 15

min Finding a Pattern 20

min In-Class Practice 10

min

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

Today’s Topics

•Tree Diagram•Organized list•Make a table

•Solving simpler…•Finding a pattern

Finding a Pattern Most frequently used

problem solving strategies.

Many times, it is used in conjunction with other problem solving strategies.

Odds and EndsProblem: What is the sum of the following series of numbers?

1 + 3 + 5 + … + 97 + 99Consider 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

SERIES SUM

1 1

1 + 3 4

1 + 3 + 5 9

1 + 3 + 5 + 7 16

1 + 3 + 5 + 7 + 9

25

Connect the DotsProblem: 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 circle

1 2 3 4 5 6 … 15

Number of new segments

0 1 2 3 4 5 … 14

Total number of segments

0 1 3 6 10

15

… ?

In-Class PracticeProblem: 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 = 385Series B 4 + 16 + 36 + 64 + … + 324 + 400 = ?

Series B = 4 x Series A = 4 x 385 = 1540

In-Class PracticeProblem: What is the units digit of the product when one hundred 7s are

multiplied?Solution: 7 = 77 x 7 = 497 x 7 x 7 = 3437 x 7 x 7 x 7 = 24017 x 7 x 7 x 7 x 7 = 16,8077 x 7 x 7 x 7 x 7 x 7 = 117,649The 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.