agenda – week 5
DESCRIPTION
Turn in homework for credit Attendance5 min Week 4 homework review15 min Finding a Pattern20 min In-Class Practice10 min. Agenda – Week 5. Drawing a picture or diagram Making an organized list Making a table Solving a simpler related problem Finding a pattern - PowerPoint PPT PresentationTRANSCRIPT
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.