Transcript Problem Solving Techniques

5-Minute Check on Activity 1-1
Problem Solving Techniques:
1. What do we need to get from the information given to us about
a problem?
All relevant information on the problem
2. What was the problem from yesterday?
Do we have time to get the new book before class starts?
3. What did we do to help solve the problem?
We drew a graph (model) with a time-line.
Click the mouse button or press the Space Bar to display the answers.
Activity 1 - 2
The Handshake
Objectives
• Organize information
• Develop problem-solving strategies
– Draw a picture
– Recognize a pattern
– Do a simpler problem
• Communicate problem-solving ides
Vocabulary
• Arithmetic sequence – a list of numbers in which consecutive
numbers share a common difference
• Geometric sequence – a list of numbers in which consecutive
numbers share a common ratio
• Fibonacci sequence – a list of numbers in which consecutive
numbers are added to get the next number
• Inductive reasoning – arrives at a general conclusion form
specific examples
• Deductive reasoning – uses laws and properties to
prove/disprove conjectures
4 Steps in Problem Solving
1. Understand the problem
(determine what’s involved)
2. Devise a plan
(look for connections to obtain the idea of a solution)
3. Carry out the plan
4. Look back at the completed solution
(review and discuss it)
from George Polya’s book, How to Solve It
Problem Solving Summary
• Problem Solving Strategies
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–
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–
–
Discussing the problem
Organizing information
Drawing a picture
Recognizing patterns
Doing a simpler problem
• Four-step process
–
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Understand the problem
Devise a plan
Carry out the plan
Look back at the completed solution
Description
This mathematics course involves working with other
students in the class, so form a group of 3, 4, or 5
students. Introduce yourself to every other student in
your group with a firm handshake. Share some
information about yourself with the other members of
your group.
Handshakes Table
Number of students in group Number of handshakes
1
2
3
3
6
4
10
5
15
6
21
7
2 students:
AB

3 students:
A  B, A  C, and B  C



4 students:
A  B, A  C, A  D, B  C, B  D, and C  D






Handshakes
Describe a rule for determining the number of
handshakes in a group of
A. seven students
Start adding 1 less than 7 and 2 less than 7 until you
get down to 1: 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes
B. students in our class
Start adding 1 less than x and 2 less than x until you
get down to 1:
C. n students
Start adding 1 less than n and 2 less than n until you
get down to 1:
The Classroom
• Square tables in a classroom could be
arranged in various clusters
• Figure out the number of students at each
cluster
Classroom Table
Number of tables in cluster
1
2
3
4
5
6
7
Number of students
4
6
8
10
12
14
16
A
1 table:
A, B, C, D
B
1
D
C
2 tables:
3 tables:
B
A, B, C, D and E, F
A, B, C, D, E, F and H, G
B
A
E
H
1
2
3
C
F
G
D
A
E
1
2
C
F
D
Class Room Seating
Describe the pattern that connects the number
of square tables in a cluster and the total
number of students that can be seated. Write a
rule in sentences that will determine the total
number of students that can site in a cluster of
a given number of square tables, n.
Pattern: add a table, add two students
Rule: Starting with 4 students at one table, with every table you
add, you add two more students.
Math: 4 + 2(n – 1)
Class Room Seating
24 students are in a science course at MSHS
a. How many tables must be put together to
seat a group of 6 students? 2
b. How many clusters of tables are needed
for that class?
24  6 = 4
How would we use square table clusters in our
class?
Summary and Homework
• Summary
– Problem Solving Strategies
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•
•
•
•
Discussing the problem
Organizing information
Drawing a picture
Recognizing patterns
Doing a simpler problem
– Four-step process
•
•
•
•
Understand the problem
Devise a plan
Carry out the plan
Look back at the completed solution
• Homework
– pg 6-9; 1-7, 9