5-Minute Check on Activity 1-1

1
5-Minute Check on Activity 1-1

• Problem Solving Techniques
• What do we need to get from the information given
  to us about a problem?
• What was the problem from yesterday?
• What did we do to help solve the problem?

All relevant information on the problem
Do we have time to get the new book before class
starts?
We drew a graph (model) with a time-line.
Click the mouse button or press the Space Bar to
display the answers.
2
Activity 1 - 2

• The Handshake

3
Objectives

• Organize information
• Develop problem-solving strategies
• Draw a picture
• Recognize a pattern
• Do a simpler problem
• Communicate problem-solving ides

4
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

5
4 Steps in Problem Solving

1. Understand the problem (determine whats
   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 Polyas book, How to Solve It
6
Problem Solving Summary

• Problem Solving Strategies
• 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

7
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.

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Handshakes Table
Number of students in group Number of handshakes
2
3
4
5
6
7
1
3
6
10
15
21
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 ?
? ? ? ?
?
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Handshakes

• Describe a rule for determining the number of
  handshakes in a group of A. seven
  studentsB. students in our classC. n
  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
Start adding 1 less than x and 2 less than x
until you get down to 1
Start adding 1 less than n and 2 less than n
until you get down to 1
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The Classroom

• Square tables in a classroom could be arranged in
  various clusters
• Figure out the number of students at each cluster

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Classroom Table
Number of tables in cluster Number of students
1
2
3
4
5
6
7
4
6
8
10
12
14
16
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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)
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Class Room Seating

• There are 24 students in a science course at
  MSHSA. How many tables must be put together to
  seat a group of 6 students?B. How many
  clusters of tables are needed for that class?
• How would we use square table clusters in our
  class?

2
24 ? 6 4
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Summary and Homework

• Summary
• Problem Solving Strategies
• 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