Crossing the River with Dogs

1
Problem Solving Strategy
LOOK for a PATTERN
2
Look for a Pattern

• We make sense of our universe by inventing
  patterns to describe it. Mathematics has often
  been called the science of patterns. As a
  problem-solving strategy, recognizing patterns
  enables you to reduce a complex problem to a
  pattern and then use the pattern to find a
  solution or predict a behavior.
• Finding patterns in sequences (an ordered string
  of numbers tied together by a consistent rule, or
  set of rules to determine the next term in the
  sequence) is a skill that you can develop.
  Practice will sharpen your pattern-seeking
  skills.
• The key to finding most patterns is to organize a
  problems information in a chart, table, or other
  systematic list so that the patterns jump out at
  you.

3
Look for a Pattern

• Write down the sequence, and extend it if you
  can.
• Make a chart that matches each element of the
  sequence with its position number in the
  sequence.
• Check the differences between the terms of a
  numeric sequence and try to relate the terms to
  their position numbers.
• If seeing the differences between the terms
  doesnt help, try other operations such as
  multiplication, division, and squaring, or use a
  combination of operations.

4
Look for a Pattern

• Pattern recognition can be very useful when
  trying to solve real-world problems.
• An astronomer uses a spectrometer to record and
  observe patterns in the frequencies of light
  radiated from a distant star.
• Investors study the stock market to decide when
  to buy and sell stocks.
• Students observe classes to determine whether or
  not they can behave in a particular manner by the
  way teachers react to their behavior or the
  behavior of students in the classroom.
• Patterns are found everywhere wallpaper,
  traffic patterns, criminal cases, numbers,
  peoples behavior, architectural design, etc.
  Patterns turn up in many places. Keep your eyes
  open for them!

5
Howling Dogs

• While jogging, Shawna noticed that dogs would
  hear her and bark. After the first dog had barked
  for about 15 seconds, two other dogs would join
  in and bark. In about another 15 seconds, it
  seemed that each barking dog would inspire two
  more dogs to start barking. Of course, long after
  Shawna passed the first dog, it continued to
  bark, as dogs are inclined to do. After about 3
  minutes, how many dogs were barking (as a result
  of Shawna's passing the first dog)?

6
Try ideas.

7
Write down a sequence.

• 1 dog
• 1 2 3 dogs
• 3 6 9 dogs

8
Make a chart.
9
Calculate differences.
2
6
18
54
10
Try other operations as needed.
x 3
x 3
x 3
x 3
11
Describe the pattern with symbols.

12
Strategy Look for a pattern

• Write down the sequence, and extend it if you
  can.
• Make a chart.
• Calculate differences.
• Try other operations as needed.
• Describe the pattern with symbols.

13
Now its your turn.

• Open your problem solving book and go to the
  section on Find a Pattern (pages 15-16).
• Print off a problem solving sheet and do a
  complete solution to a problem from this
  sectiondo one and submit it or do more for
  extra fun. (Email Virus, and/or Free Internet)
• Email your complete solution, with your steps
  clearly shown to NCAMath_at_district87.org or put
  them in Nancy Powells mail box!
• Have fun and Problem solve!