LEAP FROGS

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LEAP FROGS

• EMM 111 Mathematics Numeracy
• Assignment 2 Investigation Seminars

An investigation by Amanda Spencer
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What was I investigating?

• 4 counters placed on game board (see Diagram 1).
• AIM- to reverse the positions of counters using
  the least amount of spaces.
• RULES- you are only allowed to slide counters
  into a vacant space or leap over one counter into
  a vacant space.

Diagram 1
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Processes used throughout Investigation

• STEP 1 Think of something to investigate
• STEP 2 Draw game board using appropriate number
  of spaces
• STEP 3 Place counters in appropriate spaces
• STEP 4 Move counters to desired spaces, counting
  moves
• STEP 5 Draw tables showing number of spaces,
  moves counters
• STEP 6 Tabulate information using Microsoft
  Excel
• STEP 7 Make PowerPoint presentation
• STEP 8 PRESENT!!

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THE FIRST RESULT

• I moved the counters from their original
  positions (see Diagram 1) to the positions shown
  in Diagram 2, in a minimum of 10 moves.
• This can be seen in the table below.

Diagram 1
Diagram 2
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Results of leaping into any space
Diagram 1 shows original starting position
Diagram 2 shows first 2 moves
Diagram 3 shows final 2 moves
Diagram 4 shows final position
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Results of leaping into any space

• The table above shows that the minimum number of
  moves needed was the same as the number of
  counters.

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Results of moving several spaces into a vacant
space
Diagram 1
Diagram 1 shows original starting positions,
while Diagram 2 shows final positions of counters
Diagram 2
The table shows that the majority of minimum
moves needed to reach the positions shown in
Diagram 2 was 6
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Results using different starting positions

• Diagram 1 shows the original starting positions
  of counters
• Diagram 2 shows the final positions of counters

Diagram 1
Diagram 2
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Results using different starting positions

• The table below shows the minimum moves needed to
  reverse counters.
• There is no obvious pattern.

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Results of adding more spaces

• The graph and table show the results of this
  investigation

• 5 or 6 spaces-
• minimum moves double amount of spaces

• 7 or more spaces-
• minimum moves increased by 4 each time

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Results of using 5 counters and extra spaces

• I added an extra counter (see Diagram 1)
• AIM- to reverse counters in least amount of moves
  until counters were on the position shown in
  Diagram 2

Diagram 1
Diagram 2

• It can be seen in the table
• that there was no obvious pattern
• found

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Conclusion

• Specific steps used throughout investigation
• Technology played a major role
• Processes more important than solutions
• There are more problems to investigate
• Curriculum Knowledge and Assessment sections