Welcome To Our Investigation

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Welcome To Our Investigation
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Kaley Gabrielle
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Home and Contents Page

• Welcome
• Home Contents
• Our Question
• Our First Interpretation Kaley
• Our First Interpretation Gabrielle
• Consider this
• Our Scratch Pad
• Have a go!
• Curriculum Links
• Content Strands
• Our Conclusions
• The Final Solution
• What have we learnt?
• Thankyou EMM111

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Our Question!
Draw any triangle, and choose a point within it.
Construct a line from each vertex, through the
point, to the opposite side. Name the intervals
made on the sides of the triangle a,b,c,d,e and f
in that order. Measure the six intervals made on
the sides of the triangle carefully. Calculate
the expression a/d X b/e X c/f
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Our First Interpretation
Kaleys turn The lengths of a b c d e and f,
will vary according to where the point is placed
within the triangle.
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b
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f
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a
c
e
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e
d
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Our First Interpretation
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Gabrielles Turn The lengths of a b c d e f
will vary according to, the size and shape of the
triangle. Eg a large scalene, a medium
equilateral or a small isosceles. The results
will also vary due to the placement of the
intervals around the triangle.
a
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a
f
f
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e
d
c
a
c
d
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Consider this!

• What if the triangles shape changes, will this
  change the answer?
• What if the size of the triangle changes, will
  this affect the answer?
• What if the position of the point is varied will
  this influence the answer?
• What if the position of the labels a b c d e and
  f, are varied will this make a difference?

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Our Scratch Pad
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Have a go yourself!

• Click on the following link to open up an Excel
  Spreadsheet, you will notice that we have a
  number of different figures, if you change the
  figures you will notice a pattern, can you see
  it?
• Excel Spreadsheet

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Our Conclusions

• Conclusions we can draw from this investigation
  are
• The two sides that are next two each other are
  equal for example on the scratch pad, triangle D,
  a f both equal 1.3 cm, b e both equal 2.7cm
  and c d both equal 2cm.
• And due to this the answer in almost all 12
  sample triangles were equal or similar, eg .99,
  1.002, .9928, .996, 1.0001, 0.99975, 0.9992 which
  all in turn round up to 1.0.
• Except when we varied the type of triangle to a
  Scalene triangle, the answer differed, 7.0875,
  24.75, 0.335.
• In triangle h, an Equilateral triangle, on the
  scratch pad there posed a problem. By theory this
  should of produced an answer of 1cm, however the
  answer was 0.5625. Given the previous examples
  can you formulate a reason for error????

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Our Solution

• a/d X b/e X c/f 1
• Except If the triangle is a Scalene triangle,
  this formula will give a different answer (not
  rounding up to 1), because none of the sides are
  equal therefore, the congruency test will not
  work.

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Curriculum Links

• This problem could be applied to a number of
  Working Mathematically Substrands and Content
  Substrands in the NSW K-6 Syllabus, these are as
  follows.
• Questioning Ask questions in relation to
  mathematical situations and personal mathematical
  experiences
• Applying Strategies Develop, select and use a
  range of strategies including the appropriate
  technology to explore and solve the problem.
• Communicating Develop mathematical language and
  representation to formulate and express
  ideas/conclusions.
• Reasoning Develop and use processes for
  exploring relationships, check solutions and give
  reasons for conclusions.
• Reflecting Reflect on experiences and
  understanding making connections with existing
  knowledge and understanding.

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Content Substrands

• This problem can be integrated into a number of
  the content strands in the NSW K-6 Mathematics
  Syllabus these are as follows
• NUMBER MEASUREMENT
• Whole Numbers Length
• Addition SPACE GEOMETRY
• Multiplication/Division Two-dimensional Space
• Fractions/Decimals DATA
• Chance Representation
• PATTERNS ALGERBRA
• Algebraic Techniques
• Number Patterns

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What have we learnt?

• Investigations are a way of solving a problem,
  in which the answer is not quite obvious to us.
• Investigations can be fun, and are a great way
  of engaging children with mathematics.
• We have also learnt about various aspects of
  congruency.
• Built on existing knowledge of the variety of
  Triangles and the properties of each.
• Through investigation a problem can be broken
  down into a series of parts which inturn develops
  mathematical thinking.

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Thankyou

• Thankyou EMM111 for your attention during our
  presentation.
• Kaley Hartin Gabrielle Manga

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