Mathematical Environments

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Mathematical Environments

• Jennifer Piggott

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Outline

• The session will involve investigating some
  fruitful mathematical
• environments.
• We will work on problems and environments
  available on the
• NRICH website and will examine their potential to
  meet the needs
• of a range of curriculum contexts.
• We will look in detail at two or three examples
  based on
• Isosceles triangles
• Circular Geoboards
• Cuisenaire rods

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Making Rectangles Making Squares

• You have 20 equilateral triangles all of the same
  size as well as the same number of 30, 30, 120
  isosceles triangles with the shorter sides the
  same length as the equilateral triangles.
• Using these triangles how many differently shaped
  rectangles can you build? Can you make a square?
• What other questions does this environment invite
  you to ask?
• PublishedApril 2001.

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More questions

• How many triangular n-animals can you make?
• (Triangular animals are polyominoes made with
  equilateral triangles).
• Create a shape using the two types of triangles
  and calculate the fraction of the shape made with
  each type of triangle.

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Circular Geoboards

• Nine-Pin Triangles (July 2005)
• How many different triangles can you make on a
  circular pegboard that has nine pegs?
• Triangles all around (July 2005)
• How many different triangles can you draw on a
  circular pegboard which has four equally spaced
  pegs?What are the angles of each triangle?If
  you have a six-peg circular pegboard, how many
  different triangles are possible now?What are
  their angles?How many different triangles could
  you draw on an eight-peg board?Can you find the
  angles of each?

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Triangle Pin Down (July 2005)

• A right-angled triangle has been drawn on the
  four-pin board.Can you draw the same type of
  triangle on a three-pin board?How many pins
  could there be on the board for you to be able to
  draw the same type of triangle?Do you notice
  anything about the number of pins for which this
  is possible?What kind of triangle is drawn on
  the six-pin board?How many pins could there be
  on the board for you to be able to draw the same
  type of triangle?Do you notice anything about
  the number of pins for which this is
  possible?Can you name the type of triangle
  drawn on the nine-pin board?On what size board
  could you draw the same type of triangle?Do you
  notice anything about the number of pins for
  which this is possible?

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Other problems in July 2005

• Triangle Pin down
• Use the interactivity to investigate what kinds
  of triangles can be drawn on peg boards with
  different numbers of pegs.
• Triangles in Circles
• How many different triangles can you make which
  consist of the centre point and two of the points
  on the edge? Can you work out each of their
  angles?

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Board Block Challenge (July 2005)

• Firstly, choose the number of pegs on your
  board.Decide what shapes you will be allowed to
  make. You could allow
• triangles and quadrilaterals
• triangles, quadrilaterals and pentagons
• Take it in turns to add a band to the board to
  make any of the shapes you are allowing. A band
  can share a peg with other bands, but the shapes
  must not overlap (except along the edges and
  pegs). A player loses when they cannot make a
  shape on their turn.For your choice of shapes,
  how does the winning strategy change as you
  increase the number of pegs on the board?

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Other Problems from July

• Subtended Angles
• Right Angles
• Pegboard Quads
• Sine and Cosine for Connected Angles

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Squares

• Square it (Oct 2004)
• Tilted Squares (Sept 2004)
• Square coordinates (Feb 2005)
• A tilted Square (Jan 2003)

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Cuisenaire (Oct 2005)

• Train game
• This is a game for two players. You need one
  Cuisenaire rod of each length between 1 (white)
  and 10 (orange), or you can just write down the
  numbers on a piece of paper. Decide who is
  going to go first, and choose a distance between
  11 and 55.

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Other resources (Oct 2005)

• Colour building
• Different by one
• Rod fractions
• General environment

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November - Probability

• Spinners
• Epidemic modelling
• Simple probability environments
• Articles

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For slides and more

• www.nrich.maths.org
• Search for
• Rochdale 2005