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Mathematical Environments

Mathematical Environments. Jennifer Piggott. 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

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Mathematical Environments

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  1. Mathematical Environments Jennifer Piggott

  2. 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

  3. 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? Published:April 2001.

  4. 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.

  5. 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?

  6. 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?

  7. 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?

  8. 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?

  9. Other Problems from July • Subtended Angles • Right Angles • Pegboard Quads • Sine and Cosine for Connected Angles

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

  11. 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.

  12. Other resources (Oct 2005) • Colour building • Different by one • Rod fractions • General environment

  13. November - Probability • Spinners • Epidemic modelling • Simple probability environments • Articles

  14. For slides and more www.nrich.maths.org Search for: Rochdale 2005

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