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S5 Mathematics Coordinate Geometry

S5 Mathematics Coordinate Geometry. Equation of straight line. Lam Shek Ki (Po Leung Kuk Mrs. Ma Kam Ming-Cheung Foon Sien College). Main ideas. Abstraction through nominalisation Making meaning in mathematics through: language, visuals & the symbolic The Teaching Learning Cycle.

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S5 Mathematics Coordinate Geometry

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  1. S5 MathematicsCoordinate Geometry Equation of straight line Lam Shek Ki (Po Leung Kuk Mrs. Ma Kam Ming-Cheung Foon Sien College)

  2. Main ideas • Abstraction through nominalisation • Making meaning in mathematics through: language, visuals & the symbolic • The Teaching Learning Cycle

  3. Content(According to CG) S1 to S3 • Distance between two points. • Coordinates of mid-point. • Internal division of a line segment. • Polar Coordinates. • Slope of a straight line.

  4. Content(According to CG) S5 • Equation of a straight line • Finding the slope and intercepts from the equation of a straight line • Intersection of straight lines • Equation of a circle • Coordinates of centre and length of radius

  5. Direct instruction Given any straight line, there is an equation so that the points lying on the straight line must satisfy this equation, this equation is called the equation of the straight line. … Why? How? What?

  6. A point lying on the line A point not lying on the line Pack in Pointslying on the straight line (x, y) : symbolic representation of a point x-coordinate y-coordinate 3x+2y=5 (Equation of a straight line) nominal group

  7. Problems Some students : - do not understand “x” means “x-coordinate” - cannot accept “x = 2” represents a straight line. - don’t know why the point-slope form can help to find the equation - ……

  8. A point lying on the line A point not lying on the line Unpack Pointslying on the straight line (x, y) : symbolic representation of a point x-coordinate y-coordinate 3x+2y=5 (Equation of a straight line) nominal group

  9. LANGUAGE language & visual language & symbolic LANGUAGE VISUAL & SYMBOLIC VISUAL SYMBOLIC visual & symbolic A point (x, y)

  10. Unpack the meaning of Equation of straight line by guessing the common feature of the points lying on the straight line.

  11. y 5 L1 4 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 x  y (3,3) (-2,3) x = y (-5,2) (1,1) (-2,-2) (x,y) x-coordinate = y-coordinate

  12. y 5 L1 4 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 x  y (3,3) x = y (-2,3) (-5,2) (1,1) (-2,-2) (x,y) x-coordinate = y-coordinate

  13. y 5 L1 4 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 x  y (3,3) (-2,3) x = y (-5,2) (1,1) (-2,-2) (x,y) x-coordinate = y-coordinate Visual representation of “lying …” and “not lying…”

  14. y 5 L2 4 3 (-1,3) 2 (-3,2) 1 (1,1) x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 x+y 2 (x,y) -2 (4,-2) -3 The sum of x-coordinate and y-coordinate is 2 -4 -5 x + y=2

  15. Mathematical concepts Setting the context Teacher modelling and deconstructing Students constructing independently Teacher and students constructing jointly Developing a mathematical concepts

  16. y 5 4 L3 3 2 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 x - y=3 (x,y) (4,1) (2,-1) (-1,-4)

  17. Findings • For every straight line, the coordinates of the points on the straight line have a common feature. Express that feature mathematically Equation of the straight line • Moreover, the coordinates of the points that do not lie on the straight line do not have that feature.

  18. Abstraction through nominalisation x-coordinate  x common feature  Equation of of straight line straight line A point having  The coordinates the feature satisfy the equation Abstraction

  19. Vertical lines (-3 , 2) The x-coordinate of any point lying on the straight line is -3. Equation: x = -3

  20. y 5 L5 4 3 2 (-3,2) 1 x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 (-3,0) -1 -2 -3 (-3,-3) -4 -5 x =-3 The x-coordinate is -3

  21. y 5 4 3 2 (-3,2) (1,2) (3,2) L4 1 (x,y) x -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 -1 The y-coordinate is 2 -2 -3 -4 -5 y =2

  22. Horizontal line (3, 2) The y-coordinate of any point lying on the straight line is 2 Equation: y = 2

  23. Conclusion Indentify and unpack the nominal groups Experience the process of abstraction  Make use of the meaning-making system in mathematics  Scaffolding : The teaching learning cycle

  24. Thank you!

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