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

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.

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

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. … What? Why? How?

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

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 - … …

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

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

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

x y L1L1 (1,1) (3,3) (-2,-2)(x,y) x = y (-2,3) x  y (-5,2) x-coordinate = y-coordinate

x y L1L1 (1,1) (3,3) (-2,-2)(x,y) x = y (-2,3) x  y (-5,2) x-coordinate = y-coordinate

x y L1L1 (1,1) (3,3) (-2,-2)(x,y) x = y (-2,3) x  y (-5,2) x-coordinate = y-coordinate Visual representation of “ lying …” and “ not lying …”

x y L2L2 (1,1) (-1,3) (4,-2) x + y=2 (-3,2) x+y  2 (x,y) The sum of x-coordinate and y-coordinate is 2

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

x y L3L3 (4,1) (2,-1) (-1,-4) (x,y) x - y=3

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

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

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

x y L5L5 (-3,-3) (-3,0) (-3,2) x =-3 The x-coordinate is -3

x y L4L4 (3,2)(1,2)(-3,2) y =2 (x,y) The y-coordinate is 2

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

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

Thank you!