S5 Mathematics Coordinate Geometry Equation of straight line Lam Shek Ki (Po Leung Kuk Mrs. Ma Kam...
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Transcript of S5 Mathematics Coordinate Geometry Equation of straight line Lam Shek Ki (Po Leung Kuk Mrs. Ma Kam...
S5 MathematicsCoordinate 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-coordinate y-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 innominal 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-coordinate y-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)
Unp
ack
nominal group
VISUAL SYMBOLIC
LANGUAGE
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
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L1
(1,1)
(3,3)
(-2,-2)
(x,y)
x = y(-2,3)
x y
(-5,2)
x-coordinate = y-coordinate
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L1
(1,1)
(3,3)
(-2,-2)
(x,y)
x = y(-2,3)
x y
(-5,2)
x-coordinate = y-coordinate
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L1
(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…”
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L2
(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
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 line straight 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.
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L5
(-3,-3)
(-3,0)
(-3,2)
x =-3
The x-coordinate is -3
0 1 2 3 4 5 6 7-1-2-3-4-5-6
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
L4
(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