s5 mathematics coordinate geometry equation of straight line lam shek ki (po leung kuk mrs. ma kam...

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

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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

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

L3

(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 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

Thank you!