Teaching of loci in key-stage 4

CHIANG Kin-namMathematics Education Section

LEE Wing-yeongHKASME

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1985 vs. 1999

1. Equation of Straight Line2. Locus3. Equation of Circle

1. Locus2. Equation of Straight Line3. Equation of Circle

Teaching Approaches

Decompose the mathematical concept into developmental steps that enable students to learn the concept more easily

Use Cooperative Learning Strategy (Group Activities)

Use of Information Technology Describing the locus in words and in

mathematical forms Giving reasons or proof for your description

Main Tasks (Activities)

1. To help students to construct their own understanding

2. To help students to transfer mathematical knowledge

DistanceSlope

Main Tasks

3. To create situations that will foster their making the necessary mental constructions

Qualitative treatment of locus –e.g.1 Railway

e.g. 2:Dogs and rope

Conditions

5 common loci Points equidistant to a given

point.

Points equidistant to a given line.

5 common loci Points equidistant to two

given point

Points equidistant from two parallel lines.

Points equidistant from two intersection line

A systematic way for discovering a required locus ( a five-step procedure )

draw a diagram which includes the given information continue drawing points until a pattern emerges connect the points using a broken line or curve describe the locus in words verify by checking that:

– if a point is on the locus, then it satisfies the given condition(s) and

– if a point satisfies the given condition(s), then the point lies on the locus

Suggested Class ActivitiesSketchpad files1. Rolling box

2. Sliding ladder;…

3. Rolling coins

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Resources Assessment items Materials in the web-based resources on the

Learning and Teaching of Selected New Topics

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