Teaching of loci in key-stage 4

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Teaching of loci in key-stage 4
http//loci.no-ip.com

• CHIANG Kin-nam
• Mathematics Education Section
• LEE Wing-yeong
• HKASME

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1985 vs. 1999

• Equation of Straight Line
• Locus
• Equation of Circle

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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

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Main Tasks (Activities)

1. To help students to construct their own
   understanding
2. To help students to transfer mathematical
   knowledge

Distance
Slope
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Main Tasks

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

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Qualitative treatment of locus e.g.1 Railway
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e.g. 2Dogs and rope
Conditions
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5 common loci

• Points equidistant to a given point.

• Points equidistant to a given line.

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5 common loci

• Points equidistant to two given point

• Points equidistant from two parallel lines.

• Points equidistant from two intersection line

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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

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Suggested Class ActivitiesSketchpad files

1. Rolling box
2. Sliding ladder
3. Rolling coins

http//loci.no-ip.com
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Resources

• Assessment items
• Materials in the web-based resources on the
  Learning and Teaching of Selected New Topics
• http//loci.no-ip.com