1. Teaching of loci in key-stage 4 CHIANG Kin-nam Mathematics Education Section LEE Wing-yeong HKASME http://loci.no-ip.com

2. 1985 vs. 1999 1.Equation of Straight Line 2.Locus 3.Equation of Circle 1.Locus 2.Equation of Straight Line 3.Equation of Circle

3. 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

4. Main Tasks (Activities) 1. To help students to construct their own understanding 2. To help students to transfer mathematical knowledge Distance Slope

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

6. Qualitative treatment of locus – e.g.1 Railway

7. e.g. 2: Dogs and rope Conditions

8. 5 common loci  Points equidistant to a given point.  Points equidistant to a given line.

9. 5 common loci  Points equidistant to two given point  Points equidistant from two parallel lines.  Points equidistant from two intersection line

10. 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

11. Suggested Class Activities Sketchpad files 1. Rolling box 2. Sliding ladder;… 3. Rolling coins http://loci.no-ip.com

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