Suggestions for Follow-up Actions (KS3-MS2-1: Students can use the formulas for circumferences and areas of circles) (11 Feb 2014, accessible on tablet devices)

Possible problems in students' learning (for reference only)

• Students do not recognize that the value circumference ÷ diameter is a constant.
• Students do not know that π = circumference ÷ diameter.
• Students think that 22/7 and 3.14 are the exact values of π..
• Students mix up the formulas for circumferences and areas of circles.
• Students mix up the diameter with radius when they use the formulas.

Suggestions for Follow-up Actions

Name	Emphasis	Description	Problem addressed (see above)	Suggested duration (minutes)	Available for self - learning?
Circumference and Diameter Preview Download	Recognize the relationship between circumferences and diameters	With the HTML5 dynamic figure and the worksheet, students measure the circumferences of circles of diameters 1 cm, 2 cm, 3 cm and other diameters. By calculating the value of π = circumference ÷ diameter, students recognize that the circumference is about 3.14 times the diameter and the formula for the circumference.		25
Area of Circles Preview Download	Explore the formula for the area of circles	With the HTML5 dynamic figure and the worksheet, students dissect a circle into sectors. By rearranging the sectors and increasing the number of sectors, students explore the formula for the area of the circle by observing the shape obtained when the number of sectors tends to infinity.		25

* The list of possible problems is for teachers' reference only and is not meant to be exhaustive or prescriptive. Teachers can always adapt the activities/materials in order to cater for students' needs.

Other Resources

• OR, C.M. (to be published). Pedagogical Design Focusing on Learning Difficulties – Area of Circles. Assessment and Learning, 1.
  http://wlts.edb.hkedcity.net/filemanager/file/mathematics/tc/ks3/ks3ms21/other_resource/or(2012)_circle_area.pdf

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