Variety of perimeters with fixed area: Difference between revisions
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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" /> | ||
<br /> | |||
== Guidance notes == | |||
<br /> | |||
'''1) Overview''' | |||
<br /> | |||
After learning the concepts of perimeters and areas, it is easy for students to think that figures with larger perimeters would also have larger areas, and vice versa. This applet helps teachers to explore with students the variety of the perimeters of a figure formed by several congruent squares touching side by side. Together with the complementary applet "28888 Variety of Areas with Fixed Perimeter", teachers can clarify with students that a figure with a larger area may have a smaller perimeter, and areas and perimeters are two different concepts. | |||
<br /> | |||
'''2) Learning Objective''' | |||
<br /> | |||
* Recognize figures with same areas could have different perimeters. | |||
* Recognize the strategy of minimizing the perimeters of figures with the same areas. | |||
<br /> | |||
'''3) Teaching Approach''' | |||
<br /> | |||
An inquiry teaching approach is expected. Students are asked to arrange 3 to 9 squares to form different figures and find their possible perimeters. Teacher then guide students to express their strategies of getting the largest and smallest perimeter with a certain number of squares. | |||
<br /> | |||
'''4) Teacher’s Note''' | |||
<br /> | |||
For each number of squares, ask students to record the possible perimeters in the table of the applet; | |||
Guide students to focus on the change of the perimeter when a square is dragged to a new position; | |||
Discuss with students the strategy of minimizing the perimeter, especially for 4 and 9 squares. | |||
Revision as of 16:37, 27 March 2013
Guidance notes
1) Overview
After learning the concepts of perimeters and areas, it is easy for students to think that figures with larger perimeters would also have larger areas, and vice versa. This applet helps teachers to explore with students the variety of the perimeters of a figure formed by several congruent squares touching side by side. Together with the complementary applet "28888 Variety of Areas with Fixed Perimeter", teachers can clarify with students that a figure with a larger area may have a smaller perimeter, and areas and perimeters are two different concepts.
2) Learning Objective
- Recognize figures with same areas could have different perimeters.
- Recognize the strategy of minimizing the perimeters of figures with the same areas.
3) Teaching Approach
An inquiry teaching approach is expected. Students are asked to arrange 3 to 9 squares to form different figures and find their possible perimeters. Teacher then guide students to express their strategies of getting the largest and smallest perimeter with a certain number of squares.
4) Teacher’s Note
For each number of squares, ask students to record the possible perimeters in the table of the applet; Guide students to focus on the change of the perimeter when a square is dragged to a new position; Discuss with students the strategy of minimizing the perimeter, especially for 4 and 9 squares.
