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OER4Schools/Collecting and interpreting information: Difference between revisions

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= Further Tasters of EBL: Investigating characteristics of polygons =  
= Further Tasters of EBL: Investigating characteristics of polygons =  


{{activity|stgw| on investigating characteristics of polygons|20 }}  Working in your small group of three to four participants, complete the following activity using GeoGebra.  In this activity, we will like you to experiment with drawing different polygons that you may not have seen before (i.e. be creative!). Draw 10 different shaped polygons using GeoGebra. As you draw, think about what is the same and what is different between those polygons, and how you could classify them into different groups.


You may like to refer to this YouTube clip if you are not certain about how to make use of GeoGebra:


{{: Video/Simple_Polygons_in_Geogebra.mp4 }}
{{activity|stgw| on investigating characteristics of polygons|20 }}


Take some time to look at the different polygons you have drawn and try to find similar characteristics in some or all of the polygons. Try to group these polygons together and classify them with some sort of descriptor. For instance, some of them may look symmetrical, some may look like regular polygons, or some may have right angles. Be prepared to discuss with your group participants how you have classified them. Share your findings with the other participants and share whether such an activity can be used in the class as a quick taster of what EBL is about.
Working in your small group of three to four participants, complete the following activity which uses GeoGebra. In this activity, we would like you to experiment with drawing rectangles with different numbers of squares.  


{{ednote|text=
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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="false" showMenuBar="false" showToolBar="false" showToolBarHelp="true" />
Try to encourage the participants to draw polygons of different shapes, and to really try to make them different. The polygons should not just be different sizes of the same shape. It is possible that some shapes may just look like the magnification or reduction of size of other shapes but hopefully, participants can draw shapes of different number of sides, length of sides and/or internal angles.


Note that while the instructions for the task are short, it will take some time to complete the task. Make sure you limit the time appropriately, so that there’s enough time for the remainder of the workshop. Decide whether or not to show the following video to illustrate the enquiry nature of this kind of problem-solving task:
<br />


{{: Video/Art_of_Problem_Solving_Classifying_Quadrilaterals.mp4 }}
You may like to refer to the following guidance notes for some ideas on how to make use of this GeoGebra resource:
== Guidance notes ==


You can also refer to this clip (already used in the last session):
<br />
{{: Video/12 13 Abel 2 4 rectangles 5-desktop.m4v }}
'''1) Overview'''
<br />
 
After learning the concepts of perimeter and area, 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 [[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 Objectives'''
<br />
 
*  Recognise that figures with the same areas could have different perimeters.
*  Recognise the strategy of minimizing the perimeters of figures with the same areas.
 
<br />
'''3) Teaching Approach'''
<br />
 
An enquiry 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.
 
 
Take some time to explore the applet. Share your findings with the other participants and share whether such an activity can be used in the class as a quick taster of what EBL is about.
 
{{ednote|text=
 
Note that while the instructions for the task are short, it will take some time to complete the task. Make sure you limit the time appropriately, so that there’s enough time for the remainder of the workshop.  


The following task may be used as an alternative if preferred or if there is no GeoGebra resource:  
The following task may be used as an alternative if preferred or if there is no GeoGebra resource:  
Retrieved from "https://oer.opendeved.net/wiki/Special:MobileDiff/18351"