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| # Is there any other way by which you can deduce the formula for area of a circle ? | | # Is there any other way by which you can deduce the formula for area of a circle ? |
| | | |
− | ===Activity No # === | + | ===Activity No # 2. Proving area of the circle = п r² using geogebra applet.=== |
| {| style="height:10px; float:right; align:center;" | | {| style="height:10px; float:right; align:center;" |
| |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> | | |<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"> |
| ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> | | ''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div> |
| |} | | |} |
− | *Estimated Time | + | *Estimated Time: 45mins |
− | *Materials/ Resources needed | + | *Materials/ Resources needed; |
− | *Prerequisites/Instructions, if any | + | Laptop, geogebra file, projector and a pointer. |
− | *Multimedia resources | + | *Prerequisites/Instructions, if any: |
| + | Prior knowledge of circle, radius, square and area of square. |
| + | *Multimedia resources: Laptop. |
| *Website interactives/ links/ / Geogebra Applets | | *Website interactives/ links/ / Geogebra Applets |
− | *Process/ Developmental Questions | + | *Process: |
− | *Evaluation | + | # Show the students the two figures circle and square. |
− | *Question Corner | + | # Tell them that the radius and side of square are of same measure as it would help us in deducing the formula for area of circle. |
| + | # Formulas are easy ways of calculating area . |
| + | # If formulas are not known then the entire area in question can be divided into small squares of 1 unit measure and can deduce the formula of the whiole. |
| + | # First the number of full squares is counted. |
| + | # Then two half squares would add up to 1 full square. |
| + | # Ignore less than quarter . Take 3/4 as full. |
| + | # Finally adding up the whole number would give us the full area of the figure in question. |
| + | # Divide area of circle with that of square and deduce formula for square with known formula for square. |
| + | *Developmental Questions: |
| + | # Which are these two figures? |
| + | # What inputs do you need to draw a circle ? And for a square ? |
| + | # What do you observe as constant in the two figures ? |
| + | # Do you think the size of both the figures are same ? |
| + | # How do we find it ? |
| + | # What is the formula to find the area of a square ? |
| + | # When we do not know the formula for area, how do we deduce it ? |
| + | # Count the number of squares in the entire area of circle ? |
| + | # How to add half and quarter squares ? |
| + | # Approximately how many total 1 unit squares cover the circle ? |
| + | # So, what is the area of the circle ? |
| + | # What are we trying to deduce (get) through this activity ? |
| + | # Fine lets try dividing the area of circle with area of square and observe the proceedings while we try to deduce the formula for area of circle. |
| + | *Evaluation; |
| + | # Has the student understood the concept of area. |
| + | # Was the student aligned with the assignment and was he able to follow the sequence of steps ? |
| + | # Is the student able to appreciate the analogy ? |
| + | *Question Corner; |
| + | # What is Pi ? |
| + | # What do you understand by area ? |
| + | # What is the formula to find the area of square and that of a circle ? |
| | | |
| = Hints for difficult problems = | | = Hints for difficult problems = |