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− | {{subst;Math-Activity}}
| + | __FORCETOC__ |
| + | =Activity -Situation that leads to Quadratic Equations= |
| + | |
| + | ==Estimated Time==15 Minutes |
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| + | ==Materials/ Resources needed==White papers |
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| + | ==Prerequisites/Instructions, if any== |
| + | #pupils know how to factorise trinomials and complete the square |
| + | #pupils are familiar with the meaning of "square" and the concept of "perfect |
| + | square". |
| + | |
| + | ==Multimedia resources== |
| + | ==Website interactives/ links/ simulations/ Geogebra Applets== |
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| + | [http://academic.sun.ac.za/mathed/malati/Files/Equity991.pdf '''more about quadratic equation'''] |
| + | |
| + | ==Process (How to do the activity)== |
| + | '''A gardener wants his garden to have an interesting geometrical appearance.''' |
| + | He decides on the following rules for building the flowerbeds |
| + | They must all be rectangular. |
| + | The perimeter and the area must be the same. |
| + | 1. How many different flowerbeds can the gardener make if one of the sides is |
| + | 3 units less than the other side as shown in the diagram below: |
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| + | 2. How many different flowerbeds can the gardener make if both sides are the same |
| + | length, as shown in the diagram below: |
| + | |
| + | ==Developmental Questions (What discussion questions)== |
| + | |
| + | #pupils should be encouraged to use their own informal methods before being |
| + | introduced to formal solution procedures. |
| + | #revisit the concept (meaning) of the solution of an equation. The number |
| + | of solutions of an equation (no solution; 1 solution, 2 solutions or many solutions) |
| + | will be dripped. |
| + | #out of this they will extract the notion of a quadratic equation, so as to distinguish it |
| + | #finally, we will reflect on the solution procedures. |
| + | |
| + | ==Evaluation (Questions for assessment of the child)== |
| + | *pupils will probably have no other method available but to solve these |
| + | equations using numerical methods<br> (setting up a table or proceeding with guess and |
| + | improve). <br>*The pupils might set up tables from the original equations:<br> |
| + | x 2 − 7x −6<br> |
| + | 6 − 12 −6<br> |
| + | 10 − 12 −6<br> |
| + | x x(x − 3) 4x − 6<br> |
| + | 3 0 4 <br> |
| + | *The pupils need to be encouraged to move through the numbers to find the solutions |
| + | and to make sense of the solution in the context of the problem.<br> |
| + | *It also needs to be made explicit here that we are now dealing with an equation that |
| + | involves a term with an unknown of the second degree. |
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| + | Image:http://upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Regular_polygon_4_annotated.svg/220px-Regular_polygon_4_annotated.svg.png |
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| + | ==Question Corner== |
| + | ==Activity Keywords== |
| + | |
| + | [[Category:Quadratic Equations]] |