==Estimated Time==15 Minutes

==Materials/ Resources needed==White papers

## Prerequisites/Instructions, if any

1. pupils know how to factorise trinomials and complete the square
2. pupils are familiar with the meaning of "square" and the concept of "perfect

square".

## 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:

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)

1. pupils should be encouraged to use their own informal methods before being

introduced to formal solution procedures.

1. 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.

1. out of this they will extract the notion of a quadratic equation, so as to distinguish it
2. 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
(setting up a table or proceeding with guess and improve).
*The pupils might set up tables from the original equations:
x 2 − 7x −6
6 − 12 −6
10 − 12 −6
x x(x − 3) 4x − 6
3 0 4

• 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.

• 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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