Sharp EL-531RH Teachers Manual page 53

Factorizing Quadratics
Use the calculator in the same way to find similar equations for the expressions below.
2 + 7x + 10
x
2 + 7x + 12
x
2
x + 6x + 8
2 + 10x + 16
x
2
x + x - 6
2 + 5x + 14
x
• • • • • • • • • • • Using the activity in the classroom • • • • • • • • • • •
It is assumed that students will have done some work on quadratic functions prior to this activity.
For example, students may have been attempting to solve a range of quadratic equations given in a
variety of forms. Some of these equations could possibly be solved via inverse relationships, (e.g.
2 - 4 = 15), while some may be already given in factorized form and so could be solved directly.
x
Others may have to be solved by trial and improvement. This could lead to students concluding
that factorizing is a useful technique in solving quadratic equations.
The activity could then be introduced as an investigation into factorizing quadratic expressions.
The teacher could do an example on the board, and then other expressions could be given
to the students to factorize, using trial-and-improvement methods on their calculator.
It is important that students are encouraged to reflect on the factorized expressions and look
for strategies to help them factorize quadratics. These strategies should be collated together
and discussed.
• • • • • • • • • • • • • • • Points for students to discuss • • • • • • • • • • • • • •
It may be useful to go over with some students how to enter and evaluate algebraic expressions
on the calculator.
Further Ideas
The idea can be adapted to focus on the equivalence of other algebraic expressions, including
factorizing linear expressions such as 4x + 6.
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High school