Understand the difference(s) between equations and inequalities Solve linear inequalities and construct inequalities from word problems Solve simultaneous equations in two variables using a variety of strategies Model and find solutions to real life problems by contructing and graphing linear inequalities
Conceptual Framework
relationships systems, equivalence, simplification in the context of Scientific and Technical Innovation
Statements of Inquiry
Relationships between two variables can be expressed as an equation or an inequality, that in turn can help solve complex problems
Factual
How can we solve systems of equations with two variables?
How can we represent an inequality on the coordinate plane?
How can we use the graphical representation of inequalities to find the best solution(s)?
Conceptual
Why is it helpful to represent equations or inequalities graphically?
How are equations different from inequalities?
Debatable
How do we choose the best solution in the feasible region?
Description
This unit will explore situations in which there are multiple relationships between two variables. The relationship between two variables is often linear. These relationships can be expressed as systems of linear equations or inequalities. By the end of the Unit the students will be able to determine the constraints of a given problem, derive inequalities from these and then use technology to represent them graphically. Technical innovations allows us to graph these systems of inequalities easily. From the graphical representation they will then be able to find the feasible region, if one exists, and be able to answer questions on optimisation. However, before exploring inequalities the students will review how to solve simultaneous linear equations and how to plot linear graphs. The treatment of linear inequalities is very similar, thus this review acts as a perfect scaffold. The act of finding the optimum solution from the feasible region between linear inequalities is known as linear programming.
Learning Outcomes
Review solving linear equations and inequalities in one variable
Solve pairs of linear equations simultaneously - using substitution, elimination, equating expressions and graphing calculators
Solve systems of linear inequalities graphically in two variables