MA5.2-8NA Equations | Mathematics Stage 5.1/5.2 Year 9 2014 Summary of Sub Strands Duration: 3.5 weeks S4 Equations Start Date: Completion Date Teacher and Class: Unit overview Outcomes Big Ideas/Guiding Questions Throughout this unit of work students will revisit solution of linear equations as covered in stage 4. They will investigate more complex equations and the solutions to inequalities. They will substitute into equations and convert word problems into equations to solve. They will solve quadratic equations of the form x2 + bx + c =0 and solve simultaneous linear equations both graphically and using algebraic techniques MA5.21WM selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.22WM interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems MA5.23WM constructs arguments to prove and justify results MA5.28NA solves linear and simple quadratic equations, linear inequalities and linear simultaneous equations, using analytical and graphical techniques Key Words linear equation, solve, pronumerals, backtrack, balance, guess, check , improve, solve, expand, , reverse, inverse, solution, variable, opposite, unknown, substitute, quadratic equation, expression, operation, number plane, number line, elimination, substitution, quadratic equation, coefficient, parabola, subject, inequation, inequality
Reg Content Teaching, learning and assessment Resources At the end of this unit the student should be able to: Stage 5.2 - Equations Students: Solve linear equations (ACMNA215) solve linear equations, including equations that involve grouping symbols, eg Solve linear equations involving simple algebraic fractions (ACMNA240) solve linear equations involving one or more simple algebraic fractions, eg compare and contrast different algebraic techniques for solving linear equations and justify a choice for a particular case (Communicating, Reasoning) Substitute values into formulas to determine an unknown (ACMNA234) solve equations arising from substitution into formulas, eg given and , , solve for substitute into formulas from other strands of the syllabus or from other subjects to solve problems and interpret solutions, eg (Problem General Note: Students must be encouraged as a matter of routine to always check their solutions by substitution First two dot points are revision and extension of Stage 4 content, so review processes of backtracking, balancing etc. Before extending into harder examples. The concept of lowest common multiple will need to be revisited to solve algebraic equations involving fractions. Also discuss if you cannot find the LCM just multiple the denominators of the fraction, stressing that you will need to look at simplifying your answer. Also it is important to stress that if there is more than one term in the numerator, grouping symbol need to be inserted to ensure the correct sign of coefficient is obtained when multiplying by the LCM. Adjustments Lower ability students will need fractional equations to have smaller denominators, as their table skills may be poor and they may experience difficulty finding the LCM of larger numbers. To extend students graph y equal to the equation and solve the equation graphically. Graphing software Geogebra, sketchpad and quickgraph can assist students to graph. Resources as outlined in Stage 4 Simple Equations may be used as a revision tool Interactive solving equations - in a game form