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# Topic 4 Year 9 Mathematics

 Mathematics Topic Solving Linear simultaneous equations algebraically No of lessons 12 When is it happening Term 1 What will students learn Be able to solve and manipulate linear equations with one or more variables, Understand that addition and subtraction of simultaneous equations can result in the elimination of a variable, Understand how substitution can be used to manipulate algebra Be able to reduce the number of variables in an equation through substitution Experience varying representations of algebra to seek opportunities to substitute Experience pattern spotting and conjecturing to establish formal methods for eliminating variables Be able to use equivalent equations – through scaling and rearranging – to solve simultaneous equations Understand how equivalence can be maintained while scaling and rearranging equations Understand how variables and unknowns interact within a system of equations Key Knowledge that students should know at the end of 'Topic' This is the knowledge that students will meet for the first time in this topic Students look at equivalent equations, a forming equivalent equations through two main methods: (i) rearranging, and (ii) scaling. Students begin using one equation to solve another. Students make deductions from two equations within the same system of equations by addition and subtraction. Students look at cases in which addition and subtraction of linear equations with 2 variables results in the elimination of a variable. Students investigate how scaling can help to force a matching absolute coefficient, and use this to solve simultaneous equations through elimination of a variable. Students look at a new representation for simultaneous equations – Venn diagrams. Focus is drawn on the relationship between the intersection of the Venn and the algebraic solution. Students look at substitution between equations Students solve simultaneous equations through substitution to remove a variable. Rearranging before substituting, or rearranging allow simpler substitution is looked at as a specific focus. Students consider when equations hide within each other and how substitution can be used more flexibly. This is knowledge that students may have met before but will need to deepen their understanding Students look at models for solving equations that they have seen in earlier units. Students can revisit and practice solving (mainly) linear equations. Key Skills that students should be able to demonstrate at the end of 'Topic' This is the skills  that students will meet for the first time in this topic To solve linear one step and two step equations This is skills that students may have met before but will need to develop algebra manipulation Key vocabulary that students should know and understand The Big Question Can you solve simultaneous equations using a variety of methods Key questions that students should be able to answer at the end of the 'Topic' Can you solve one and two step equations? Can you  identify pairs of equations that are equivalent? Can you use one equation to solve another equation within a system of equations (or solve simple ‘simultaneous equations? Can you deduce new equations by addition and subtraction of equations? Can you eliminate a variable to  make both variables solvable? Can you scale equations and force matching coefficients to solve simultaneous equations? Can you rearrange equations? Can you list many solutions to linear equations with 2 variables? Can you form equations by substituting? Can you solve simultaneous equations with 2 variables by substituting to reduce variables? Can you rearrange an equation to support substitution into another equation? Can you substitute entire expressions?