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# Topic 5 Year 9 Mathematics

 Mathematics Topic Solving graphically No of lessons 8 When is it happening Term 1 What will students learn Understand coordinates as solutions to linear equations, including intersections as simultaneous solutions. Be able to solve simultaneous linear equations graphically . Experience visualising trends in and intersections of linear equations.                  Understand parallel lines have no solution as they do not intersect. Be able to identify whether a pair of simultaneous equations have a  solution algebraically and graphically.  Experience connecting graphical and algebraic representations of linear relationships. 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 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 continue to practice solving linear simultaneous equations. The rearranging practice in Week 1 is used to help organise and simplify the calculations. Students look at a new representation for simultaneous equations – Venn diagrams. Focus is drawn on the Students look at substitution between equations as a means reducing the number of variables. relationship between the intersection of the Venn and the algebraic solution. Students solve simultaneous equations through substitution to remove a variable. Two methods are looked at but rearranging is not necessary. 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 Angles are revisited and defined as a measure of turn. Rays are used to emphasise the irrelevance of the length of the ‘sides’ to the size of the angle. Formal notation and congruence are introduced. 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 Finding the roots of an equation This is skills that students may have met before but will need to develop Reading graphs Key vocabulary that students should know and understand The Big Question Can you solve simultaneous equations graphically? Key questions that students should be able to answer at the end of the 'Topic' Can you understand how linear equations are represented graphically? Can you find solutions (coordinates) for linear equations arranged in various ways? Can you estimate or find solutions to simultaneous linear equations from graphs? Can you visualise linear relationships? Can you identify the intersections of a pair of lines on a graph? Can you identify whether a pair of lines are parallel from their equations? Can you find solutions to simultaneous inequalities graphically? Can you identify from a graph whether a pair of simultaneous equations have 0, 1 or multiple solutions?