Mathematical skills  Straight Lines and Simultaneous Equations Sheffield University

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The material will cover topics and content which could be presented anywhere from GCSE level up to and including mathematics transition into 1st year University engineering. The difference between these resources and other resources available on the internet is the focus on understanding how the mathematics works using simple human intuition; the hope is that this will make it more accessible to students struggling to 'memorise' techniques while not understanding why they work.
These videos give an introduction to straight lines. Where do they come from and, for example, what does the formulation y=mx+c represent? Having understood what a straight line represents, the videos move onto concepts of simultaneous equations, that is, when two straight lines meet. The videos begin by giving simple everyday examples of scenarios where straight lines occur and where the intersection is meaningful. Finally, the videos introduce simple techniques for solving for the intersection points, again focussing on commonsense approaches rather than abstract concepts.

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Simultaneous equations 1  what is a straight line
Lectures aimed at giving an introduction to the definitions and meanings of simple block diagrams and easy to understand methods for computing relationships between loop inputs and outputs. Lecture 1 focuses on what is a transfer function?

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Simultaneous equations 2  equation of a straight line in everyday terms
Introduces the concept of straight lines using everyday scenarios which are easy to relate to. Introduces concepts of gradient and intercept with the vertical axis, again in terms of everyday scenarios.

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Simultaneous equations 3  algebraic formulae for a straight line
Develops video 2 by introducing the concept of 'abstract' variables to represent the terms in a straight line and hence the general equation form of 'y=mx+c'.

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Simultaneous equations 4  intercepts of straight lines
Use a number of everyday scenarios to explain the meaning and importance of simultaneous equations and the intercept point.

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Simultaneous equations 5  simple solution method
Gives a simple everyday interpretation of simultaneous equations from which the video demonstrates a solution method which is simple and intuitive with minimal reliance on abstract mathematics.

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Simultaneous equations 6  tutorial sheet
Gives a number of worked examples of solving simultaneous equations. Students can pause the video and try the examples themselves before watching the solutions.