Introduction These are discussion notes on how graphs are utilized in Mathematics and Technology. They are meant for Grade 11 learners who have basic knowledge of three main types of graphs namely: bar, pie and line graphs. The first section introduces students to the concept of graphs and its general applications. The second part discusses the types of graphs, their distinct features and use. The objective of this discussion is to provide learners with foundation knowledge and understanding of graphs and their application in Mathematic and Sciences.Introduction to Graphs Graphs are visual diagrams that are used to present data and information in a manner that is easy to understand, compare and establish the trends. Without graphs, it is very difficult to make sense of information with many data sets. Graphs are widely used in Mathematics and Sciences to study the relationship among variables and solve equations. For instance, the relationship between volume and temperature can be established by conducting an experiment and plotting a graph of temperature against volume based on the results got from the experiment. This will give a straight line graph which meets the horizontal axis at a point referred to as absolute temperature. The straightness of the graph shows that temperature and volume have a linear positive relationship. Meaning that increase in temperature causes an increase in volume. So from this graph students can determine absolute temperature and establish how these two physical quantities relate. Experiment only produces data and the graphs enable the experimenter to interpret the results.
Types of graphsBar graph
This is one of the most used graphs. It consists of rectangular bars of different lengths arranged either vertically or horizontally. The length of each bar is proportional to the value of the variable being presented. The value, amount, or the frequency of a variable is displayed on the vertical axis. Bar graphs are used to develop frequency curves in Mathematics. Frequency curves, on the other hand, are used to determine percentiles. For instance, a teacher may use frequency curve determine the upper quartile score in English. Upper quartile score is the 75th score in the distribution.Line Graphs This type of graph is usually used to show the changes in values of quantity with respect to changes in values of another quantity. In Mathematics, the quantities or the variable are often represented in terms of x and y. The independent variable is displayed on the horizontal axis while the dependent variable is plotted on the vertical axis. The independent variable is the quantity that is being manipulated while the dependent variable is the quantity that changes. This type of graph is used to solve quadratic equations in Mathematics. The x and y values of the equation are plotted and a smooth curve that joins the points drawn. The x values at the points where the curve meets the horizontal axis give the solution of the equation. Line graph is also used to show trends. For instance, a graph of voltage against current in Technology depict that voltage supplied is directly proportional to current produced in metallic substances.Pie Graphs The horizontal and vertical axis are absent in this type of graph. For this reason, it can only be used in presentation of data and information from one variable. It consists of a circle subdivided into slices. The size of each slice is proportional to the value it represents. This graph is used to teach the concepts of fraction in Mathematics.
