Graphical Solutions to Problems in Context
Students are required to use a variety of graphs to approximate solutions to contextual problems. Students should be familiar with a variety of functions such as distance–time graphs, exponential and reciprocal graphs. This resource package provides a number of suggestions and activities designed to provide students with the opportunity to develop and practise these skills.
Visit the secondary mathematics webpage to access all lists.
Interpreting Distance-Time Graphs with a Computer A5
To begin with, download the program 'Traffic' and ensure that the program will run on your system. The program models a number of different situations in which a car, or a number of cars, travel along a stretch of road. When the program pauses, this is an opportunity for students to discuss what they have seen. Continuing with the computer program, the position of the car at different stages of the journey is plotted and then a distance-time graph is drawn. The options section allows the program to be adapted so that, for example, students only see the graph which then has to be interpreted. There is also the option to consider velocity-time graphs. This resource provides a good introduction to travel graphs with plenty of opportunity for discussion.
Interpreting Distance – Time Graphs A6 *suitable for home teaching*
This resource provides an ideal follow-up activity. Students explore a variety of distance-time graphs, some where the object has constant speed, others in which the object is accelerating. Students are required to match a description of the action with a distance-time graph, a table of values and a description of speeds and accelerations and decelerations. The activity sheet entitled The race requires students to interpret a graph of a car race.
Mobile Phones
In this activity students are given two mobile phone tariffs and are required to explore in what circumstances one tariff is preferable to the other. Students should be required to plan how they are to tackle the task before they embark on it.
Feeding back how they are going to approach the task is an important part of this task. At this point, any group who have not suggested they represent the situation using a graph would require intervention. The progression table allows constructive feedback to be given under the headings of representing, analysing, interpreting and evaluating and communicating and reflecting. Examples of student responses are ideal for moderation purposes before students embark upon the task.
Using Graphs
Pack one of this resource contains a number of activities requiring students to interpret graphs. Old oak requires students to answer questions relating to the growth of an oak tree, Graphs asks students to use the graph to covert between degrees Celsius and degree Fahrenheit, and the activity Helicopter photographs makes an excellent follow up to the first activity in this list as it asks students to consider photographs of cars travelling along a stretch of road and predict what will happen as the cars travel at different speeds. The activity Overtaking requires students to analyse the motion of two cars travelling towards each other.
Pack two contains further distance-time and velocity-time related activities. There are also activities requiring students to interpret graphs produced from different contexts, although few of these activities require students to read off values from the graphs.
Graphs
The resource Real-life graphs contains a number of ideas useful as starter questions, extension questions or as probing questions to test understanding. Suggestions include explaining the differences between different distance-time graphs, exploring what the graphs would look like as two people run around a running track, comparing graphs of height against volume as liquid is poured into differently shaped containers and explore how the ‘suvat’ equations, met in science, relate to velocity-time graphs.
Max Box
This Virtual Textbook resource is an interactive excel program which provides dynamic drawings and graphs related to the classic maximum volume of a box problem. There are two versions of the problem, one starting with a square base and the other with a rectangular base.
Each interactive sheet shows the height, width and length of the box as the height changes. In addition to the dynamic drawings the program shows a graph of the volume of the box against the height. Tangents can be shown on the graphs so that the student can see approximately where the maximum point is.
