Interpreting Information Presented on a Graph:
Subject : Mathematics
Class : JSS 2
Term : Second Term
Week : Week 11
Topic :
Graphs
- Interpreting Information
Presented on a Graph:
Gradient;
Vertical and Horizontal Lines;
Intercepts with Axes - Description of Continuous and
Discontinuous Graphs - Linear Graphs in Real Life
Situations:
Distance-Time Graph;
Travel Graph;
Conversion Graph;
Velocity-Time Graph
Previous Lesson :
Objective: Students will be able to interpret and analyze linear graphs in real-life situations.
Materials Needed:
- Whiteboard and markers
- Handout with examples of linear graphs
- Calculators
Content :
Interpreting Information
Presented on a Graph:
Gradient;
Vertical and Horizontal Lines;
Intercepts with Axes
Interpreting information presented on a graph can be a fun and useful skill to have. Here are some key concepts to help you understand what graphs can tell us:
- Gradient: The gradient of a line on a graph tells us how steep the line is. If a line has a positive gradient, it means it’s going up from left to right. If it has a negative gradient, it means it’s going down from left to right. For example, in the graph below, the red line has a positive gradient because it goes up from left to right, while the blue line has a negative gradient because it goes down from left to right.
- Vertical and Horizontal Lines: A vertical line on a graph goes straight up and down, while a horizontal line goes straight across from left to right. For example, in the graph below, the red line is vertical because it goes straight up and down, while the blue line is horizontal because it goes straight across from left to right.
- Intercepts with Axes: The intercepts of a line on a graph are where it crosses the x-axis (the horizontal line) and the y-axis (the vertical line). For example, in the graph below, the red line intercepts the x-axis at x = 2 and the y-axis at y = 3, while the blue line intercepts the x-axis at x = -1 and the y-axis at y = 1.
By understanding these key concepts, you can start to make sense of the information presented on graphs and use it to answer questions and solve problems
Description of Continuous and
Discontinuous Graphs
Graphs can be classified into two types: continuous and discontinuous. Here’s an explanation of both types with some examples:
- Continuous Graphs: A continuous graph is a graph in which the points are connected with a line, and there are no gaps or interruptions in the line. For example, the graph of a line y = 2x + 1 is a continuous graph because it is a straight line with no gaps or jumps.
Another example of a continuous graph is the graph of a sine wave. A sine wave is a smooth, curving line that repeats itself over and over again. The graph of a sine wave is continuous because there are no gaps or jumps in the line.
- Discontinuous Graphs: A discontinuous graph is a graph in which the points are not connected with a line, and there are gaps or interruptions in the line. For example, the graph of the function y = 1/x is a discontinuous graph because it has a vertical asymptote (a point where the function goes to infinity) at x = 0. At this point, the function is undefined, so there is a gap in the graph.
Another example of a discontinuous graph is a step function. A step function is a function that jumps from one value to another at certain points. The graph of a step function is discontinuous because there are gaps or jumps in the line.
Understanding the difference between continuous and discontinuous graphs can help us better interpret and analyze data presented in graphs
Linear graphs can be used to represent various real-life situations. Here are some examples of linear graphs and their corresponding real-life situations:
Distance-Time Graph: A distance-time graph shows the distance traveled by an object over a period of time. For example, the graph below shows the distance traveled by a car over 5 hours. The line on the graph is straight, which means that the car is traveling at a constant speed.
Distance-Time Graph Example
Travel Graph: A travel graph shows the distance traveled by a person or vehicle during a journey. For example, the graph below shows the distance traveled by a cyclist during a 20-kilometer ride. The line on the graph is straight, which means that the cyclist is traveling at a constant speed.
Travel Graph Example
Conversion Graph: A conversion graph shows how one measurement unit can be converted to another. For example, the graph below shows the conversion from Celsius to Fahrenheit. The line on the graph is straight, which means that the relationship between the two temperature scales is linear.
Conversion Graph Example
Velocity-Time Graph: A velocity-time graph shows the velocity (speed and direction) of an object over time. For example, the graph below shows the velocity of a car during a 10-second period. The line on the graph is straight, which means that the car is moving at a constant velocity.
Velocity-Time Graph Example
Understanding linear graphs in real-life situations can help us interpret and analyze data, make predictions, and solve problems
Linear graphs can be used to represent various real-life situations. Here are some examples of linear graphs and their corresponding real-life situations:
- Distance-Time Graph: A distance-time graph shows the distance traveled by an object over a period of time. For example, the graph below shows the distance traveled by a car over 5 hours. The line on the graph is straight, which means that the car is traveling at a constant speed.
- Travel Graph: A travel graph shows the distance traveled by a person or vehicle during a journey. For example, the graph below shows the distance traveled by a cyclist during a 20-kilometer ride. The line on the graph is straight, which means that the cyclist is traveling at a constant speed.
- Conversion Graph: A conversion graph shows how one measurement unit can be converted to another. For example, the graph below shows the conversion from Celsius to Fahrenheit. The line on the graph is straight, which means that the relationship between the two temperature scales is linear.
- Velocity-Time Graph: A velocity-time graph shows the velocity (speed and direction) of an object over time. For example, the graph below shows the velocity of a car during a 10-second period. The line on the graph is straight, which means that the car is moving at a constant velocity.
Understanding linear graphs in real-life situations can help us interpret and analyze data, make predictions, and solve problems
Evaluation
- What is a continuous graph? A) A graph with gaps or interruptions B) A graph with a smooth line that has no gaps or interruptions C) A graph with a line that jumps from one point to another D) A graph that cannot be plotted on a coordinate plane
- What does the gradient of a line on a graph represent? A) The steepness of the line B) The distance between two points on the line C) The area underneath the line D) The slope of the line at a given point
- What is a travel graph used to represent? A) The distance traveled by an object over a period of time B) The temperature of a room over a period of time C) The number of people in a room over a period of time D) The amount of money earned over a period of time
- What does the intercept of a line on a graph represent? A) The point where the line intersects the x-axis B) The point where the line intersects the y-axis C) The point where the line intersects another line D) The point where the line changes direction
- What is a velocity-time graph used to represent? A) The distance traveled by an object over a period of time B) The temperature of a room over a period of time C) The speed and direction of an object over a period of time D) The number of people in a room over a period of time
- What is a step function? A) A function that jumps from one value to another at certain points B) A function that is continuous and smooth C) A function that is always increasing D) A function that is always decreasing
- What is a conversion graph used to represent? A) How one measurement unit can be converted to another B) The relationship between two different graphs C) The intersection of two lines on a graph D) The rate of change of a variable over time
- What does the gradient of a vertical line on a graph equal to? A) Zero B) Undefined C) One D) Negative one
- What is a discontinuous graph? A) A graph with a smooth line that has no gaps or interruptions B) A graph with a line that jumps from one point to another C) A graph with gaps or interruptions in the line D) A graph that cannot be plotted on a coordinate plane
- What does the gradient of a horizontal line on a graph equal to? A) Zero B) Undefined C) One D) Negative one
Lesson Presentation
Introduction (10 minutes):
- Begin by asking students if they know what a graph is and how it can be used.
- Explain that a graph is a visual representation of data and that it can be used to analyze and interpret information.
- Introduce the topic of linear graphs and explain that they are graphs that have a straight line.
Body (25 minutes):
- Provide examples of linear graphs and explain how they can be used to represent real-life situations.
- Demonstrate how to calculate the gradient of a line on a graph and explain what it represents.
- Provide examples of continuous and discontinuous graphs and explain the difference between them.
- Demonstrate how to calculate the intercepts of a line on a graph and explain what they represent.
- Provide examples of velocity-time graphs, distance-time graphs, travel graphs, and conversion graphs, and explain how they can be used to represent different types of data.
Activity (10 minutes):
- Hand out a worksheet with examples of linear graphs and ask students to identify the gradient, intercepts, and real-life situation it represents.
- Circulate the classroom and provide assistance as needed.
Conclusion (5 minutes):
- Review the key concepts covered in the lesson.
- Ask students to summarize what they have learned.
- Encourage students to practice interpreting and analyzing graphs on their own.
Assessment:
- Assess student understanding through class participation and completion of the worksheet activity.
- Provide feedback to students on their progress and address any areas of confusion.
Extensions:
- Encourage students to create their own linear graphs to represent real-life situations.
- Have students research and present on different types of graphs and their uses
Weekly Assessment /Test
- A ________ graph is a graph in which the points are connected with a line and there are no gaps or interruptions in the line.
- The gradient of a line on a graph tells us how ________ the line is.
- A ________ graph shows the distance traveled by an object over a period of time.
- The intercepts of a line on a graph are where it crosses the ________ and the ________.
- A ________ function is a function that jumps from one value to another at certain points.
- A ________ graph shows how one measurement unit can be converted to another.
- A vertical line on a graph goes straight up and down and has a gradient of ________.
- A ________ graph shows the velocity of an object over time.
- A ________ graph is a graph in which the points are not connected with a line and there are gaps or interruptions in the line.
- The gradient of a horizontal line on a graph is ________.