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Reading Graphs
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Abstract
This lesson is designed to introduce students to graphing functions and to reading simple functions from graphs. Many of the examples are motivated by a situation described by the graph.Objectives
Upon completion of this lesson, students will:
- have practiced plotting functions on the Cartesian coordinate plane
- seen several categories of functions, including lines and parabolas
- be able to read a graph, answering questions about the situation described by the graph
Standards Addressed:
Textbooks Aligned:
Student Prerequisites
- Arithmetic: Student must be able to:
- perform integer and fractional arithmetic
- plot points on the Cartesian coordinate system
- read the coordinates of a point from a graph
- Algebraic: Students must be able to:
- work with very simple algebraic expressions
- Technological: Students must be able to:
- perform basic mouse manipulations such as point, click and drag
- use a browser for experimenting with the activities
Teacher Preparation
Students will need: - Access to a browser
- Pencil and graph paper
- Copies of supplemental materials for the activities:
Key Terms
| concave up | A curve is "concave up" when it is a concave shape, meaning curved like the inside of a bowl, with the two ends of the curve pointing up |
| constant functions | Functions that stay the same no matter what the variable does are called constant functions |
| constants | In math, things that do not change: for example distance, volume, mass, are called constants. The things that do change are called variables |
| coordinate plane | A plane with a point selected as an origin, some length selected as a unit of distance, and two perpendicular lines that intersect at the origin, with positive and negative direction selected on each line. Traditionally, the lines are called x (drawn from left to right, with positive direction to the right of the origin) and y (drawn from bottom to top, with positive direction upward of the origin). Coordinates of a point are determined by the distance of this point from the lines, and the signs of the coordinates are determined by whether the point is in the positive or in the negative direction from the origin |
| coordinates | A unique ordered pair of numbers that identifies a point on the coordinate plane. The first number in the ordered pair identifies the position with regard to the x-axis while the second number identifies the position on the y-axis |
| function | A function f of a variable x is a rule that assigns to each number x in the function's domain a single number f(x). The word "single" in this definition is very important |
| graph | A visual representation of data that displays the relationship among variables, usually cast along x and y axes. |
| origin | In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero (0,0) |
| velocity | The rate of change of position over time is velocity, calculated by dividing distance by time |
Lesson Outline
This lesson assumes that the students are familiar with information from the Graphs and Functions lesson.These activities can be done individually or in teams of as many as four students. Teams work best for the story-telling activities. Allow for 2-3 hours of class time for the entire lesson if all portions are done in class.
- Focus and Review
Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:
- Can anyone give me an example of a function? Can anyone give me an example of an everyday situation that a function can be applied to?
- Objectives
Let the students know what it is they will be doing and learning today. Say something like this:
- Today, class, we are going to learn more about functions.
- We are going to use the computers to learn more about functions, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.
- Teacher Input
- Lead a discussion on gathering information from graphs.
- Lead a discussion on making new graphs from old ones: graphs involving distance, velocity, and acceleration.
- Guided Practice
- Have the students try to build graphs from several situations using graph paper.
- Independent Practice
- Have the students try to build formulas from several situations, and then graph them using Graph Sketcher.
- Closure
- You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.
Alternate Outlines
This lesson can be rearranged in several ways.
- Omit the discussion on distance, velocity and acceleration.
Suggested Follow-Up
After these discussions and activities, students will have more experience with functions and relationship between the English description, graphical and algebraic representations. The next lesson, Impossible Graphs, shows the students that not all graphs make sense in certain situations.
