Quadratics, #2-Data Tables
Part of Curriculum Unit:The Quadratic Function, an Introduction
Abstract help
Students will examine data tables that mix data that is linear, quadratic or neither of these and try to identify the function family respresented by the data.
Students should work with at least one other person to encourage discussion.
Directions to students should include:
a. Identify the tables as data representing linear or quadratic or neither.
b. For linear functions, students should write the appropriate rule.
c. For other functions, students should defend their conclusions with their observations about quadratic outputs from Lesson One. They may be encouraged but not required to attempt to find a function rule.
This is an opportunity for students to:
1. Consider data patterns and relate them to observations about the graph.
2. Review finding the rule for linear data.
3. Enlarge their observations about quadratic function behavior.
Students should work with at least one other person to encourage discussion.
Directions to students should include:
a. Identify the tables as data representing linear or quadratic or neither.
b. For linear functions, students should write the appropriate rule.
c. For other functions, students should defend their conclusions with their observations about quadratic outputs from Lesson One. They may be encouraged but not required to attempt to find a function rule.
This is an opportunity for students to:
1. Consider data patterns and relate them to observations about the graph.
2. Review finding the rule for linear data.
3. Enlarge their observations about quadratic function behavior.
National Standards help
Understanding patterns and functional relationships
By building on the patterns observed in the graphs.
Understand how mathematical ideas build on one another to produce a coherent whole.
By relating characteristics of data and appearance of the graphs.
Recognize and use connections among different mathematical ideas
By relating graphs and tables and function rules.
By building on the patterns observed in the graphs.
Understand how mathematical ideas build on one another to produce a coherent whole.
By relating characteristics of data and appearance of the graphs.
Recognize and use connections among different mathematical ideas
By relating graphs and tables and function rules.
Pre-requisite Skills help
Students should have completed Lesson One or equivalent in order to have experience with the quadratic characteristic of increasing and then decreasing or decreasing and then increasing outputs.
Students should be comfortable with function notation.
Students should be comfortable with function notation.
Teacher Information help
Graph paper might be made available so that students could plot and observe the graph as they make their decision.
If the technology is available to enter the points and test with a curve fit utility, it might be an option - however, since general characteristics are the goal here and linear rules have previously been studied, the curve fit might be more appropriate as a check on conclusions especially if an attempt was made to find the quadratic rules.
A full class discussion or reports from students would be appropriate as a concluding activity.
If the technology is available to enter the points and test with a curve fit utility, it might be an option - however, since general characteristics are the goal here and linear rules have previously been studied, the curve fit might be more appropriate as a check on conclusions especially if an attempt was made to find the quadratic rules.
A full class discussion or reports from students would be appropriate as a concluding activity.
Student Activity help
Tables available on Web page
Assessment help
Assessment here should be informal observation and questioning as the activity evolves.
Observation of participation in whole group discussion which accumulates conclusions and reasoning.
Observation of participation in whole group discussion which accumulates conclusions and reasoning.
Technology Requirements/Integration help
None is necessary unless teacher uses optional grapher or curve fitting tool.