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Grade Level: 6-8
Introduction:
Students are introduced to the math concept of function as early as
sixth grade. By the end of the first year in algebra, the concept is
more thoroughly formalized. A full understanding will make advanced
high school math and science less stressful and more meaningful. It
will even lend a richer meaning to the social sciences and language
arts for functions are basically about relationships and
connections.
Objective:
Students will explore the concept of functions as relationships, as
machines, as equations, and as graphs.
Prior Knowledge:
A good understanding of the arithmetical operations, some knowledge
of equations and graphing in the coordinate plane are desirable but
not necessary.
Resources:
At minimum students should have worksheets, graph paper, and pencil.
This lesson can be enriched with a computer spreadsheet or graphing
calculator.
Process, Evaluation, and Conclusion:
The students will follow the instructions on the worksheets and
complete them. Upon completion students should be able to define,
illustrate, and apply the concept of function orally and in writing.
Though the students should be authentically assessed, a suggested
evaluation is included.
Index:
Worksheet 1: Functions as Relationships (HTML) or (PDF)
Students will complete a worksheet recognizing cause and effect relationships.
Worksheet 2: Functions as Machines (HTML) or (PDF)
Students will investigate how inputs are transformed by machines to outputs.
Worksheet 3: Functions as Equations (HTML) or (PDF)
Students will investigate how relationships can be quantified.
The Function Machine
Interactive function machine.
Machine Worksheet (HTML) or (PDF)
A worksheet to accompany the function machine.
Functions as Graphs
Graphic presentation of the same relationships.
Functions as Graphs Worksheet (HTML) or (PDF)
A worksheet to reinforce functions expressed graphically.
Finding the Function (Equation or Rule)
Given the graph or data, students are asked to express the function (rule).
TI-82 Regression
Step-by-step directions to use the TI-82 graphing calculator to express the function (rule).
California Academic Content Standards:
Grade 8-12:
Algebra I
1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable
4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12
5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification of each step
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4)
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions
17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion