Ohio Resource Center
Lessons
Supply and Demand
Discipline
Mathematics
9, 10, 11
Professional Commentary

This activity focuses on having students create and solve systems of linear equations in real-world settings. By solving a system of two equations in two unknowns, students find the equilibrium point for supply and demand. Students should be familiar with finding linear equations from two points or from the slope and y-intercept. Graphing calculators are not necessary for this activity, but could be used to extend the ideas. Activity sheets, suggestions for assessment, and a lesson extension are included. This lesson plan originally appeared in the October 1991 issue of The Mathematics Teacher. (author/sw)

Common Core State Standards for Mathematics
High School - Algebra
Reasoning with Equations and Inequalities
Solve systems of equations
HSA-REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
C.
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
D.
Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
H.
Solve systems of linear equations involving two variables graphically and symbolically.
1.
Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.
7.
Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.
8.
Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.
10.
Solve 2 by 2 systems of linear equations graphically and by simple substitution.
11.
Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution.
2.
Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.
3.
Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
9.
Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
3.
Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height.
10.
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
11.
Solve real-world problems that can be modeled, using systems of linear equations and inequalities.
Mathematical Processes Standard
Benchmarks (8–10)
B.
Apply mathematical knowledge and skills routinely in other content areas and practical situations.
E.
Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.
F.
Use precise mathematical language and notations to represent problem situations and mathematical ideas.
Principles and Standards for School Mathematics
Algebra Standard
Understand patterns, relations, and functions
Expectations (9–12)
understand relations and functions and select, convert flexibly among, and use various representations for them;
Represent and analyze mathematical situations and structures using algebraic symbols
Expectations (9–12)
understand relations and functions and select, convert flexibly among, and use various representations for them;
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
Use mathematical models to represent and understand quantitative relationships
Expectations (6–8)
model and solve contextualized problems using various representations, such as graphs, tables, and equations.
Expectations (9–12)
understand relations and functions and select, convert flexibly among, and use various representations for them;
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
draw reasonable conclusions about a situation being modeled.
Connections Standard
Recognize and apply mathematics in contexts outside of mathematics
Representation Standard
Create and use representations to organize, record, and communicate mathematical ideas
Select, apply, and translate among mathematical representations to solve problems
Use representations to model and interpret physical, social, and mathematical phenomena