Illuminations: Supply and Demand

# Supply and Demand

 In this grades 9–12 activity, students write and solve a system of linear equations in a real-world setting. Students should be familiar with finding linear equations from 2 points or from the slope and y-intercept. Graphing calculators are not necessary for this activity, but could be used to extend the ideas found on the second activity sheet. Parts of this lesson plan were adapted from the October 1991 edition of Mathematics Teacher.

### Learning Objectives

 By the end of this lesson, students will: Explain factors that affect supply and demand Find linear equations for given sets of supply and demand data Find the equilibrium point for a system of supply and demand equations Translate between table, graph, and equation representations for supply and demand data

### Materials

 Class Fundraiser Activity Sheet Game Cartridges and Silver Dollars Activity Sheet Straightedge for drawing lines Transparency of Activity Sheet 1 (optional)

### Questions for Students

 Explain the different ways the data from each problem can be represented. Which representation do you prefer? Why? Which representation is best for getting accurate values? Explain why. Which representation is best for seeing the trends of the data? Explain why. Explain how it is possible to look at 3 categories of data on a 2 dimensional graph.

### Assessment Options

 Provide additional questions involving systems of equation questions. Ask student groups to develop their own scenarios for a system of equations. You can provide the equations, or ask the groups to find their own. Have students propose an item for sale. Survey students to see how many would purchase the item if it were offered at several prices and then use the data to determine the best price and the number of items that should be made.

### Extensions

 Introduce students to systems of inequalities Have students work with systems of equations with 3 variables and 3 unknowns Show students how to use a calculator as a tool to solve the system

### Teacher Reflection

 Which method(s) did students prefer? How well were students able to communicate the “why” for their preference? Would it suffice for students to use their method of choice on assessments? Why or why not?

### NCTM Standards and Expectations

 Algebra 9-12Use symbolic algebra to represent and explain mathematical relationships. 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. Draw reasonable conclusions about a situation being modeled.

2 periods

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### Lessons

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