Algebraic Problem Solving Using Spreadsheets:|
A unit for grade 9
Why solve problems with spreadsheets?
- to help students visualize mathematical concepts;
- to permit more realistic problems to be tackled;
- to allow students to analyze a situation using multiple representations;
- to prepare students to use computers in later mathematics courses.
Traditionally, the focus of mathematical problem solving in high school has been the development and solution of algebraic equations; however many students rush through textbook exercises using word clues and available numbers in predictable routines to arrive at answers. They are frequently nervous about tackling any problem that does not mimic a type already "learned".
- Computer programs can provide new insight by adding to the algebraic model the ability to analyze complicated numerical data through charts and graphs. This can help students visualize aspects of a problem which may not be apparent in the algebraic solution.
- Spreadsheets facilitate experimentation with numerical data which gives students the freedom to play with different possibilities and to really try to understand the problem.
- Spreadsheet addresses are concrete examples of variables. They can dynamically take on different values and can be manipulated to create formulas and equations to model simple linear relations in grade 9, or periodic and exponential functions in senior grades.
This unit was very well received by four grade 9 mixed ability classes. The students were actively involved in solving the problems. Although some students later had difficulty setting up and solving the problems algebraically without the computer they were frequently successful at solving even quite complicated problems by drawing up a handmade spreadsheet.
Three results stood out: students employed a wide variety of solutions when they were not limited by "problem type", they displayed considerable skill in creating and manipulating formulas, and they approached new and different problems with confidence.
This unit takes four days in the lab and a follow up day in class. Before students begin this unit they should have:
- Used a spreadsheet such as MSWorks or ClarisWorksfor listing data and plotting points. For an introduction, see Jan Garner's Spreadsheet Basics.
- Completed some work on simplifying algebraic expressions.
- Completed some work on solving simple equations.
- Formulas on a spreadsheet
Students follow two lab sheets on entering formulas using a spreadsheet and complete an assignment on their own.
- Setting up a problem on a spreadsheet
Students learn to set up a problem and develop their own formula by working through two examples.
- Spreadsheet problems
Students work in pairs to solve a variety of problems. There is a sheet of extra problems for those who finish early.
- Follow-up in the classroom