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Balance or Tilt?

Curriculum Tie:


  

Summary:
The activities in this lesson will give students opportunities to explore the algebra concepts of variable, constant, expressions and equations.

Main Curriculum Tie:
Mathematics - 6th Grade
Standard 2 Objective 2
Write, interpret, and use mathematical expressions, equations, and formulas to represent and solve problems that correspond to given situations.

Materials:

Additional Resources

Book

  • Navigating Through Algebra in Grades 3-5, by Gilbert J. Cuevas and Karol Yeatts; ISBN 0-87353-500-7

Attachments

Background For Teachers:
Variables, expressions, and equations are important concepts in the study of algebra. For this activity, students should know and use the correct terms. A constant is a quantity that stays the same. A variable is a quantity that can change. An expression is like a phrase, it has no equal sign. An equation is a mathematical statement that says two expressions are equal to each other.

Intended Learning Outcomes:
2. Become mathematical problem solvers.
3. Reason mathematically.

Instructional Procedures:
Invitation to Learn
Use a balance scale and small wooden blocks to demonstrate if the scale is balanced or if it is not. Model several different situations so the students know what happens to the side that weighs more, the side that weighs less, and when the amounts are equal. Have students write what happened in their math journals.

Instructional Procedures

  1. Explain to students that like the balance scale, equations need to be balanced, or equal.
  2. Students write the definitions of variable, constant, expression, and equation in their journals.
  3. Review with students how to solve two-step equations. Lesson plans for this are in the 2003 CORE Academy Handbook.
  4. Draw a scale on the overhead using an expression on each side. Ask the students if the scale shows the correct balance. If not, how should we fix it? Should one side be lower than the other?
  5. Give a few more examples to the class.
  6. Students complete the Balance or Tilt? worksheet.
  7. Discuss the worksheet as a class.
  8. Students write a paragraph explaining the steps they use to solve equations in their math journals.

Extensions:

  • Add the words constant, variable, expression and equation to your spelling and vocabulary units.
  • Students brainstorm a list of variables and constants found in space:

Variables: age of stars, distance between stars
Constants: speed of light, distance light travels in one year, the size of each planet.

  • Create word problems that represent given equations using variables. From given word problems, students write equations using variables.

Family Connections

  • Students make up three different equations to take home and have a family member solve. Explain to the family member how to solve the equation, if needed.
  • Students make a list of five variables and five constants that they find in or around their home.
    Example: Number of people in family is a constant, number of hours they do chores each day is a variable.

Assessment Plan:

  • Class discussion.
  • Balance or Tilt? worksheet and the paragraph and definitions in their math journal.

Bibliography:
Research Basis

Schifter, D. (1997) Developing operation sense as a foundation for algebra. http://eric.ed.gov ERIC # ED408152

This paper points out the importance of operation sense in the preparation for algebra. Implications of this work include the idea that diagrams, graphs, and tables are important for students to understand.

Swafford, J.O., & Langral, C.W. (2000). Grade 6 students’ preinstructional use of equations to describe and represent problem situations. Journal for Research in Mathematics Education, 31(1), 89-112.

This study investigates sixth grade students’ use of equations to describe and represent problem situations. The students showed a remarkable ability to generalize problem situations and to write equations using variables.

Author:
Utah LessonPlans

Created Date :
Feb 27 2006 12:16 PM
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