Illuminations: Exploration of a Balance

Exploration of a Balance

Maintaining the Balance

In this lesson for grades 3‑5, students participate in activities in which they focus on patterns and relations that can be developed from the exploration of balance, mass, length of the mass arm, and the position of the fulcrum. The focus of this lesson is determining the position necessary to balance uneven objects and the effect on balance of moving the fulcrum.

Learning Objectives
 
Students will:
  • construct and use a two-pan balance
  • compare mass of two objects
  • construct a horizontal bar graph showing the results of their measurement
  • determine position necessary to balance uneven objects
  • identify the effect on balance of moving the fulcrum

Materials
 
Maintaining the Balance Activity Sheet
Crayons, tape, 2 small styrofoam cups, and a centimeter ruler for each group
Paper clips of like mass
A collection of small objects to be weighed
Shifting the Balance Activity Sheet

Instructional Plan

To begin the lesson, review with students the various uses and types of balances. Review the term fulcrum, both as a vocabulary word and its purpose.

Note: This lesson includes two activities for students. It is recommended that the activities be completed in the sequence presented below.

Activity 1

Distribute the Maintaining the Balance activity sheet to each student.

Maintaining the Balance Activity Sheet Maintaining the Balance Activity Sheet

Give each group a thirty-centimeter ruler, two small styrofoam cups, a large crayon, tape, a collection of small objects, and paper clips of like mass. Guide the students as they label the paper cups A and B. Assist the groups as they construct the pan-balance scale.

 

 

Ask the students to observe the distance of each cup from the center, the fulcrum.

Tell the students to place a small plastic toy in cup A. Ask the students to estimate how many paper clips are required to balance the toy. Guide the students as they balance the toy.

Show the students how to color a box of the graph on the Maintaining the Balance Activity Sheet for each unit of mass, or paper clip. Help them to color part of a box if the state of balance can be determined to be between units, that is, if fractional units are needed to complete the balance. If objects with mass greater than thirteen paper clips are used, the graph will need to be extended.

 

Activity 2

Distribute the Shifting the Balance activity sheet to each student.

Shifting the Balance Activity Sheet Shifting the Balance Activity Sheet

Give each group a thirty-centimeter ruler, two small styrofoam cups, a large crayon, tape, and a collection of small objects. Guide the students as they label the paper cups A and B.

Direct the groups of students to determine which member of a pair of objects is heavier by testing them on a balance with cups equidistant from the fulcrum.

Guide them as the move cup B, containing the lighter element of each pair, until they rind a location at which the two cups balance. Have students record the observations they make as each pair is weighed.

Have students return cup B to an end position when it balances cup A. Have students repeat the procedure as the fulcrum is moved.

Allow time for the students to complete the Shifting the Balance activity sheet. Students may need to create additional tables to contain their data.

Assessment Options
 
  1. Encourage comparisons between the recorded masses of various objects by asking students to find all objects that are heavier than, just as heavy as, or lighter than the first toy weighed.
  2. Students can record comparisons on a chart.

     
    Object selected Lighter objects About the same mass Heavier objects
           
           

  3. Ask students to express the results of comparison of objects using the terms heavier than, lighter than,  and similar in mass to in the comparisons. Record relational statements using structures such as the following:

    _______________   is heavier than _______________________.

    _______________   is lighter than ________________________.

    _______________  is similar in mass to ___________________.

  4. Provide a commercial pan balance, gram masses, and small objects in standard units, such as grams.

     

     

  5. Have students write descriptions of how to place various pairs of objects so that they balance.

Extensions
 
  1. Develop understanding of the relationship that the product of the length of the mass arm and the mass of one object is equal to the product of the length of the mass arm and the mass of the second object when the scale is balanced.

NCTM Standards and Expectations
 
Algebra 3-5
  1. Represent and analyze patterns and functions, using words, tables, and graphs.
Measurement 3-5
  1. Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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