TITLE:  LEARNING ABOUT RATIOS: A SANDWICH STUDY

AUTHOR:  Sheryl Weinberg; Southeast Island School
         District, Ketchikan, AK

GRADE LEVEL/SUBJECT:  4-6

OVERVIEW:  Ratios can be a difficult idea for elementary
students to grasp.  Spending time manipulating "real"
objects provides a tangible reference when later dealing
with the concept .. in either an abstract or practical
fashion.

PURPOSE:  The purpose of this activity is to provide
students with a concrete introduction to the concept of
ratios.

OBJECTIVES:  As a result of the activity, students will be
able to:
1.  Orally define ratio.
2.  Demonstrate the ability to create ratios with     given
substances.
3.  Label ratios.
4.  Generalize the concept, creating a ratio with a
    self-selected material.

RESOURCES/MATERIALS:  chalk, peanut butter and jelly (one
container per group), measuring spoons or cups, butter
knives, paper towels, damp sponges, teacher developed
graphs, pencils and paper for students

sample graph:  Peanut Butter and Jelly Study

Peanut Butter    Jelly  Rating
  5 T      0 T    1 2 3 4 5 6
  4 T      1 T    1 2 3 4 5 6
  3 T      2 T    1 2 3 4 5 6
  2 T      3 T    1 2 3 4 5 6
  1 T      4 T    1 2 3 4 5 6
  0 T      5 T    1 2 3 4 5 6

ACTIVITIES AND PROCEDURES:
  1.  Prior to class beginning, write RATIO in large letters
in the center of the chalkboard.  State objectives of
lesson.  Ask students to tell what they think the term
means.  List student comments on the board.
  2.  Randomly select 10 students to come forward.  Divide
the pupils into groups by sex.  Have seated learners count
the number of boys and girls.  Write the numbers above each
group, separated by a colon.  Explain that this expression
identifies the ratio of boys to girls called forward.
Physically structure two additional examples (ex: students
by hair color, lunch to milk tickets, pupils that write with
pens to those that use pencils.)  Label examples.  Return to
the term on the board and student comments.  Have students
identify which, if any, ideas identified what a ratio is.
Guide pupils in defining the term.
  2.  Divide class into groups.  Direct each group to make a
series of six peanut butter and jelly sandwiches, each
containing a different ratio of the given spreads.  Pupils
are to label each ratio.  Cut each sandwich into pieces.
  3.  Conduct a taste test of the preferred ratio.  Have
each student within the group taste each sandwich and rate
it on a scale of one to six.
  4.  Direct pupils to graph and report the results of the
trial individually, and then for the group.
  5.  Have each group share their charts with the rest of
the class.  Compare and contrast differences.

TYING IT ALL TOGETHER:
  1.  Direct students to write what they learned about
ratios.  Ask them to verbally share what they wrote.
Encourage students to describe any ratios that they are
familiar with.
  2.  Have students divide themselves into triads or
quartets.  Explain that each group is expected to identify
substances for  a ratio study similar to the one conducted
with peanut butter and jelly (ex: lemons to sugar to water,
red to white paint to create the most desirable shade of
pink...)  Groups should develop a material list, method of
study, and format for presentation of results.  Indicate
which day students should be prepared to conduct and present
their tests.