COMPANION WEBSITE ACTIVITY
Quarters, Quarts, and More Quarters: A Fraction Unit
Level: 3-6
Setting: individual, small group, and whole group
1
Objective: Students recognize and represent the fraction 4 in common and decimal forms from their experiences.
Materials: quarters, grid paper, fraction circles, manila paper
This unit focuses on activities that deal with the concepts
of one-quarter and twenty-five hundredths. The activities build on children’s present knowledge to review and
extend their understanding of the many areas of their
lives in which the concepts appear. When the unit is concluded, children will have reinforced their understanding
of one-quarter as one of four equal parts of a whole and
the numerals 14 and 0.25 as numerals for these parts.
Session 1: How Are Quarters Used?
Begin by asking, “How many settings can you think of
in which the idea of one-quarter is used? I want you to
write a sentence in which you tell one way in which you
have recently used quarter, one-quarter of, twenty-five
hundredths, or any other word or words that mean the
same as these terms.” Examples of responses given by
children in one class include:
• “My mother gave me a quarter for each window I
washed.”
• “At the end of the first quarter, our team had a 7-to-3
lead.”
• Set up learning stations, such as one for linear measure
that has foot and metric rulers, yard- and metersticks, and
measuring tapes in metric units and inches. Create similar
stations with devices for measuring weight, capacity, and
time.
• Have children work in cooperative groups, one or two
groups at each station. They are to study the measuring
devices to determine ways in which one-quarter is associated with them. One student in each group should make
a list of the group’s findings. In some instances they list
devices or measurements that are a quarter of a unit, such
as “a 14 -teaspoon measuring spoon,” “a 14 -cup mark on a
measuring cup,” and “a quarter-yard mark on a yardstick.” In other instances, the quarter must be determined
by the children. They might indicate such things as “15
minutes is a quarter of an hour,” “3 inches are a quarter of a foot,” “4 ounces is a quarter of a pound,” “25
centimeters is 0.25 of a meter,” and “250 grams is 0.25
of a kilogram.” Allow time for each group to work at two
stations.
• Discuss the items on each list. Students should be ready to
demonstrate the accuracy of each item on their lists.
Session 3: Pattern Blocks
Materials: Pattern blocks
• “I used a quarter of a cup of butter when I made a batch
of vanilla cookies.”
• Provide each student with a handful of pattern-block
pieces, including at least four green triangle pieces and
these instructions: “Make a design in which green triangles are one-quarter of the design’s area. Draw a copy of
your design; color the green part(s) of your design. Write a
statement in which you explain how you know that green
is one-quarter of your design.”
• “Twenty-five cents is twenty-five hundredths of a dollar
and is called a ‘quarter.’”
• The drawings and explanations can become part of the
bulletin board begun in the first session.
• “I ate a quarter of the pizza my family had for dinner last
night.”
• “A quart of milk is one-quarter of a gallon.”
• “The sale sign said one-quarter off all merchandise on the
table.”
• “I live about one-quarter mile from school.”
• “This line is twenty-five hundredths of a meter long.”
When the children have finished, have them share their
sentences. As the discussion proceeds, categorize the
ways in which quarters is used. Categories might include
distance or length, money, time, and capacity. The nature
and variety of children’s responses give clues about
their understanding of common and decimal fractions.
Responses within a narrow range of uses are an indication that the children have a limited understanding of the
concepts involved.
A connection between mathematics and art can be
made by having the children make pictures to portray
their uses of quarter. These drawings will make up part of
a bulletin board display they will make during the course
of the unit.
Session 2: Quarters and Measurement
Materials: Measuring devices, such as rulers and tape measures;
small- and large-capacity containers; scales; clocks and stopwatches that measure seconds. Devices should measure in both
metric and English units.
Session 4: Equivalent Common and Decimal Fractions
Materials: Fraction strips, geometric fraction models, base-10
materials
• Each child will have a set of fraction strips, geometric
models, or base-10 materials. Children with fraction strips
or geometric models begin by locating a one-quarter
piece; children with base-10 materials show 0.25 with
their materials.
• During this activity, children use their models and imaginations to determine as many common fractions that are
equivalent to 14 or decimal fractions that are equivalent to
0.25 as they can. (Children working with decimal models
must have the content and pedagogical readiness necessary to visualize how hundredths can be subdivided to
show thousandths, ten-thousandths, and so on. Refrain
from telling them that 0.25 can be changed to 0.250 by
affixing a zero.)
Courtesy of Safe-T Classroom
Products, Inc.
• After each child has identified a number of equivalent
common or decimal fractions, ask: “Does anyone have a
common fraction with a denominator larger than 32?”
Have children who have such denominators write their
equivalent common fractions on the chalkboard or on an
overhead projector transparency. Order the common fractions, with largest denominator on the left and smallest
on the right. Fill in any gaps so that there is a complete sequence of equivalent common fractions from largest to 14 .
Children can verify equivalencies with calculators capable
of working with common fractions, using the simplification function on their machines.
Pattern block
• Children who used base-10 materials should be asked to
list their decimal fractions. It will become evident that the
decimal fractions 0.25, 0.250, 0.2500, and so on are all
equivalent.
Session 5: A Visit to Paula Porter’s Pizza Parlor
• Begin with this story: “Paula Porter is ready to open
her new pizza parlor. Paula’s is going to be different
from other pizza parlors because her pizzas will have a
rectangular shape. She will conduct a contest in which
customers will cut a pizza into four equal-size pieces in
imaginative ways. The patron whose pizza is judged the
most imaginative will be given a free pizza each month
for a year. Each person in the contest gets to eat the pizza
she or he cuts.”
• Follow the story with these instructions: “You are going
to practice for Paula’s contest. Use paper from your notepad to represent Paula’s pizzas. Decide what you think
is the most imaginative way to cut the pizza into four
equal-size pieces. You will be limited to five tries, so think
about how you will make your cuts before you do any
cutting. Remember: Equal-size does not mean that each
of the four pieces has to have the same shape as the other
pieces. Be ready to explain how you know that your pizza
is cut into four equivalent-size pieces.”
• Have students add their “pizzas” to the bulletin board
display. Allow time for them to study the pizzas before
they vote for the one that is cut in the most imaginative
way. Discussion of the different cuts will enrich children’s
understanding of the many ways one-fourth can be represented. “Most imaginative” is subjective. Point out that all
shapes that meet the criterion of showing a pizza cut into
four equal-size pieces are really winners. (When items are
removed from the bulletin board, children can put them in
their mathematics folders.)
• If possible, arrange with the school’s food service to have
pizza for lunch on the day of this activity.