
Fractions Introduced Conceptually
Introduction: Fractions are used in many ways. Before rushing into how to do
arithmetic with fractions, students should experience what fractions mean. Why do we really use fractions? How do fractions express real ideas that we use or experience? Only after the concept makes sense does the arithmetic make sense.
Purpose: To help students develop an understanding
of the meaning and use of fractions from everyday
experiences. Some of these lessons develop thematically with
other units, some are designed to be reinforced daily.
Background: Some of these lessons were used in a
1st2nd grade multiage setting. The rest can be used in
third and fourth grades, as well as, reinforced at higher
grades. 
Reformatted: January 2010 

How Are Fractions Used? This series of sample exercises demonstrate the many common uses of fractions. They demonstrate what the fractions mean in the discussion. Use exercises like these, until the students can express the concept of fractions. Then move onto arithmetic. These exercises are designed to be used daily to fill in small periods of time, say, as a warmup activity.
 Parts of a Whole  sharing, splitting equally
Money Activities:
What part of a dollar is a penny, a dime, a quarter,
50¢, 66¢. How did the quarter get it's name?
What do we call a 50¢ piece? What could we call the
dime, nickel or cent?

Pizza Activities:
Have students discuss, and demonstrate by drawing,
whether they want 1/6, 1/8, 1/12, or 1/16 of the pizza.
Demonstrate by cutting the pizza and handing out the
pieces.

 Comparing Parts of a Group  "what part of...," "... out of ...."
Calendar Activity:
Each day when the date is written have a student write
out what fraction of the month, week, year, or school
year has passed. Advanced students may reduce the
fractions or discuss why the fraction can not be reduced.

Reading Activity:
Have students count the letters in a sentence, and
determine what fraction of the letters are e, t, or a.
What fraction of the words have more than one
syllable?

Students in Class Activity:
Each day pick a characteristic such as wearing red,
bringing lunch, playing ball, girls, done their
assignments, etc. Determine what fraction of the class is
in this group.

Money in your Pocket:
Have students determine what fraction of their money
is nickels. There may be two correct answers, first: the
fraction of the counted number of coins, second: the
fraction of the value of the coins.

 Property of Measurement 
part of inches, feet, hours, days, ....
Clocks Activities  Hours:
Have students determine what part of an hour is 1, 6,
15, 30, or 60 minutes. Point out what we call "half
past," or "quarter till." Have them draw a clock and
shade the area from the hour until quarter after.

Clocks  Minutes:
Have students determine what part of one minute is: 1,
15, 60, or 90 seconds. Compare these answers to similar
question for hours.

Clocks  Days:
Have students determine what part of a day is: 1 hour,
2 hours, 8 hours, and 12 hours. Have students estimate
what part of a day they spend in school, sleeping,
eating, watching TV.

Clocks  School:
Have students estimate what part of the school day is
spent in lunch, recess, math, or gym. Which of these is
the largest?

Ruler Activities:
Have students draw lines that are 1/4", 1/2," 3/4",
5/8", 11/16." Have them determine which line is longer?
Have students practice mixed numbers by drawing lines of
length 1 1/2", 2 3/4, 5 1/8,
etc. Have students draw lines 2 1/2" and 5/2" and compare their lengths. Have students
explain how they did their comparisons. Have students
measure items around the room.

Liquid Measurement Activities:
Have student use a measuring cup or a graduated
cylinder. They should actually have a chance to look at the markings on the cup. What fraction of a cup is 4 oz. or 8 oz? How
many cups (accurate to 1/8th) does it take to fill
another container, such as a mug?

 Comparisons in Measurement  ratio, twice as much, half as long, unit weight,
speed
Liquid Measurement:
Have students determine what fraction of a quart jar
is held by a drinking glass. What part of a gallon is a
quart? Why do we call that part of a gallon a "quart?"

Distance Measurement:
Have students determine the ratio of the width of the
room to the length of the room, or the width of their
desk to the length of their desk, or the size of their
desk to the teacher's desk.

Weight:
Have students determine the ratio of the weight of two
different objects that they might want to carry. Have
them discuss what this ratio says about strength, or
workload.

Weight per item:
Have students determine the weight of a piece of candy
by weighing a box of candy and dividing by the number of
pieces. Compare this to the weight of one piece.

Speed:
Measure out 50ft and use a stop watch to determine how
much time it takes a student to run that distance. Show
them how the ratio of distance / time is their speed. Let
them discuss whether a faster student will have a longer
or shorter time.

 Probability and Statistics expected value, predict how often, is it frequent
or rare
Dice Activity:
Have students roll a die many times and count how many
times they rolled a 3, and how many times they rolled
total. Have them guess how many 3s they will get with a
different number of rolls. Have them compare their
results to the ratio of the number of 3s on a die to the
number of faces (1/6.)

Color chips Activity:
Place chips of different colors in a container. have
students pick out a chip, record the color, and replace
the chip many times. Have them compare the ratio of times
they picked a red to the total number of picks. Have them
compare this to the ratio of reds to the total number of
chips in the bag.


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Comments:
Repeating many activities, like the ones above, will help students understand the uses of fractions. It will help prepare them for their higher math classes in higher grades. Activities like this will help them reason about the answers they get to arithmetic problems. By thinking about what fractions mean, they can look at their arithmetic and ask, "Does this result make sense?" "Can I take 1/2 a pizza plus 1/3 a pizza to get a total of 1/6 a pizza? No. The result is too small!"
Encourage students to notice where they observe fractions in
everyday life. Encourage them to notice how fractions can be used to
create ideas such as speed, unit weight, or probability. Read package
labels to promote the idea of unit weight or grams per serving. Have
students notice similarities in speech such as "Half as much," and
"Twice as much." If half is a fraction then maybe twice (2/1) is a
fraction also.
Extra: Promoting Algebra Concepts with Fractions:
Once students have got the idea of 1 being anything divided by
itself, extend the pattern to include variables and arithmetic
operations. Fill in the numerator or denominator to make each
fraction equal 1:
With this exercise you can motivate the idea that anything,
even if we don't know what it is (a variable), fits the pattern.
1 
2 
3 
4 


345 

2+2 
83+12



pi 
b+b 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

1 
2 


5 
10 

1,083



x 
y 




