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ACTIONS WITH FRACTIONS
MASTER TEACHER
Gladys Tilley
GRADES: K-2
OVERVIEW
This lesson provides students with an understanding that fractions are equal
parts of a whole and that fractions, as equal parts of a whole, can be separated
and reassembled to form that same whole. This lesson uses the hands on
approach with learners interacting with each other and the teacher.
Real-life, concrete experiences and a video segment teach about equal and fair
shares as it involves fractions and fractional parts.
ITV SERIES
Mathica's Mathshop: Sweet Dreams
LEARNING OBJECTIVES
Students will be able to:
*identify equal parts of the whole
*determine how many parts make up the whole
*compare fractional parts to the whole
*demonstrate fractional numbers in everyday situations
*define fractional parts as equal parts of the whole
*identify fractional parts 1/2, 1/4, 1/3
MATERIALS
(for teacher)
4 white 9" paper plates
3 colored 9" paper plates
1 chart tablet
1 dark marker
1 pair scissors
3 apples
1 knife
1 cutting board
1 timer
1 small bottle lemon juice
1 cookie sheet
net or cheesecloth to cover cookie sheet
1 roll paper towels
3 plastic knives
(for learners)
3 white 9" paper plates per learner plus extras for those who
need more practice
1 pair scissors per learner
1 box of 8 crayons per learner
1 napkin/paper towel per learner
1 large baggie per learner
For Rotations
A.
1 apple per learner
1 plastic knife per learner plus extras in case of breakage
container for apples
paper towels or napkins for cleanup
B.
1 soft flour tortilla per learner
1-2 jars smooth peanut butter
1-2 jars jelly
8 plastic knives for this rotation napkin/paper towel per learner
C.
1 large box of cereal
storage container for cereal
napkins/paper towels - 1 per learner
D.
clay or playdough (1 stick per learner) plastic knives or tongue depressors (1
per learner)
paper towels (1 per learner for cleanup)
E.
10-12 lbs. rice, beans, or sand
large covered container for rice, beans or sand
6-8 measuring cups showing 1/2, 1/4, 1/3
4-6 scoops (may use the ones that come in detergent boxes)
F.
2-3 gallons of punch
1 pitcher for punch
1 paper cup per learner
2 - 1 or 2 cup measuring cups showing 1/2, 1/4, 1/3
napkins/paper towels (1 per learner)
waste basket
VOCABULARY
fractions one-fourth
equal parts one-third
fair share divide
whole separate
one-half
PREVIEWING ACTIVITIES
With learners seated on carpet, ask them to pair up with a buddy and talk about
a new learning word - "fractions." Tell them you would like them
to tell each other if they have heard the word before and what they think it
means. They will have 5 minutes for their discussions. (Set timer
for 5 minutes.)
At the end of 5 minutes, call on one learner from each pair to tell if they
have heard the word before and what they think it means. Record answers on
chart. (Accept all responses.)
Call up a pair of learners. Ask the group. "How many
learners are in our set?" (Ans. 2)
"Correct. In our set we have two learners. Who can tell me a
way to divide our set of learners into two parts so that we will have as many
learners in one set as in the other?" (Accept all responses.)
Use the two learners to do as students suggest until the learners are
divided, one on one side and one on the other side. Lead learners into
understanding that they have just separated/divided a whole set of 2 into halves
and that one is one-half of two. As you say this, place the two learners
side by side in front of you and then separate them to show that two is the
whole set and that to divide them equally is to place 1/2 of the set on one side
and the other 1/2 of the set on the other side. Then, they can be placed
side by side again to demonstrate that the set can be put together again to form
the whole set. Tell learners that each fractional part that they
separated/divided was an equal part of the whole.
At this point in the lesson, check the chart to see if any pair was correct
or close to the definition of what a fraction is. Compliment all pairs on
their ideas given. Tell learners that for the next few math classes, they
will be focusing on working with fractions and that fractions can be fun.
Ask learners to stand. Discuss how the entire class can be divided into
half so that one-half of the class is on one end of the carpet area and the
other one-half is on the other end of the carpet. (NOTE: If an odd
number of learners, teacher becomes the even number for this lesson.) Tell
learners to remember how the set of two learners was divided into halves so that
they can begin to place one learner here and one learner there until all
have been placed and the class is equally divided. Count each group to
ensure that there is the same number in both groups. Have learners
verbalize that the whole group has been divided into two groups of the same size
and that each group is 1/2 of the whole group.
With everyone seated again on the carpet, ask, "Would each of you like
to divide something into halves or equal shares?" (Response looked
for is "yes".) Produce a white paper plate. Ask,
"Is this a whole paper plate or is it in pieces?" (Ans.
"A whole paper plate.") Say, "Watch carefully."
Fold the paper plate in half, showing how to match the edges. Crease
firmly. Open the plate and draw a line down the fold line with the marker.
Hold the open plate before the learners. Ask: "Is there an equal
share on both sides of the marker line? Is each side the same size? How do
you know?" (Accept all answers.) Produce scissors and cut the
plate on the fold line. Ask, "How many parts of the plate do I
have?" (Ans. 2) "Are they the same size? Is each an equal
share?" After responses, ask, "How can we make sure?"
(Accept all responses.) Lay one half on the other half to show that they
are the same size. Pass the pieces around for examination by the class.
When the halves return, produce 2 whole colored paper plates and fit one of the
halves on one. Ask learners to tell what part of the whole colored plate
is covered by the cut white plate. (Ans. 1/2). Pass the halves and
two whole plates around for examination so that the students can fit the
one-half on the whole. From time to time as the plates are passed, you may
ask a learner to show the whole plate and the one-half plate or you may change
up and ask a learner to tell you the names of the parts s/he is holding.
When the whole and half plates return, fit the halves onto one whole plate.
Ask, "Can we say that each half is an equal part of the whole?"
(Ans. Yes.) Ask, "What do we call each fractional part of
the whole that is divided equally into two parts?" (Ans.
One-half.) Say, "Now it is your turn. I would like for
you to show me how each of you can divide your plates into halves. At your
work stations, you will fold your paper plates into halves, color 1/2 and cut
your plates into halves. Do we understand what to do?" If all
understand, proceed. If not, reteach how to separate the halves.
When all are working, monitor the group as learners fold, color and cut, giving
assistance when needed. Have extra plates on hand for those who may need
one. When all have finished, have learners place 1/2 over the other 1/2 to
see if the parts are equal. They are asked to tell what each equal part is
called.
Say, "Let me see your eyes, please. Place your halves into the zip
lock bags I am giving you and lay the bag, scissors and crayons down."
When all have done what was asked, say, "Watch me."
Produce a white paper plate and fold it in half. Learners may tell what
each part is called. Holding the paper plate, say, "We can take
this paper plate and turn it into another fraction that has four equal parts.
Can you tell me how to do this? Remember, we already know how to fold it
into two equal parts." (Accept all suggestions.) Finally, fold
the paper plate into half, creasing it firmly. Then fold this half into
half, unfold, draw lines on the folds and cut the plate into fourths. If
you do not wish to use this method you may choose to fold the plate into half,
draw a line and cut. Fold the other half, draw a line and cut.
Either way you will have the fourths. (It may be ideal to show the
learners both ways so that they can choose which method is easier for them.)
Say, "Can anyone tell me what the equal fractional parts are called
if there are four equal parts?" Lead learners into the understanding
that when a whole is divided into four equal parts, each part is called
one-fourth. Fit the four parts onto a whole colored paper plate and pass
the pieces around for examination. (If you have demonstrated both methods, send
two sets around.) Ask learners, at random, to tell what each part is
called.
When the whole and the fourths are returned, again say, "Now it is your
turn. This time you will fold your paper plates into halves and then
fourths, cut out your fourths and color 1/4 . Does everyone understand
what we are to do?" If all understand, proceed. If not, reteach
folding and cutting into fourths. Again, after the paper plates are passed
out, monitor the folding and cutting, giving assistance where needed.
(Have extra paper plates on hand if needed.) As you monitor, ask learners
what fractional part of the plate they will color. (Ans. 1/4)
Also, ask them what fractional parts they had when they did the first fold.
(Ans. 1/2) When all have completed the fourths, ask learners to hold up
the equal part they colored and tell what part of the whole it is. (Ans. 1/4)
When they have verbalized 'one-fourth' have them place the fourths into the
ziplock bag with the halves.
Say, "Stand. You have 2 arms and 2 legs. How many is
in this set?" (Ans. 4). Say, "Shake 1/4 of this set.
Good! You have hands. How many are in this set?" (Ans. 2)
Say, "Great! Wave 1/2 of this set. How many are in your
set of eyes?" (Ans. 2) Say, "Wonderful! With 1/2 of your
set of hands, cover 1/2 of your set of eyes. That's great! How many
bodies do each of you have in your set?" (Ans. 1). Say,
"Wow! Wiggle the whole set!" After they have wiggled for
no more than a minute, stop them.
Say, "Now that we have wiggled some of our own fractions, let us
come quietly to the carpet because I have a serious problem to solve. I
have three apples. (Show 3 apples.) I know about halves. That's two
equal shares. I know about fourths. That's four equal shares.
Now I have these three apples. Is there anyone who can tell what to call
one part of a set with three equal parts? If I had 2, I would know.
If I had four, I would know. I don't have 2 or 4, I have 3. Who can
help?" (Accept all suggestions.) If no one says 'thirds', say,
"I know! Let's count them ordinally. Maybe we can come up with
an answer. Let's count. First, second, third." (Point to the
apples as each ordinal number is said.) Say, "Let's count
again. First, second, third. That sounds about right! Thirds!!
Do you think that we can call each apple one-third of the set?" (Ans.
Yes!) Whew! I am so glad that problem is solved. What do we
call each part when there are three parts equally divided? (Ans.
One-third) Call up 3 learners. Say, "Can we divide this
set into three equal parts?" (Ans. Yes) Ask,
"How?" Have learners tell how to do this. Say,
"Great!" Call up three more learners. Ask, "How many are in
our set?" (Ans. 6) "Can we separate this set into 3
equal parts? What can we do now?" Lead learners into placing
the learners into three groups of 1 each and then placing the last three
learners in the same groups - one in each group. Ask, "How many are
in each group?" (Ans. 2) "Is there an equal number in each
group?" (Ans. Yes) Ask, "Can we say that our set of
six learners has been equally divided into thirds and has three groups of
two?" (Ans. Yes) "What do we call each group of three when
we use its fractional name?" (Ans. 1/3) Say, "If we take
our thirds and put them back together to make the whole group, how many will we
have?" (Ans. 6) Have the three one-thirds get back
together and have learners count them. (Congratulate the learners on their
understanding of the fractional parts and their participation.)
FOCUS FOR VIEWING
Say, "I thought I would never solve that problem. You came to
my rescue for that one. Now I have an even bigger problem and I am really
going to need all the help I can get to solve it. It involves these three
apples again. Here is my problem. I have invited friends to come
over to share my apples. I forgot that I only have three apples and I
invited 12 friends. I don't know what to do. I can't go to the
store. The store is closed for the holiday. My friends will be here
any minute and I have only three apples. What can I do? Who
has an idea about how to share these three apples among 12 friends?"
Listen as learners give suggestions. You may wish to jot them down on the
chart as they are given. To give the students a specific responsibility
while viewing, say, "I have a friend who may be able to help. One of
you may have come up with the correct solution but I do not want to cut my
apples until I hear what my friend has to say. Please help me look and
listen. We may find an answer to my problem of how to divide my three apples
among 12 friends."
VIEWING ACTIVITIES
At this time, put on the video Mathica's
Mathshop: Sweet Dreams. Start the video when the witch enters and
says, "Little people making merry in the moonlight. Bah!" Pause
the video when Mathica says, "How can the witch divide 3 apples to make 12
fair shares?" Ask learners, "Is that the same as my
problem?" (Ans. Yes) At this point, review how learners said to
solve the problem.
Resume the video. Pause the video when Mathica cuts
the 3 apples into halves. Say, "There are only 6 halves. The
witch needs 12 pieces. What should she do now?" (Accept all
suggestions.)
Resume the video. Pause the video when
Mathica cuts the first apple's halves into halves and the witch says,
"Can't you hurry this bit?" Ask, "How many pieces has the
first apple been cut into?" (Ans. 4) Say, "If Mathica cuts the
second apple into four pieces, how many pieces will that be?" (Ans.
8) Ask, "How can she get 12 pieces?" (Accept all answers.)
Resume the video. Stop the video when the
witch says, "Now everyone will have a quarter of an apple."
Ask, "Did my friend tell me how to solve my problem with 3
apples?" (Ans. Yes.) "Let us check our predictions to see
if anyone came close or said exactly what I should do." Praise
learners for their suggestions after checking predictions. Say,
"Now tell me how to cut my 3 apples so that I may have 12 pieces for my
guests. Who will tell me what I should do first? Remember what
Mathica did first." Call on learners and follow their instructions
until the 12 pieces are cut. Put the pieces into a ziplock bag and say,
"Thanks, again learners, I am so happy you were here to help me."
Say, "While cutting the apples into fractional parts, do you suppose we
used our five senses?" (Ans. Yes) Say, Who can tell
what our five senses are?" (Accept answers from volunteers.)
Say, "Great! Now, who can tell me how each sense was used?"
(Again, accept answers from volunteers.) If no one mentions 'hearing',
ask, "Did anyone hear the apples?" If they say 'no', tell them
that apples can be heard when they are cut. Then say, "I forgot
something. One-half of my guests are staying on for about three days.
They like to eat apples a certain way. Let us work together to fix their
apple shares for them. We have 12 apple pieces in the bag. We will
need to take one-half of them out. How many will that be?"
(Ans. 6) Say, "You are correct." Take 6 pieces out
of the bag and lay them on the cutting board. Say, "My guests who are
staying like dried apples. I will have to take these six pieces and dry
them. In order to do this, I will need to take the peel off, take the
seeds out and slice the pieces very thin, put them on a cookie sheet, sprinkle
them with lemon juice, cover the pan with cheese cloth and set the pan in the
sun for 2 or 3 days for drying. I will need 3 volunteers to help me."
(Choose three volunteers and guide them through the steps.) Say, "I
certainly am glad I remembered about those guests. Thank you for
helping." (Give paper towels for clean up.) Girls and boys,
what we have just done is the way the Native Americans, early pioneers and
settlers in our country used to preserve their food. They did not have
refrigerators and freezers as we have today.
POST-VIEWING ACTIVITIES
Say, "Now that we have solved my problems, it is your turn to experience
and explore fractions some more. We will have six rotations in which you
will participate and have fun learning more about fractions. In one
rotation, you will be able to divide apples into fractions just as Mathica did.
In another called "Time Out For Tortillas," you will be able to create
sandwiches and discuss their fractional parts. In a third called
"Break-fast, Anyone?" you will divide cereal into fractional parts.
In the fourth called "Shall We Eat These Fractions?" you will be able
to use clay to create food fractions. The fifth rotation is called
"Rice". Here you will experience measuring parts of a whole by
using measuring cups and scoops to practice fractions we have used and
discussed. And, in the sixth called "Drinks, Everyone!" you will
be given the opportunity to pour a specified fractional punch drink. Shall
we begin? The first 5 rotations are set up for 4 learners each.
After finishing all 5 rotations, it's on tonumber 6 "Drinks,
Everyone!" Assign learners to rotation stations or they may choose
where they wish to start.
Rotation A Apples
Materials : 1 apple for each learner in the rotation, 1 plastic knife per
learner, container for apples, napkins/paper towels for each rotation member.
Procedure:
1. Distribute apples, knives, napkins to each learner.
2. Each learner cuts his/her apple into halves as Mathica did.
3. They then cut the halves into halves.
4. Three of the group gets together to count and see if there are enough
pieces for twelve guests.
5. The fourth member joins with two members and they count to see if there
are enough pieces for twelve guests.
6. After discussing their fractional parts, these learners enjoy their
apple snack before moving on to another rotation where learners have finished.
Rotation B Time Out For Tortillas
Materials: 20-30 soft flour tortillas for entire rotation period, 1
plastic knife for each learner in the rotation, 2 jars of peanut butter, 2
plastic knives for the peanut butter jars, 2 jars of jelly, 2 plastic knives for
the jelly jars, 1 paper towel/napkin per rotation member
Procedure:
1. Learners fold and cut tortillas in half and tell what fractional parts
they have cut their tortillas into.
2. They fold both halves into half and cut again. They tell how many
parts of the tortillas they have now and what each fractional part is called.
3. Learners put the tortillas back to form the 'whole'.
4. They make peanut butter and jelly sandwiches and tell about the
fractional parts they eat.
Rotation C Breakfast, Anyone?
Materials: cereal (teacher's choice) 1 large box, paper towels, storage
container for cereal
Procedure:
1. Distribute one paper towel to each group member and demonstrate how to
fold the paper towel into thirds.
2. Each learner takes 6 pieces of cereal from the container. Ask,
"How many is 1/3 of 6?"
3. When this is decided, learners take 3 more to make 9 pieces and find
1/3 of 9. They continue taking 3 pieces of cereal each time and
finding 1/3 of the total until they reach 15-18 pieces.
4. Learners eat the cereal, if they wish, before moving on to the next
rotation.
Rotation D Shall We Eat These
Fractions?
Material: clay or playdough for each group member (1 stick per member),
plastic knives or tongue depressors (1 per group member), small rolling pins (1
per group member - optional), paper towels for clean up
Procedure:
1. Each group member is given a piece of clay and a plastic knife or
tongue depressor.
2. Learners are asked to roll circular pizzas and cut into equal shares
for the number of members in their group or members in their families.
They discuss the number of pieces and what each fractional part is called.
3. When the pizzas are completed, learners roll square, rectangular, long,
watermelon shaped pieces, etc. and cut each into fair shares for the group
members or their family members and again discuss the fractional fair shares.
4. At the end of rotation, clay is rolled into a ball for the next group
before clean up.
Rotation E Rice, Beans Or Sand
Materials: rice, beans or sand (whatever is most available to the teacher-
approximately 10-12 lbs.), 1 large covered container for rice, beans, or sand,
6-8 measuring cups showing 1/2, 1/4, 1/3, scoops (1 per group member - may use
the ones in detergent boxes)
Procedure:
1. Learners experiment with filling their measuring cups to 1/2, 1/4, and
1/3 and verbalizing to each other what fractional parts of the 'rice' is in
their measuring cups. EX. "I have 1/2 cup of rice."
2. When they are familiar with this routine, they are asked to use extra
measuring cups to discover how many halves, thirds and fourths cups of 'rice'
make one cup and any new discoveries they can make about fractional parts and
discuss.
When a learner has gone through all 5 rotation stations, s/he will go
immediately to Rotation
F.
Rotation F Drinks, Everyone!
Materials: 2-3 gallons of punch, 1 paper cup per learner, pitcher, 2
measuring cups showing 1/2, 1/4, 1/3, napkins/paper towels (1 per learner),
waste basket
Procedure:
1. Teacher pours punch into pitcher (approximately 1/2 pitcher full so
that the learners can lift pitcher easily. Teacher keeps pouring punch as
needed.).
2. As learners finish their rotations and come to 'Drinks, Everyone?', the
teacher asks each learner to pour 1/2 cup of punch into a measuring cup.
3. Teacher checks the '1/2' and the learner pours the punch into his/her
paper cup and drinks, if s/he wishes.
ACTION PLAN
Learners will interact with parents and other family members in their kitchens
when they are cooking. Learners will help with measuring using fractional
parts 1/2, 1/4, 1/3 and any other fractions parents would like to help learners
with. Parents are asked to write about their learners' measuring
experiences in journal style. After a week, the 'journal' is sent to the
classroom to be shared with classmates.
Learners will visit their local or area Botanical Garden to learn about
plants grown in their area and about plant propagation from seeds.
Learners will listen to area Garden Club representatives talk about plant
propagation and caring for plants.
County Extension Centers will be contacted so that learners may go to the
Centers or have a County Extension Agent visit learners for demonstrations on
planting seeds and lessons on plant care.
EXTENSIONS
SOCIAL STUDIES / SCIENCE
Learners save the seeds from their apples and plant them. They will find
out how to care for their seeds in order to help an apple tree grow. Use
literature with this activity. Read and discuss the story of Johnny
Appleseed by Steven Kellogg or another favorite author.
MATH / LITERATURE / ART / WRITING
Read and discuss Give Me Half by Stuart J. Murphy. (This is a MathStart
book for understanding halves.) After the discussion, have learners draw
and color their favorite story parts or dictate what their favorite part is
about. Learners share what their favorite parts are about. The pages
are then put together in chronological order and bound into a book for the
classroom library.
BIBLIOGRAPHY
Adler, David A., Fraction Fun
Dennis, J. Richard, Fractions Are Parts of Things
Ginsburg, Mirra, Two Greedy Bears
Giganti, Paul, Each Orange Has Eight Slices
Hutchins, Pat, The Doorbell Rang
Leedy, Loreen, Fraction Action
Martin, Jannelle, Equal Ed
McMillan, Bruce, Eating Fractions
Moncure, Jane Belk, How Many Ways Can You Cut A Pie?
Murphy, Sturat J., Give Me Half
Pinczes, Elinor, One Hundred Hungry Ants
Updated: April 01, 2008
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