A RELATIVELY FAR OUT IDEA: ESTIMATING
Grades 4 - 5
Estimation is a resourceful tool used in the study of outer
space. In this lesson the students will probe the best methods of estimating.
They will apply that knowledge to estimating the relative size and distance
of each planet from the sun so that they can build a small model of the
solar system. Co-operative learning groups, hands-on activities, the use
of tables and graphs, and the interactive video provide opportunities for
learning.
Eddie Files* #2: Estimating: Going To The Dogs
*a multicultural series featuring characters from diverse cultural backgrounds
Students will be able to:
- problem solve through estimation.
- identify the nine planets in our solar system.
- identify characteristics of the planets.
- estimate the relative size of each planet by the size of the earth.
- measure the distance of each planet from the sun using a converted
scale table.
- construct a model of the solar system using these relative measurements.
- collect information using tables.
- interpret information on tables.
- make predictions on how to solve estimating problems.
- use a math journal to record information.
- calculate using a hand calculator.
- compare and contrast using Venn diagrams.
- compare and contrast in the construction of line graphs.
For class:
Previewing and Activity 1
- 1 14-oz box of Magic Mix cereal by Kountry Fresh (Winn Dixie) (The
students will want to eat the cereal, so it is suggested you have a second
box for consumption since what they use will be handled by the group).
- 1 5-quart ice cream bucket
- 1 4-oz. plastic cup
- 1 container of gold glitter
- 1 clear empty film dispenser
- 1/8 tsp measuring spoon
- 1 overhead calculator
- 1 overhead copy of chart 1A
Activity 2
- overhead copy of chart 1A -completed (cont. on next page.)
- 1 beach ball
- 1 marble
- 1 measuring tape
- 2 rulers
For each group:
Previewing and Activity 1
- 1 4 oz cup (bathroom cup size)
- 1 sheet of notebook paper
- 1 sheet of 9" x 11" black construction paper
- 2 calculators if possible (1 is feasible)
Activity 2
- 1 box of modeling clay
- clothes hanger wire cut: 1- 39cm;
- 1- 30cm; 1- 19cm
- 5 wire clothes hangers of the same size and color
- 10 index card strips
- 10 strips of scotch tape
- 16 tie wraps (from trash bags or bread bags)
- 3 inexpensive paper plates
- crayons
- stapler
For each student:
Previewing and Activity 1
- 1 post-it note placed on each desk before class begins.
- 1 metric ruler
- 1 toothpick
- 1 magnifying glass
- 1 pencil
- 1 math journal (paper bound in a folder)
- 1 information gathering chart 1A
Activity 2
- information gathering chart 1A -completed
- 1 table on distance 1B
- 1 grid sheet 1C
- 1 ruler
The class should now be in groups of approximately 4 students.
Teacher: "Star gazing is a great past time. Some people view the stars
and planets to see what constellations they can find. Others study the stars,
planets, and other heavenly celestial bodies. Does anyone know the name
of those people who study the planet, stars and other celestial bodies?"
(astronomers)
Teacher: "Who can be an astronomer?" (any girl or boy)
Teacher: "What do astronomers use to help them in their studies?"
(telescopes)
Teacher: "Do you suppose that astronomers would be able to count all
the stars in the sky?" (accept varied answers at this time)
Teacher holds up a container of glitter and says, "Do you think we
could count the glitter in this container?" (accept yes or no)
Teacher: "What is the problem with counting the glitter?" (They
are so little and so many.)
Teacher: "How many specks of glitter do you think there are? Write
down your estimate on the post it." (answers will vary)
Teacher allows time to share estimates.
Teacher: "These estimates are so different. I'm not sure who is the
closest. So, I am going to give you some things to help you come up with
a closer estimate."
The teacher passes out to each group 1 sheet of 9" X 11" black
construction paper, magnifying glasses, calculator, and 1 toothpick per
student. The teacher then drops 1/8 tsp. of gold glitter onto each group's
black paper.
Teacher: "On this paper I am giving to each group, I am going to sprinkle
1/8 tsp. of gold glitter. These will be our stars to study. Your magnifying
glass will be your telescope."
Teacher: "Now, with your group, I want you to get a close estimate
on the 1/8 tsp. of stars that you have on your paper. Raise your hand when
your group is finished."
Teacher calls on each group when they are all finished for their estimates.
Record them on the overhead.
Teacher: "Why do you think that each group came close to the same amount
of gold stars?" (Because each group got 1/8 tsp. of glitter and it
is not as many as in the whole container.)
Teacher: "Now that we have come up with a close estimate on the 1/8
tsp. of stars, let's average the numbers to come up with one number to work
with as the closest estimate."
Teacher uses the overhead calculator and demonstrates adding up the numbers
and then dividing it by the number of groups in the class. Encourage the
students to use the calculators with you.
Teacher: "There, our number is _________."
Teacher: "Now, let's count together how many 1/8 tsp. of glitter there
are in the container. (Make sure you count the ones given to each group.)
Teacher: "In your group I want you to use these numbers and come up
with a way to figure out how many specks of glitter are in this container."
(hold up the container)
Teacher rotates to each group to assess their progress. When the groups
are finished ask for how they solved the problem.
When the groups appear finished ask: Teacher: "Tell me, giving a close
estimate, how many specks of glitter can this container hold?" (Accept
answers. If one group is way off from the others calculate their figures
on the overhead calculator. Encourage them to calculate with you. Record
each group's second estimates on the chalkboard next to their original estimate.)
Teacher: "What can you understand by looking at your two estimates?
Interpret this information, please." (The original estimates are varied.
The second estimates from each group are closer in amount than the first
estimates. This means we are closer to the real number and have made a better
estimate.)
IF the students do not note the differences tell them.
Teacher goes to each group at this point and collects the glitter on the
black paper.
Teacher: "The stars in our solar system are more numerous than this
gold glitter. How do you suppose astronomers count stars?" (Estimating)
Teacher: "What makes stars even more difficult to count is because
new stars are always being born while others are dying. Some stars are so
far away they are not easily seen.
Ask a student to erase the chalkboard.
Teacher has helpers assist in passing out math journals.
Teacher: "Now we are going to learn of other ways to make a close estimate.
Each time you hear of a way that will help you get a closer estimate on
this program, The Eddy Files, I want you to write down how they estimated
in your math journal.
Teacher: "I want you to take time right now to explain in your journal
what we are doing." (Give students time to write in their math journals.)
Teacher: "Who would like to share what they wrote?"
Allow adequate sharing time.
BEGIN (FAST FORWARD to counter 320 when Ms. Toliver
enters the classroom in an Egyptian outfit).
PAUSE when Eddie says, "What a way to start a math class!"
Teacher: "Jot down in your math journal how many cat biscuits you think
are in Ms. Toliver's bin. (Pause) Would anyone like to share their estimate?"
Allow time for students to share and record estimates on the chalkboard.
Teacher: "How did they estimate?" (guessing by looking)
Teacher: "Let's write in our journal guessing by looking as the first
method you found."
Allow time to write in math journals.
RESUME.
PAUSE when Ms. Toliver says, "I'm not still quite sure whether
you are actually close so I brought some things to make a better estimate."
Teacher: "Our estimates and the students in Ms. Toliver's class estimates
are so very different. What would help make our estimates closer to the
correct number of cat biscuits?" Let's brainstorm and I'll write down
your ideas on the board."
Allow time for students to make suggestions on how to come up with a close
estimate.
Teacher: "Let's see how Ms. Toliver's class came up with an estimate."
RESUME.
PAUSE when Eddie says, "Jeanette delegated responsibility to
her partners." Teacher: "What is the class doing but are going
about it differently?" (counting)
Teacher: "Will counting the biscuits in the small bin help to get a
close estimate?" (Maybe, if we knew how many small bins fit into the
larger bin)
Teacher: "Let's write down counting because it is an important part
of making a close estimate."
PAUSE when Eddie says, "Brandon used the little bin in the big
bin trick."
Teacher: "How would Brandon's plan help everyone get a closer estimate?"
(You can figure out how many little bins it takes to fill the big bin and
then multiply that by how many biscuits you counted in the small bin.)
Allow time for students to write down count how many little bins fit in
the large bin and then multiply the number of biscuits in the little bin
by the number of little bins that fit into the larger bin.
RESUME.
PAUSE when Ms. Toliver says, "Okay, your strategy worked!"
Teacher: "Would Pedro's plan have worked without the help of Brandon's
plan of using the little bin in the big bin idea?" (No, it would have
taken a lot longer and would be difficult to keep count.)
Teacher: "Eddie is given a difficult assignment. Let's see if we can
discover another way that would help Eddie make a close estimate."
RESUME.
PAUSE when Eddie says, "Everywhere I looked there was nothing
but dogs!"
Teacher: "What is Eddie attempting to do?" (Count all the dogs
in New York City.)
Teacher: "Do you think his plan is going to work?" (No) "Why?"
(because there are so many)
Teacher: "Will the little bin in the big bin work for Eddie?"
(answers may vary) "Why or why not?" (answers may vary)
Teacher: "What do you think Eddie will do? Write down a plan in your
math journal that you think Eddie will try."
While students are writing their plan fast forward the video to ...
FAST FORWARD to (by 12 counters) when the camera focuses on a store
and an elderly man with a beard named Vincent. Eddie says," ... so
I stopped by to get some film and get some advise."
Allow time for students to share their ideas.
RESUME at the point to which you Fast Forwarded..
PAUSE when Vincent says, "What they do, Eddie, is estimate.
They take what they know and make a smart guess."
Teacher: "So, what does Eddie know so far?" (He can count a smaller
fraction of the whole)
Teacher: "What does Eddie need to do? Write in your journal what you
think Eddie needs to know." (Accept reasonable answers)
While the students are writing in their journals fast forward ...
FAST FORWARD (by 78 counters) to when you see heavy city traffic
and then you see a bus. Next you see Eddie's tally sheet. Eddie says, "So
there I was on the bus counting dogs."
Allow time for students to share their ideas.
RESUME.
PAUSE when Eddie says, "It's like what Ms. T. and Vincent said;
they estimate they make a smart guess."
Teacher: "Based on what you now know about estimation, what do you
think Eddie should do?" (take a smaller portion of a city, neighborhood
street or apartment building, and figure out how many dogs are there.) Accept
reasonable answers. This answer given does not complete the problem. It
is only the first step.
Teacher: "Let's see what plan Eddie uses."
RESUME.
STOP when Ms. Toliver says, "That's a wonderful estimate."
Teacher: "Write in your journal Eddie's plan for estimating the dogs
in New York City."
Allow sharing time.
Teacher: "How was Eddie's plan like the little bin in the big bin idea?"
(He took count in a small population and drew conclusions from the whole.
Teacher: "How was it different from the little bin in the big bin idea?"
(The number would be constantly changing. It was much bigger.)
We just saw how Eddie took what he could find out about the
number of dogs and people in his apartment. He took a small part of New
York City and made it relevant to the whole City of New York. He found that
there were 103 people and 5 dogs in his apartment building. For every 20
people there was 1 dog. He found out that there were 7,000,000 people in
New York City. He divided all the people in New York by the 20 people that
would have one dog and came up with a close estimate.
Teacher: "This is random sampling because not all apartments would
have the same number of dogs. It is a good way, though, to get an idea of
about how many dogs there are."
Teacher: "We are going to do some heavenly close estimating. I want
you to take what you have learned on how to make a good close estimate and
find out how many moons are in this box of Magic Mix cereal."
Teacher holds up the box so the class can see the size of the box.
Teacher: "It would take too long to try to pick all of them out. Like
Ms. Toliver, I want a close estimate so I am going to shake this box up
real good so that nothing is settled to the bottom of the box. I am going
to give each group a cup of cereal to help you make a close estimate."
Teacher scoops out 1 small cup of cereal to each group.
Teacher leaves the cereal box, 1 small cup, and the cereal in a 5 quart
ice cream tub on a table easily accessible for student use in measuring
the contents.
Teacher: "You may only send one representative from your group to investigate
the cereal box at this table. Make sure that person knows what they need
to find out before they go to the table."
Teacher rotates groups to assess progress and understanding.
Teacher: "Share your estimate and explain how you came up with your
answer."
Take the time for each group to share their results. Tell them the exact
number in the box so that they can compare the exact number with their estimated
number.
Teacher: "A job well done! I feel good about your estimates. Do you?"
(yes)
Teacher: "Why do you feel good about your estimates?" (because
we took what we knew and made a smart guess)
The teacher may choose to do more estimating by estimating the number of
stars. The students may be anxious to eat the cereal. Dispose with what
they have been handling and have a second box for consumption.
Activity 2
Before you begin this activity have some students help you prepare the
group materials and put them in piles on a table.
Teacher: "Eddie's friend, Vincent, told him that to make an estimate
you take what you know and make a smart guess."
Teacher: "So, if we want to make our solar system in correct proportion
in size and then space, we must take what we know and estimate making a
smart guess."
Teacher: "What do we need to know to make a model of the solar system
proportionate to the size of earth?" (how big each planet is in relation
to earth)
Teacher calls on each group to report the size of their planet.
Teacher puts up the overhead copy of chart 1A that the class did in the
background lesson section of this lesson plan.
Teacher: "So if we want Earth to be 6 millimeters, about how large
would Jupiter be? (Jupiter is about 10x bigger than Earth so it would be
about 60 mm.)
Teacher: "Here is a more difficult estimate to make. If earth is 6
mm, about how big would Mercury be?" (about 2 mm; Mercury is bigger
than our moon so that means it would be smaller than earth but bigger than
Pluto because Pluto is the smallest planet and it is smaller than our moon)
Teacher: "Using your information on your chart (1A), you are to create
a model of each planet, from clay, estimating the approximate size in relation
to the size we gave planet Earth, 6mm. Use grid sheet 1C. Each box stands
for one centimeter (1 cm = 10 mm). Transfer information on the size of the
planets from 1A to 1C. Color in how many millimeters each planet will be,
using chart 1A as your information sheet. Use your metric side of your ruler
and your grid sheet 1C to help you get close to the size you need."
Teacher: "You are to make each planet, from clay, the appropriate size
and color of a small version of that planet."
Teacher: "Before you begin, you will decide who is responsible for
making each planet. Help each other if you are confused."
Teacher calls for one representative from each group to get their pile of
materials that were prepared before the lesson.
Teacher: "Take your time to do a good job. Are there any questions?
(pause) You may begin."
Teacher assists any group that is in need of help. Assess their understanding
by their product.
Teacher: "When you have completed your models lay them out in the correct
order from the sun on your group's black piece of construction paper."
Teacher: "Now, we are ready to make the sun. If the earth were the
size of a marble the sun would be the size of a beach ball."
Teacher calls on the class for an assistant and their ruler.
Teacher holds the pee wee marble for the student to measure the diameter.
(15 mm. This is nearly 2x the size of earth in our model.)
Teacher holds a beach ball for the student to measure the diameter. It may
help to hold a ruler straight out from each end to help the student measure.
Teacher asks the student to assist in measuring the diameter of the beach
ball. (approximately 45 cm.)
Teacher: "If earth were a marble and the sun a beachball and I wanted
to make the earth smaller than the marble, would the sun be larger or smaller
than the beach ball?" (smaller than the beach ball about 1/2 its size;
23 cm.)
Teacher: "So, we need the sun smaller than a beach ball but about half
the size of a beach ball. Right?" (yes)
Teacher: "That would be a lot of clay so I will pass out 3 paper plates
for you to use as the sun."
Teacher: "I will demonstrate how to make the sun for you."
Teacher follows the directions on ID.
Allow working time on the sun.
Teacher: "Now, it is time to calculate the distance of each planet
from the sun."
Teacher puts up transparency copy of 1B and passes out one copy of 1B to
each student.
Teacher: "Look at the chart 1B. What does it tell us." (the distance
of each planet from the sun)
Teacher: "Find Mercury. How far away from the sun, using centimeters
as our unit of measurement, would Mercury be?" (1/2 cm.)
Teacher: "Color in with your pencil 1/2 of the centimeter block."
Teacher quickly walks around while students are coloring to make sure they
are understanding the task.
Teacher: "Great! Now I want you to do the rest the same way."
Teacher assist students who need help.
Now is a good opportunity to reinforce subtraction if it is a need for your
students Example: Find the difference in distance between the Earth and
Saturn.
Teacher: "Now, let's look at our model sun. Each one of the hangers
extending from the sun is a holder for a planet."
Teacher: "You are to measure the distance from the sun that each planet
should be if we measured by centimeters."
Teacher: "Place your clay model on the wire. Label and tape the planet
name onto the hanger as your holder for the label, too."
Teacher: "You will need the hanger extensions for three of the planets.
Make sure you measure the extension so you can match it up with the planet
with that distance. Attach the extensions with the ties. The extensions
should overlap all of the hanger to the sun. Attach the extensions at the
sun not at the end of the "rays".
Teacher: "Are there any questions? pause "You may begin putting
your planets in orbit." Teacher rotates each group to assist groups
that are in need and to assess understanding of the assignment and content.
Teacher: "Now, you need to label each planet using the strips of index
cards and tape. Attach the planet's name to the orbit stick."
Assess progress the class is making. Help groups in need.
- Take the students on a field experience to the Museum of Science and
History/Planetarium Program. Encourage students to collect more data on
their planet.
- Invite an astronomer into your classroom to share their knowledge
of the solar system and possibly to set up one evening's viewing of the
sky through his/her telescope.
Comparing and contrasting using Venn diagrams -
Using a three ring Venn diagram choose three topics of interest from off
your chart 1A. Examples: has rings, has moons, smaller than earth, larger
than earth, colder than earth, and hotter than earth. Fill in the planets
that fit each circle. If they fit more than one circle make sure they are
in the appropriate overlapping intersection of the circles. Write a paragraph
about the likeness and differences of these planets using information on
the venn diagram. (see pattern)
Weekly estimating -
Have the students to bring in a baggy of objects up to 100. Example: noodles,
pins, buttons, paper clips, cereal, etc. ... Put an amount in a jar each
week. Have the children make estimates on small post its. Assign two students
to count the items at the end of the week. Compare the estimates. The student
with the closest estimate prepares the jar for the next week.
A far out classroom -
Create paper mache' models of the solar system in the classroom. Use the
same process as Activity 2 but change the unit for earth to 1 centimeter.
Hang from the ceiling spacing out the solar system using decimeters or feet
as the unit of measurement instead of cm. Add color by spray painting or
tempera. Add physical features to the planet to make them realistic.
Heavens above -
Have the students make paper chains out of black paper. Estimate how long
you need it to loop it every meter to the ceiling around the room in your
choice of pattern.
Gazing at the stars -
Using pre-cut stars allow the students to create constellations on brown
butcher paper connecting the stars to form the picture. Mount to the ceiling
with thumbtacks.
The talking stick -
In integrating the fourth grade curriculum or if you choose to study the
multicultural heritage of the Native Americans, you may wish to write stories
about the constellations. Have the students write a story and practice telling
it at home before they tell it in the classroom. Have the students share
their stories under the stars in a circle as a talking stick is passed around
the circle.
Nighttime stories - Read Native American literature about the universe
to the class during cool downtime after outside play. Allow the students
to lay on the floor under the stars as you read to them aloud.
Star viewing hot chocolate - During one of your night time - story
read-aloud times, allow students, in an assembly line fashion, to estimate
measurements to make hot chocolate, i.e., A chunk of Nestle's hot chocolate
mix, a finger gathering of marshmallows, and some hot water (warm), stir.
Sit back and listen to the story.
Intergalactic hop scotch - Allow student to draw, on the outside
courts, the solar system with chalk. Have them line up the planets to where
they are not too far apart to hop from one to the other. If they know the
number of moons allow them to add them to their game. You stand on the sun
to begin the game. Just like in hopscotch, you through your rock onto Mercury.
You hop on one foot over that planet with the rock to the next planet, all
the way to Pluto and back packing up your marker on the way back. You then
throw your marker to Venus. The next player is not allowed to hop onto a
planet that is occupied with a rock. They must hop over it. If the planet
has a moon, you may detour to a moon to rest before hopping to the next
planet.
Who's moving? - Make an astrolab. See pattern on 1C. Attach a straw
with tape to the side that is marked O. Attach string, with a washer attached
to it, at the upper point of the angle. Go out and find a star. Look through
the straw at the star. Hold the string in place with your hand and read
the degrees on the astrolab. Go out an hour later. Stand in the same place,
find the same star, take a reading and see if the star has moved.
Who's hot and who's cold? - Using information sheet 1A graph the
hottest temperatures for each planet. Connect the dots with red crayon and
a ruler. Go back and record the coldest temperatures on each planet. Connect
the dots with blue crayon and a ruler. Which planet has the widest range
in temperatures? Which has the closest?
Master Teacher: Mary Michael Smith
WJCT
NOTE TO TEACHER
Background Information:
Before your students can estimate to a small scale the relative size and
spacing of each planet in its orbit, they must have gathered information
on planetary size and distance from the sun.
To build the background for this lesson, teach the class how to gather the
information they need for the planet Earth using Scott Foresman, grade 4,
Discover the Wonder Module A chapter 1 or resource books on planets and
the sun. Use the information gathering chart 1A to record data. Use the
text as if it were a reference book.
After teaching the students HOW to gather information, divide the class
into 8 groups. Each group is assigned a planet, with the exception of Earth,
to research. Each group forms a circle and reads the material together,
from chapter 2 of Discover the Wonder module A, exploring and recording
the valuable information needed onto chart 1A. There is room for them to
record information that they feel is significant that is not covered on
the table. For those that finish a few minutes early they may try to record
information, on the size of the sun in relation to the earth, using library
books set up on display.
Have each group draw a picture of their planet giving it human features
but maintaining its individuality by illustrating its specific characteristics.
Give the opportunity for each group to share the special characteristics
of their planet and their drawing. Each group will transfer their information
collected on their chart 1A onto an overhead transparency at their fingertips
for further lessons.
Because space and the objects in our solar system are so big, it is important
for the students to understand that astronomers do not count the stars or
go out and measure the solar system with measuring tape. It is important
that they understand how these numerical figures are collected so they can
conceptualize just how big our solar system really is.
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