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A RELATIVELY FAR OUT IDEA: ESTIMATING
Grades 4 - 5

Overview

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.
ITV Series
Eddie Files* #2: Estimating: Going To The Dogs
*a multicultural series featuring characters from diverse cultural backgrounds
Learning Objectives
Students will be able to:
Materials
For class:
Previewing and Activity 1
Activity 2

For each group:
Previewing and Activity 1
Activity 2

For each student:
Previewing and Activity 1
Activity 2
Pre-Viewing Activities
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.
Focus Viewing
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.

Viewing Activities
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.)
Post-Viewing Activities
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.
Action Plan
Extensions
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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