how good is estimation - k12.wa.us good is estimation? ... there is a short story by leo tolstoy...

How Good is Estimation? Teaching Notes

Objective: This lesson develops the idea of estimation in measurement as it pertains to perimeter and area. TC-1 Pre-Assessment: The purpose of this activity is to gather information that will guide planning for the remainder of the lesson. It may be used formally as a “quiz” given pre- and post-lesson or informally as a warm-up that begins the conversation. If possible, it would be nice to give the pre-assessment in advance in order to help plan the lesson accordingly. Be careful not to demand correct answers on this part of the lesson. Let students get their thoughts out and then refine them throughout the lesson.

TC-2 Teacher-led Discussion: Estimation vs. Precision: The purpose of this portion of the lesson is to make sure that all students have an accurate understanding of estimation and precision. Discuss answers to pre-assessment, if not already done. A note-taking sheet has been provided, but may be replaced by whatever is common practice in the classroom. Be sure to define estimation and precision, including that estimation is not calculating and then rounding. The bottom half of the note sheet is intended to be a place for students to summarize their understanding after the next activity. However, it could also be used here to help facilitate discussion.

Here are some questions you may want to ask:

• What do you already know about estimation? When is it used? When is it not used? What strategies help you accomplish the task?

• What do you already know about precision? How do you know how precise you

need to be or can be in a situation?

• What do you already know about measurement? What units are you familiar with? How do they relate to finding the area and perimeter?

There is a short story by Leo Tolstoy called “How Much Land Does a Man Need?” that might be fun to share with students at this point. “After slowly accumulating more and more property, a greedy Russian peasant visits the Bashkirs upon hearing that they are practically giving their land away. They offer him as much land as he wants, provided he can walk its perimeter in one day. The peasant agrees and goes out on his trek but when the sun starts to set, he finds he has walked too far. Running back, the peasant collapses at the starting point just as the sun disappears behind the horizon. The Bashkirs try to congratulate him only to find him dead. In answer to the question posed in the title, the Bashkirs bury him in a hole six feet tall by two feet wide.” http://en.wikipedia.org/wiki/How_Much_Land_Does_a_Man_Need%3F

How Good is Estimation? Teacher Materials of 23

http://en.wikipedia.org/wiki/Bashkirs

http://en.wikipedia.org/wiki/How_Much_Land_Does_a_Man_Need%3F

TC-3 When to Estimate Brainstorm: The purpose of this activity is to help students to begin to talk about their ideas of estimation and its appropriateness, as well as strategies used to estimate and to choose appropriate units. Different situations have been provided that require various levels of precision and estimation strategies. There are several options for this activity depending on the needs of students and the teacher’s comfort with small group strategies. The recommended option is to use the “Fortune Cookie” activity outlined below in the answer pages. Another option is to have students do a “think, pair, share”. For this option, students look at the list of situations and think to themselves whether each would need to be measured accurately or could be estimated. For the items that could be estimated, ask students to decide if they should over or under estimate. After thinking about each item alone, students should pair up to work with a partner to come to an agreed upon answer. It might be helpful for some students to use a table or Venn diagram to help them organize their choices. Then pairs would share out to the class. Finally, the teacher could lead a class discussion going through selected situations. In addition to talking about estimation, it might be helpful to include a discussion about whether area, perimeter or volume was being estimated or measured. After completing the brainstorm activity, the bottom half of the note sheet is designed as a place for students to summarize what they heard during the class discussion. It is important, as the teacher, to facilitate student responses through questioning and avoid just telling students the right answer. TC-5 Hand Land Activity: There are several starting and stopping points in this activity so it can be altered to meet the needs of the student. Students will be using a variety of resources to estimate the area and perimeter of real and imaginary places. Students will also begin to work on enlargements, reductions and division of shapes and how it affects estimation of measurements and choice of unit.

TC-6 Part 1: Materials: White 8 ½” x 11” paper, String, Rulers with U.S. and Metric systems, Several copies of different sized grids on transparency sheets Directions: Students will trace their hands, fingers spread on the white paper. This activity may need to be modeled for lower level students. Higher-level students should need less direction/scaffolding or part one could be skipped altogether. Using the string students should be able to calculate the perimeter of their hand. Then by laying different sized grids (starting with large, working to small) over the hand, they will come up with more and more precise estimations. For lower-level students, recommend that they color in the complete square or write the corresponding counting number in the square as they count to help them keep track. Pay special attention to the students’ use of units and scale. When most students are finished, provide an opportunity for students to share their methods for improving the estimation of Hand Land and discuss the last few questions on the activity page. For question seven, lower-level students may also need to repeat the process with their fingers open.


TC-7 Part 2: Materials: String, rulers with U.S. and Metric systems, several copies of different sized grids on transparency sheets (provided), copies of maps of different countries (or states), and population data (internet site provided). This part could be time intensive to prep. Internet resources have been provided to help ease the burden and your school librarian should also be able to help. It is important when making photocopies to ensure that the maps maintain their scale. Also it is recommended to use maps that are all in the same system of measurement in order that students are not required to convert between measurement systems. The metric system would probably be the best choice because it is easier to find area of countries that are listed in square kilometers. Directions: This activity is designed to be done in partners, but could be done individually or in small groups. It is important that students get to choose a country in order to increase engagement. Also it is important to allow students to switch once if they decide they would rather do another country. They should include their reason for the switch in their answer to the first question. Students will start to notice that some countries are harder to estimate. It is also important that the first estimation be done without any tools. This will help students see how precise estimation by sight is and will help with their ability to visualize the actual area at the end of the activity. This activity is intentionally very open, giving students the opportunity to be more independent. The purpose is for students to apply what they have learned by estimating in the Hand activity to a real country. Lower-level students may need more support similar to part 1. Step 4 on the activity page serves as an opportunity for the teacher to check understanding. Before allowing the students to move on, the teacher should check to see that they completed a quality estimation and have included appropriate units for both perimeter and area. A station could be set up in the classroom for students to access the information needed to complete the activity, freeing the teacher to move around the classroom assisting students in need. When students have finished this activity, it would be valuable to have partners talk about their estimation process and how it compared to the actual area of their country. This would also be a good time to have a class discussion about the last few questions in the activity and clear up any misunderstandings about perimeter and area. Student born after 1991 may need some historical background to the break up of the USSR.


TC-8 Part 3: Materials: population data, population density map such as the Earth by Night map. This activity extends the idea of area of land to population density. It gives students the opportunity to visualize the amount of land available per person in some countries. The amount of area for question 3 might be quite large, so either have students complete their taped region in a large room, such as a gym, cafeteria, or field, or have them scale their region to a manageable size. It also might be helpful to compare the amount of land per person to something they can visualize, such as how many football fields per person. Directions: See student sheet or answer key. This could be done individually in pairs or in small groups.

TC-9 Scenarios: The following may be done as a station rotation activity, a peer teaching opportunity, or as full class discussions. Any combination of the scenarios may be used to meet the specific needs of students. I recommend that you read them all carefully to make sure the combination you choose covers all the necessary parts of the GLE. All scenarios ask student to determine the required level of precision. Below is a table outlining the topics, difficulty level and suggestions for modifications. This part of the lesson lends itself well to opportunities for formative assessment. As students are working, be sure to wander around listening to student discussion and asking questions of students to further their understanding. The scenarios could also be made into a packet and used as homework problems or given weekly as Problems of the Week. They could also be used as an alternate form of summative assessment.


Concept; Subject Difficulty Level Modications/Considerations

Scenario A

Area, Division of Land, Scale, Reasoning;

Inheritance

Average to Difficult Easier: Change (or model) problem to include just two or three people or make shape

easier. Harder: Add in more conditions

to the splitting of the land. Watch for proper use of the

scale of the map. Scenario

B Area, Perimeter,

Scale, Conversion within system;

Sewing

Easy to Average Easier: Provide a diagram Harder: Challenge students

with making a postcard as well. Students may need help with

conversions. Scenario

C Area, Perimeter, Percentage of

whole, Reasoning; History/Geography

Easy to Average Easier: Provide an old and new map to help students visualize.

Some students might need some historical background for this problem to make sense.

Scenario D

Area, Reasoning; Home Appraising

Average Easier: Lower-level students may need help developing a

method to find the area. What do you do with closet space? Wall width? Etc. They also

may need support averaging. Scenario

E Area, Perimeter, Division of Land,

Doubling, Spacing, Reasoning;

Agriculture, Sports

Difficult Easier: Maybe only assign parts of this one or this could be a good full class scenario. Providing the diagrams would

also make it easier. Scenario

F Area, Reasoning;

Sports Easy to Average Harder: Add to the problem to

require conversions within a measurement system.

TC-10 Assessment and summary: A discussion at the end of the lesson to have students share what they learned and to summarize objectives is important. The following are some questions you might ask:

• What do we now know about estimation? • In general, how do we determine when to estimate and when to measure

precisely? • How does the unit we choose impact our precision and estimation?

Assessments are included and contain multiple-choice items (6), short answer items (3) and extended response items (1). Answer Key for Student Pages follows.


How Good is Estimation? - Pre-Assessment Name: Answer Key 1. Estimate the area and perimeter of the island below. Make sure to include your work

to show your process. Area: ~16 sq. miles Perimeter: ~17 miles

2. Below is a list of formulas used to calculate area and perimeter. Distinguish which formulas are used for area by putting an A in front of the formula and those used to find perimeter by putting a P in front of the formula. Then write the name of the shape the formula each is used for after the formula.

A / P Shape? A / P Shape?

A πr2 Circle P 2(b+h) Rectangle

A b*h Rectangle/Parallelogram A ½(b*h) Triangle

P 2πr Circle A ½(b1+b2)*h Trapezoid

A s2 Square P 4*s Square

3. Circle the units that would be appropriate to use to measure area. Underline the units that would be appropriate to use to measure perimeter. kilometers miles acres square feet feet inches in2 meters yards cm square miles sq. yd. millimeters kilometers2


How Good is Estimation - Notes Name: Estimation – The process of finding an approximate measurement without exact calculation Precision – An indication of how finely a measurement is made; related to the unit of measurement and the calibration of the tool. What are some examples of situations in which estimation is a sufficient measurement? Answers will vary. Hopefully, students list some of the situations from the activity. What are some examples of situations in which estimation is not a sufficient measurement? Answers will vary. Hopefully, students list some of the situations from the activity. What are some strategies for estimating measurements? Possible answers:

Comparison to another object Taking rough measurements Measuring a piece and then extending it to the whole

Why do different situations require different levels of precision? In other words, why is it sufficient to estimate at times and at other times we need to take precise measurements? It depends on what the measurement is used for and the importance of accuracy. If the consequences of an error would be harmful or expensive then a more precise measurement would be needed. Which do you think is used more in daily life? Explain your reasoning. Daily we estimate far more often than we measure with precision. Also an estimation should always be part of an measurement in order to determine the reasonableness of the calculated answer.


TC-11 Fortune Cookie Activity: For this activity, each student pulls out a slip of paper from a “container” and responds to what is written. Preparation: The resource page provided lists several situations involving perimeter, area, and measurement of length. Feel free to add to the list as you prepare, especially including student responses from the pre-assessment, if time allows. Cut the situation resource page into strips containing one situation each. Put all of the strips into a container such as a small bucket or a hat. Directions: Each student will pull a slip of paper out of the container and read the situation aloud to the class. Then pause for one minute to give everyone a chance to think about the following two questions: 1) Is this a situation that would require precision or would estimation be appropriate? 2) What would be an appropriate measurement strategy? After the one-minute pause, the person that pulled the piece of paper out of the “container” will share their answer to the questions.

At this point the teacher has several options. They may want to stop after each person and allow a short class discussion to occur before passing the container to the next student. Or the teacher direct the container to be passed to the next person and only they are allow to respond before pulling their own slip of paper. A third option is to allow each person to respond to any prior situation before pulling his or her slip of paper. Whatever discussion process is used, the activity continues until all students have had the opportunity to pull a situation and respond. At the end of the activity, it is a good idea to have a discussion to summarize understanding and share generalizations.


Creating a budget for replacing carpet in a room.

Estimate

Buying paint to repaint a house. Estimate

A person’s weight for a small craft airplane. Precise Measurement

A person’s height for amusement park rides.

Estimate

Buying an area rug for the living room. Estimate

Buying new tiles for the bathroom floor. Precise Measurement, then buy extra

Buying new tiles for the kitchen back splash. Precise Measurement, then buy extra

The sod needed for the new sports field. Precise Measurement, then buy extra

The grass seed needed for a new lawn. Estimate

The number of items in a jar for a contest. Estimate

The amount of fabric needed for a pattern. Precise Measurement, then buy extra

The number of cookies that will fit on a sheet.

Estimate

Mechanic rebuilding an engine. Precise Measurement

The size of parking spot when parking a car.

Estimate

The size of a pizza when working at a pizza place.

Estimate

Putting up wallpaper in a room. Estimate

Putting wallpaper border up in a room. Precise Measurement, then buy extra

The wood needed for a frame for a painting.

Precise Measurement

The amount of canvas to stretch for a painting. Estimate

The amount of wood needed for crown molding.

Precise Measurement

The size of a hot tub cover Precise Measurement

The wrapping paper needed for a present. Estimate

Pharmacist filling a prescription. Precise Measurement

The amount of ribbon needed for a gift. Estimate


The distance of one lap around a lake, for training

Precise Measurement?

The size of pegboard needed to hang your tools Estimate

Measurements when framing a house Estimate

Building cabinets for a kitchen. Precise Measurement


How Good is Estimation? Name: Answer Key Hand Land Activity: Part 1 1) Trace your hand in the middle of an 8 ½” x 11” piece of paper, spreading your

fingers as wide as you can. Keep your arm as close to perpendicular to the table as possible so you can trace the bottom of your hand.

2) Use the string provided to measure the perimeter of your hand. Record the length

here, making sure to include the units you used.

Perimeter of Hand Land: ____________ 3) Obtain a 1” square grid transparency and lay it on top of your hand drawing. 4) Use a wet erase marker to retrace your hand onto the transparency.

a) Count the number of complete squares inside your hand: ___________ b) Count the number of partial squares inside your hand: _____________ c) Divide the number of partial square inside your hand by 2: __________ d) Add line a) and line c) to get the estimation of the area: ____________ e) What is the unit for the area you found in d)? _____________________

5) Is this a good estimation method? Why or why not? 6) How could you improve your estimation? Write your improvement plan and then ask

your teacher for the necessary tools to complete your second estimation. Record your process in the space below and be ready to share your results with the class.

Look for answers that include using a smaller grid. 7) How would your answers have changed if you had traced your hand with your

fingers together? Same area, smaller perimeter. Lower-level students may need to repeat the activity with their fingers together.

How Good is Estimation? Teacher Notes and Answer Key of 23

How Good is Estimation? Name: Answer Key Hand Land Activity: Part 2 Make sure when copying maps that the appropriate scale is maintained. 1) With a partner, choose a country that you would like to investigate. Obtain map from

your teacher. Name of the country: Why did you choose this country? If students switch countries, they should note why here. 2) Before doing any measurements, estimate the total area and perimeter of your

country without any tools. Be sure to include units. Area: Perimeter: 3) Using what you learned in Part 1, get a better estimation of the area and perimeter of

your country by using tools. Show your process below using words, numbers and pictures to communicate your thinking. Make sure to include the unit and scale you chose.

Make sure that the process outlined is complete. Use questions to help students fully communicate their thinking.


4) Show your estimation work to your teacher. Then obtain information about the

actual area of your country. Compare your two estimations to the actual area. 5) Find another country with a similar area to your country. How do their perimeters

compare? Compare and contrast other facts you know about the two countries. What role do perimeter and area play in what you know about the countries?

6) How would your estimation change if we enlarged the map on a copy machine? It would be easier to fit our grids. It might be harder to keep track of squares. Watch out for answers that say that the area would be bigger. 7) How would your estimation change if we reduced the map on a copy machine? There would be more partial squares and it would be harder to get a precise measurement. Watch out for answers that say that the area would be smaller. 8) What change would you have to make if your country split into smaller countries, like

the USSR did in 1991? The perimeter would increase. The area of land is still the same just divided into smaller pieces. But now places that used to be on the interior are now borders.


How Good is Estimation? Name: Answer Key Hand Land Activity: Part 3 1) On the table below, record the names and the areas of eight of the countries your

classmates presented in the last activity. Then look up the total population for each and record your findings.

Country Total Area Total Population Population Density

2) Population Density is the amount of land available in a country per person. Calculate

this value for each country and record the amount on the table. 3) Choose one of the country’s population density to recreate. Estimate the size of a

square equal to the amount of space allotted per person in one of the countries listed above. Use painter’s tape to record your estimation.

4) Measure your estimation and compare the square to the actual amount of land per

person in the country you chose. 5) Write an argument for whether or not estimation is appropriate for this activity.


6) People do not always use the full amount of land available per person in population

density calculations. What are some factors that might lead to people being concentrated in certain areas?

Being near a border or a city may attract people that are involved in business. Natural resources such as water may concentrate people in certain areas. Harsh conditions or war torn regions may deter people from certain areas. Look at a world population density map. Pick one country that seems to not use their land fully. Give specific reasons why that might be and describe a process that you would use to recalculate the population density for that country. Answers will vary. 7) Some of your classmates are having a hard time understanding the data in this activity because they are not used to kilometers. Convert the area of one country to square yards or square feet. Use estimation to help your friends see the relationship between yards and meters and how they can help you visualize the area. Write out your explanation below. Students should first calculate kilometers to meters and then use the estimate of one meter is roughly one yard. Watch out for students that do the conversion linearly and do not keep in mind that area is in square units. This is a good opportunity to help students with conversions.


Scenario A: This land is your land, this land is my land… Your rich uncle has recently died. He has left a piece of land in the woods to you (and four relatives) as an inheritance. His will has one condition. The land must be divided between each family member so that each piece has equal area and equal perimeter to all other pieces. Describe the plan you would suggest to the other family members for measuring and dividing the land. After much discussion, your cousin Joe remembers that there used to be a map of your uncle’s land in a picture frame in his office. Joe disappears briefly and comes back holding the framed map. He takes off the frame to examine the map fully and everyone notices there is writing on the back. It is the second page of the will! There is another condition. The land must be split fairly so that every family member has access to a road and to the river. Does this change how the land should be divided? If so, explain what you proposed for the new division. If not, justify how your original plan meets both criteria.

This scenario required what level of precision? a. Accurately measuring to __foot?__ (smallest unit) b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison d. Estimation by rounding measurements to easy numbers


Scenario B – Oh say, can you see? In 1989, Washington State celebrated its 100th birthday. A special Centennial flag was created for the birthday parade, except this flag was 100 times bigger! It was made of green silk and trimmed with gold fringe on three sides. Below is a scale drawing of the standard-sized flag. Fabric is sold in widths of 45 inch or 60 inch. Then the customer specifies the length of the fabric needed in yards. Fringe is also sold by the yard. Write a plan below to recreate the Centennial flag. Use words, numbers and pictures to help communicate your thinking.

This scenario required what level of precision? a. Accurately measuring to ________ (smallest unit) b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison d. Estimation by rounding measurements to easy numbers


Scenario C – The Former Soviet Union Russia is the largest country in the world with an area of about 17 million square kilometers. But nearly 15% of the country is uninhabitable. About how much is uninhabitable? What impact do you think this uninhabitable land has on the country? Prior to 1991, Russia was a part of the USSR, which was even larger with a total area of 22,402,200 km2 and a perimeter of 62,710 km. The USSR divided into 15 different countries in 1991. The table below lists those countries that were formally part of the USSR and information about their areas and perimeter. Using the information from the table, which changed more for Russia, area or perimeter? Is this always the case when a shape is divided? Use the information to defend your reasoning. Country Area Perimeter Armenia 28,400 km2 1,254 km Azerbaijan 86,100 km2 2,813 km Belarus 207,600 km2 3,098 km Estonia 43,211 km2 4,427 km Georgia 69,700 km2 1,771 km Kazakhstan 2,669,800 km2 14,976 km Kyrgyzstan 191,300 km2 3,878 km Latvia 64,589 km2 1,681 km Lithuania 65,200 km2 1,372 km Moldova 33,371 km2 1,389 km Russia 16,995,800 km2 57,570 km Tajikistan 142,700 km2 3,651 km Turkmenistan 488,100 km2 5,504 km Ukraine 603,700 km2 7,340 km Uzbekistan 425,400 km2 6,641 km This scenario required what level of precision? a. Accurately measuring to ________ (smallest unit) b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison d. Estimation by rounding measurements to easy numbers


Scenario D – Home, Sweet Home When you buy a house, the bank that is providing your mortgage wants to find out if you are paying what the house is worth. So they hire someone to come and appraise the house. This process involves comparing the price of the house to the price of other similar houses that have sold recently. One of the key characteristics compared is size. Describe a method of calculating the size of a house that would be appropriate for appraising. The house you are considering is 1,200 square feet. A house a few blocks away sold for $150,000 and has 1,000 square feet. Another house, about a mile away and 1,500 square feet in area, sold for $200,000. Estimate how much you think the house that you are considering is worth. Explain your reasoning so that you can convince someone else what you believe. There are many ways to look at this question for this scenario. Should discuss. This scenario required what level of precision? a. Accurately measuring to ________ (smallest unit) b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison d. Estimation by rounding measurements to easy numbers


Scenario E - The Farmer in the Dell Farmer Dornhecker has 40 acres of land, a half a mile wide and an eighth of a mile in length. He grows corn, wheat (summer and winter harvest), and cabbage. Farmer Dornhecker and his wife have a house and a barn on a half an acre in the Southwest corner of the farm. He has divided the rest of his land into 5 equal fields, one for each crop and one to remain fallow (or unused) for a season. Draw a diagram of Farmer Dornhecker’s farm. About how many acres are used for each crop? (1 acre = 4,840 square feet and 1 mile = 5,280 feet) Farmer Dornhecker would like to double his farm. What do you think is meant by doubling his farm? Use diagrams to represent the multiple meanings. Then give an explanation of what plan you think the farmer should use and why.


Johnny Dornhecker, the farmer’s son, loves football. He would like to ask his father if they could convert part of their farm to a practice field for his team. Johnny knows that a football field is 160 feet wide and 360 feet long including a 10-yard end zone on each end of the field. Help Johnny prepare his case to his father. Make sure to include a diagram and how the football field will impact the amount of space for Farmer Dornhecker’s crops. Mrs. Dornhecker has a garden near their house. She would like to build a picket fence around the edge to keep the animals out. Her garden is 6 feet long by 8 feet wide and she would like to have the pickets in the fence 3 inches apart. About how many pickets will she need? Mrs. Dornhecker has 40 marigold plants to put around the perimeter to keep the slugs away. About how far apart must she plant them to cover the perimeter?

This scenario required what level of precision? a. Accurately measuring to _inch_ (smallest unit) for Mrs. Dornhecker b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison d. Estimation by rounding measurements to easy numbers


Scenario F: Let’s Play Ball You and your friends love to play soccer. One of your friends says that he lives near an empty grass field. He has never seen anyone at this lot and tells the group it would be a great place to play soccer. Describe how you would help your friends determine if this lot is a good place for your games.

This should be a rough estimation. Watch for students that only describe the type of ground (i.e. nice grass, flat) and leave out size. They also should mention the orientation of the field, and things to consider such as the road. According to the FIFA Laws of the Game, there are minimum and maximum sizes for a soccer field, but the length of the field must be always longer than the width. For a regular match, a field can be anywhere inside the following dimensions:

Width: minimum 45m (50 yds) maximum 90m (100 yds) Length: minimum 90m (100 yds) maximum 120m (130 yds)

For an international match between two countries, the dimensions are much more strict:

Width: minimum 64m (70 yds) maximum 75m (80 yds) Length: minimum 100 (110 yds) maximum 110m (120 yds)

Most soccer fields are 120 yards by 75 yards. If you are building a soccer field, remember to leave at least 10 yds on both sides so players can safely leave and enter the playing field without running into obstacles. http://www.ussoccerplayers.com/news_you_can_use/364234.html The field works out to be a perfect place for your informal soccer games, and the recent World Cup has made more and more people want to join your games. But one day while playing soccer at the field, a man drives up and tells you and your friends that you are trespassing on private property and will need to leave immediately. As you are packing up your stuff, you notice that the man is posting a sign in front of the lot. You decide to come


http://www.ussoccerplayers.com/news_you_can_use/364234.html

back later and check it out. Upon reading the sign, you find out that a rich man owns the land and is looking for good ideas about how to best use it. Proposals are due at midnight tonight and the land will be given to the best plan submitted. Write a proposal for the man to build permanent soccer fields for the youth of the city. Here students should be very complete and precise. This scenario required what level of precision? a. Accurately measuring to ___yard or meter___ (smallest unit) for the second part b. Roughly calculating, then rounding appropriately up or down c. Estimation by comparison for the first part d. Estimation by rounding measurements to easy number TC-12


how good is estimation - k12.wa.us good is estimation? ... there is a short story by leo tolstoy...

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