How Good is Estimation? - Pre-Assessment
Name:
1. Estimate the area and perimeter of the island below. Make sure to include your work
to show your process.
Area:
Perimeter:
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 each
the formula is used for in the right column.
A/P
Shape?
A/P
Shape?
2
2(b+h)
b*h
½(b*h)
2πr
½(b1+b2)*h
πr
2
4*s
s
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
inches
in
square miles
sq. yd.
How Good is Estimation?
2
acres
square feet
feet
meters
yards
cm
millimeters
kilometers
2
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How Good is Estimation - Notes
Name:
Estimation –
Precision –
What are some examples of situations in which estimation is a sufficient measurement?
What are some examples of situations in which estimation is not a sufficient
measurement?
What are some strategies for estimating measurements?
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?
Which do you think is used more in daily life? Explain your reasoning
How Good is Estimation?
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Creating a budget for replacing carpet in a room. Buying paint to repaint a house.
A person’s weight for a small craft airplane.
A person’s height for amusement park rides.
Buying an area rug for the living room.
Buying new tiles for the bathroom floor.
Buying new tiles for the kitchen back splash.
The sod needed for the new sports field.
The grass seed needed for a new lawn.
The number of items in a jar for a contest.
The amount of fabric needed for a pattern.
The number of cookies that will fit on a sheet.
Mechanic rebuilding an engine.
The size of parking spot when parking a car.
The size of a pizza when working at a pizza
Putting up wallpaper in a room.
place.
Putting wallpaper border up in a room.
The wood needed for a frame for a painting.
The amount of canvas to stretch for a painting.
The amount of wood needed for crown molding.
The size of a hot tub cover
The wrapping paper needed for a present.
Pharmacist filling a prescription.
The amount of ribbon needed for a gift.
The distance of one lap around a lake, for
The size of pegboard needed to hang your tools
training
Measurements when framing a house
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Building cabinets for a kitchen.
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How Good is Estimation?
Name:
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.
7) How would your answers have changed if you had traced your hand with your fingers
together?
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How Good is Estimation?
Name:
Hand Land Activity: Part 2
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?
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.
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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?
7) How would your estimation change if we reduced the map on a copy machine?
8) What change would you have to make if your country split into smaller countries, like
the USSR did in 1991?
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How Good is Estimation?
Hand Land Activity: Part 3
Name:
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 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.
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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?
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.
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.
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Scenario A: This land is your land, this land is my land…
Your rich uncle has recently died. He
four relatives) as an inheritance. His
among family members so that each
other pieces. Describe the plan you
measuring and dividing the land.
has left a piece of land in the woods to you (and
will has one condition. The land must be divided
piece has equal area and equal perimeter to all
would suggest to the other family members for
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 ________ (smallest unit)
b. Roughly calculating, then rounding appropriately up or down
c. Estimation by comparison
d. Estimation by rounding measurements to easy numbers
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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
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Russia is the largest country in the world with an area of about 17 million km2. 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
2
Armenia
1,254
km
28,400 km
2
Azerbaijan
2,813 km
86,100 km
2
Belarus
3,098 km
207,600 km
2
Estonia
4,427 km
43,211 km
2
Georgia
1,771 km
69,700 km
2
Kazakhstan
14,976 km
2,669,800 km
2
Kyrgyzstan
3,878 km
191,300 km
2
Latvia
1,681 km
64,589 km
2
Lithuania
1,372 km
65,200 km
2
Moldova
1,389 km
33,371 km
2
Russia
57,570 km
16,995,800 km
2
Tajikistan
3,651 km
142,700 km
2
Turkmenistan 488,100 km
5,504 km
2
Ukraine
7,340 km
603,700 km
2
Uzbekistan
6,641 km
425,400 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
How Good is Estimation?
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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.
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
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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.
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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
he that a football field is 160 feet wide and 360 feet long with 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 ________ (smallest unit)
b. Roughly calculating, then rounding appropriately up or down
c. Estimation by comparison
d. Estimation by rounding measurements to easy numbers
How Good is Estimation?
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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.
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 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.
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
How Good is Estimation?
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