Transcript Estimating Sums and Differences

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Objective
Estimate sums and differences of
decimals
Vocabulary
Front-end estimation
Add or subtract the front digits
Vocabulary
Clustering
A form of estimating when all the addends
are close to the same number
Example 1 Use Estimation to Solve Problems
Example 2 Use Estimation to Solve Problems
Example 3 Use Front-End Estimation
Example 4 Use Clustering
POPULATION The table below shows the population
of the American colonies in 1770. Estimate the total
population of North Carolina and South Carolina.
Colony
Connecticut
Population
(thousands)
183.9
Colony
Population
(thousands)
New York
162.9
Delaware
35.5
North Carolina
197.2
Georgia
23.4
Pennsylvania
240.1
Maryland
202.6
Rhode Island
58.2
Massachusetts
235.3
South Carolina
124.2
New Hampshire
62.4
Virginia
447.0
New Jersey
North Carolina
South Carolina
117.4
197.2
124.2
Write colony then population
1/4
North Carolina
197.2
South Carolina
124.2
North Carolina
197.2
200
20
South Carolina
124.2
1
12
120
Round each number to the
nearest tens for easier adding
Remember: When add 1 to 9
it = 10 so place a 0 in the 9’s
place value and carry the 1
Annex a zero to hold the
one’s place value
Again, annex a zero to hold
the one’s place value
1/4
Add the numbers
North Carolina
200
South Carolina
+ 120
320
1/4
320
Colony
Connecticut
Population
(thousands)
183.9
Colony
Population
(thousands)
New York
162.9
Delaware
35.5
North Carolina
197.2
Georgia
23.4
Pennsylvania
240.1
Maryland
202.6
Rhode Island
58.2
Massachusetts
235.3
South Carolina
124.2
New Hampshire
62.4
Virginia
447.0
New Jersey
117.4
Answer: about 320 thousand
1/4
POPULATION The table below shows the population of
the American colonies in 1770. Estimate how many more
people were in Massachusetts than in Connecticut.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Answer: about 60 thousand more people
1/4
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
POPULATION The table below shows the population of
the American colonies in 1770. Estimate how many more
people lived in Rhode Island than in Georgia in 1770.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Rhode Island
Georgia
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
58.2
23.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
Write colony then population
2/4
Round each number to the
nearest ten for easier adding
and subtracting.
Rhode Island
58.2
Georgia
23.4
Rhode Island
58.2
Annex a zero to hold the
one’s place value
6
60
If less than 5, leave the place
value as is
Georgia
23.4
If 5 or greater, add 1 to the
rounding place value
Annex a zero to hold the
one’s place value
2
20
2/4
Rhode Island
Georgia
60
- 20
40
Need to find how many more
people lived in Rhode Island
than in Georgia
Decide what process?
Subtract
Numbers are Population
(thousands)
Answer: Rhode Island had 40 thousand more people
than Georgia
2/4
POPULATION The table below shows the population of
the American colonies in 1770. Estimate the total number
of people in Pennsylvania and New Jersey in 1770.
Colony
Connecticut
Delaware
Georgia
Maryland
Massachusetts
New Hampshire
New Jersey
Population
(thousands)
183.9
35.5
23.4
202.6
235.3
62.4
117.4
Colony
New York
North Carolina
Pennsylvania
Rhode Island
South Carolina
Virginia
Answer: 360 thousand people
2/4
Population
(thousands)
162.9
197.2
240.1
58.2
124.2
447.0
Estimate
14.8
+ 55.9
69
using front-end estimation.
Write the problem vertically
Add the front digits.
Then add the next digits.
Do not add the decimals
Answer: about 69
3/4
Estimate
using front-end estimation.
Answer: about 97
3/4
MULTIPLE-CHOICE TEST ITEM A cage of guinea pigs at
the pet store is given a vitamin-water solution each day.
Last week the guinea pigs consumed 21.8 ounces, 19.1
ounces, 20.3 ounces, 18.9 ounces, and 22.0 ounces of the
solution each day. Use this information to estimate the
total amount of vitamin solution consumed in one day.
A 70 oz
21.8
19.1
20.3
18.9
22.0
B 90 oz
C 100 oz
D 120 oz
Since there are several
numbers, use clustering
Write the numbers vertically
4/4
21.8 → 20
19.1 → 20
20.3 →
18.9 →
20
22.0 →
20
20  5
100
20
Clustering means to round
all numbers to the same
number
Since all the numbers are
close to 20, round all the
numbers to 20
Since all numbers are 20,
multiply by how many
numbers there are
There are 5 numbers
4/4
100 is a good estimation
A 70 oz
B 90 oz
Choose the appropriate
multiple choice answer
C 100 oz
Answer: C
4/4
D 120 oz
*
MULTIPLE-CHOICE TEST ITEM During the month of
February, Jonathon spends $14.78 on gasoline the first
week, $15.35 on gasoline during the second week,
$15.94 on gasoline during the third week, and $14.07 on
gasoline during the fourth week. Use this information to
estimate the total amount Jonathon spent on gasoline
during February.
A $35
B $50
C $60
D $100
Answer: C
4/4
Assignment
Lesson 3:4
Estimating Sums and
Differences
11 - 33 All