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LESSON 2.1 - Integers and Absolute Value
Goal: Study integers.
Warm-up:
Meteorology
Meteorology is a science that deals with the atmosphere. One branch of meteorology studies
weather and weather forecasting. Meteorologists use scientific methods to predict what the weather
will be.
Use the following information in Exercises 1-4.
Jose is the son of a farmer. For as long as Jose can remember, the weather has been a favorite topic
of conversation among his parents and other farmers. Farmers are dependent on the weather to
grow their crops. They need enough rain for the crops to grow, but not so much rain that
everything is ruined. Jose has decided to be a meteorologist when he grows up. To learn more
about precipitation, Jose set up a project. He measured the height of a bucket, marking each inch
with a black pen. He labeled the 5-inch mark with a "0," and then filled the bucket up with water to
the "0" mark. Jose set the bucket outside to catch rain. Jose planned to measure the water level
once each month from March until October. After recording each measurement, he would empty the
bucket and refill it to the "0" mark. His measurement would include the accumulated effects of rain
and evaporation. These are the measurements that Jose recorded:
Water
Level
Month
March
Water
Level
+ 3 inches
July
3 inches
April
+ 6 inches
August
2 inches
May
+ 8 inches
September
Month
+1 inch
June
 1 inch
October
+ 2 inches
Discuss and answer these questions with your group:
1. In which month did the most water accumulate?
2. In which month did the greatest loss of water occur?
3. What is the difference of the accumulation level in May and the accumulation
level in July?
4. Put the months in order, beginning with the month that had the greatest loss of water and
ending with the month that had the greatest accumulation.
END OF WARM-UP 
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Vocabulary:
Integers:
Negative integer:
Positive integer:
Absolute value:
Opposites:
EXAMPLE 1 - Graphing and Ordering Integers
Temperature The table shows the low temperatures for five days. Which day had the lowest
temperature?
To find which day had the lowest temperature, graph each integer on a number line.
Daily Low Temperatures
Day
Temperature (°C)
Monday
8
Tuesday
–4
Wednesday
–1
Thursday
–8
Friday
6
Remember that
negative integers lie
to the left of 0 and
positive integers lie
to the right of 0.
ANSWER:
Think: If numbers on a
number line increase as
you move to the right,
which number is the
smallest?
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Now You Try It! Graph the integers. Then order the integers from least to greatest.
1. 7, –5, 9, –10, –2
0, –25, 45, –50, 30
2.
EXAMPLE 2 - Finding Absolute Value
Animals A seagull is flying at an altitude of 107 feet and a shark is swimming at a depth of –112
feet relative to sea level. Which animal is farther from sea level?
Solution
Seagull: | 107 | =
Shark: | –112 | =
The absolute value
of a number n is
written as | n |.
ANSWER:
Example 3 - Finding Opposites
Write the opposite of the integer.
a. 9
b. –14
The integer "–14"can be
read "negative14" or "the
opposite of 14."
c. –( –8 )
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Now You Try It!
3. Write the opposite: –1
4. | –6 |
5. –(20)
6. | 5 |
7. –(-105)
8. |-105|
Discuss and answer the following questions with your group:
1. Why do negative numbers exist?
2. When are negative numbers used in the real world?
3. Explain how the terms absolute value and opposite are different.
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