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Statements of Order in the Real World

Videos to help Grade 6 students understand order and absolute value when examining real world scenarios.

New York State Common Core Math Grade 6, Module 3, Lesson 13

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Lesson 13 Student Outcomes

Students apply understanding of order and absolute value when examining real world scenarios. Students realize, for instance, that the depth of a location below sea level is the absolute value of a negative number, while the height of an object above sea level is the absolute value of a positive number.

Lesson 13 Summary

When comparing values in real world situations, descriptive words will help you to determine if the number represents a positive or negative number. Making this distinction is critical when solving problems in the real world. Also critical is to understand how an inequality statement about an absolute value compares to an inequality statement about the number itself.

Opening Exercise
A radio disc jockey reports that the temperature outside his studio has changed degrees since he came on the air this morning. Discuss with your group what listeners can conclude from this report.

Example 1: Ordering Numbers in the Real World
A $25 credit and a $25 charge appear similar, yet they are very different. Describe what is similar about the two transactions.
How do the two transactions differ?

Exercises 1ִ
1. Scientists are studying temperatures and weather patterns in the Northern Hemisphere. They recorded temperatures (in degrees Celsius) in the table below, as reported in emails from various participants. Represent each reported temperature using a rational number. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately represent the given temperatures.

2. Jamiӳ bank account statement shows the transactions below. Represent each transaction as a rational number describing how it changes Jamiӳ account balance, then order the rational numbers from greatest to least. Explain why the rational numbers that you chose appropriately reflect the given transactions.

3. During the summer, Madison monitors the water level in her parents' swimming pool to make sure it is not too far above or below normal. The table below shows the numbers she recorded in July and August to represent how the water levels compare to normal. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately reflect the given water levels.

4. Changes in the weather can be predicted by changes in the barometric pressure. Over several weeks, Stephanie recorded changes in barometric pressure seen on her barometer to compare to local weather forecasts. Her observations are recorded in the table below. Use rational numbers to record the indicated changes in the pressure in the second row of the table. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately represent the given pressure changes.

Example 2: Using Absolute Value to Solve Real-World Problems
The captain of a fishing vessel is standing on the deck at 23 feet above sea level. He holds a rope tied to his fishing net that is below him underwater at a depth of 38 feet.
Draw a diagram using a number line, then use absolute value to compare the lengths of rope in and out of the water.

Example 3: Making Sense of Absolute Value and Statements of Inequality
A recent television commercial asked viewers "Do you have over $10,000 in credit card debt?"
What types of numbers are associated with the word "debt" and why? Write a number that represents the value from the television commercial.
Give one example of "over $10,000 in credit card debt" then write a rational number that represents your example. How do the debts compare and how do the rational numbers that describe them compare? Explain.

Lesson 13 Exit Ticket

1. Loni and Daryl call each other from opposite sides of Watertown. Their locations are shown on the number line below using miles. Use absolute value to explain who is a further distance (in miles) from Watertown. How much closer is one than the other?

2. Claude recently read that no one has ever scuba-dived more than 330 meters below sea level. Describe what this means in terms of elevation using sea level as a reference point. Problem Set
1. Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.

2. The fuel gauge in Nic’s car says that he has 26 miles to go until his tank is empty. He passed a fuel station 19 miles ago, and a sign says there is a town only 8 miles ahead. If he takes a chance and drives ahead to the town and there isn’t a fuel station there, does he have enough fuel to go back to the last station? Include a diagram along a number line, and use absolute value to find your answer.

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