We included HMH Into Math Grade 6 Answer Key PDF Module 1 Lesson 2 Compare and Order Integers on a Number Line to make students experts in learning maths.
HMH Into Math Grade 6 Module 1 Lesson 2 Answer Key Compare and Order Integers on a Number Line
I Can order integers from least to greatest and use inequalities to compare integers.
Spark Your Learning
The thermometer shows temperatures that are above zero and temperatures that are below zero. Find a temperature to complete each statement. Then describe a thermometer to someone who may not have seen one.
Turn and Talk Describe the location of a temperature warmer than 20 °F on a thermometer. Can you extend the drawing of the thermometer to show warmer and colder temperatures? Describe how.
Answer:
The temperature 20 °F is above zero level and the temperature is warmer.
Build Understanding
1. The table below shows the elevations above or below sea level of several lakes. Sea level is considered to be an elevation of zero feet.
A. How could you use a horizontal number line to compare the elevations?
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Answer:
We could use the number line to describe which elevation is greater or smaller from the sea level.
B. What happens to the elevations as you move right on the number line?
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Answer:
As we move to the right on a horizontal number line, the value gets larger. Those numbers are called positive numbers because they are greater than zero.
C. What happens to the elevations as you move left on the number line?
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Answer:
As we move left on the number line the value gets smaller. Those numbers are called negative numbers because they are less than zero.
D. Which lake is at a lower elevation, Springbrook Lake or Forest Lake? Explain your reasoning.
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Answer:
Springbrook Lake.
Explanation:
Elevation for Springbrook Lake is -75.2 and in the forest, the lake is 90. By comparing both the lake which is negative in value is at a lower elevation.
The lake Springbrook Lake is at a lower elevation.
E. Which lake is at a higher elevation, Beldon Lake or Springbrook Lake? Explain your reasoning.
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Answer:
Beldon Lake.
Explanation:
Given Beldon is -18.5 and Springbrook lake is -75.2.
By comparing both Beldon lake is at a higher elevation than Springbrook lake.
F. How can you use a number line to order the elevations?
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Answer:
Elevations above sea level are positive and below sea level are negative. We can use the number line to compare and order positive and negative values.
Turn and Talk Describe another situation that uses elevations to describe locations. Give an example.
2. Deshaun, Chris, Tonya, and Austin play a game. Each turn, a player can lose a point or win a point. At the end of the game the scores are as shown.
A. Graph the scores on the number line.
Answer:
B. Is Deshaun’s or Tonya’s score greater? Explain how you know.
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Answer:
Deshaun’s score is greater.
Explanation:
Given Deshaun’s score has 2 and Tonya’s score has -5.
By comparing their scores Deshaun’s score is greater.
C. Is Chris’s score greater than Tonya’s? Explain how you used the number line to compare the numbers.
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Answer:
Chris’s score is greater than Tonya’s. By using the number line we can compare the numbers which are greater.
D. From left to right, do the values on the number line increase or decrease? Explain.
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Answer:
Increase.
Explanation:
From left to right, the values on the number line increase.
The mathematical sentences -3 < 5 and 2 > -4 are examples of inequalities.
The symbol “<” is read “is less than.” So, -3 < 5 means “-3 is less than 5.” The symbol “>” is read “is greater than.” So, 2 > -4 means “2 is greater than -4.”
Connect to Vocabulary
An inequality is a mathematical sentence that shows the relationship between quantities that are not equal.
3. In golf, scores are based on par. If someone scores less than par, their score is recorded as a negative integer. If someone scores more than par, their score is recorded as a positive integer. After two holes, Jaylen’s score was -3, Kyro’s score was 1, and Keyana’s score was 3.
A. Use a number line to order the scores. Write the scores in order from least to greatest.
Explain your reasoning.
B. What two inequalities could you write to compare Jaylen’s and Kyro’s scores? If a lower score is better, explain who did better, Jaylen or Kyro.
C. Two new golfers, Jon and Tiana, are in a competition. Tiana scores a -3 and Jon scores a -1. Write an inequality to compare their scores. Since in golf the lowest score wins, who won the match? Explain.
Check Understanding
Question 1.
Two research submarines are exploring a coral reef. Submarine 1 is at an elevation of -58 feet. Submarine 2 is at an elevation of -65 feet. Which elevation is farther from sea level? Explain.
Answer:
Submarine 2 elevation is farther from sea level.
Explanation:
Submarine 2 is at an elevation of -65 feet. So Submarine 2 elevation is farther from sea level.
Question 2.
Write an inequality to compare -24 and -14.
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Answer:
The inequality is <.
Explanation:
An inequality to compare -24 and -14 is <.
-24 < -14.
On Your Own
Question 3.
The temperatures on four mornings are -8 °F, -2 °F, -11 °F, and 0 °F.
A. Graph the temperatures on the number line.
Answer:
B. What was the temperature on the coldest morning?
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Answer:
-11 °F
Explanation:
The temperature on the coldest morning is -11 °F.
C. What was the temperature on the warmest morning?
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Answer:
0 °F.
Explanation:
The temperature on the warmest morning is 0 °F.
D. Use the number line to write the temperatures from least to greatest.
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Answer:
-8 °F <-2 °F < -11 °F < 0 °F.
Question 4.
Reason Bank accounts can have a positive or negative balance. When a person takes out more money than is in the account, the account’s balance will be negative. A bank account’s
balance is -$26. Graph -26 on the number line. If a second bank account has a balance that is less than -$26, identify a possible second balance. Write an inequality to compare the balances.
Answer:
Question 5.
The depth of a deep-sea diver can be represented by a negative integer. If the diver is 5 feet below the
surface of the water, then the diver’s elevation is -5 feet.
A. One diver’s elevation is -30 feet and another’s is -25 feet. Which number is less? Graph the
elevations on the number line to answer the question.
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Answer:
The number -30 feet is less than -25 feet.
B. Write an inequality to compare the two elevations. Use the number line to answer the question.
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Answer:
-30 feet < -25 feet.
An inequality to compare the two elevations is <.
C. What does 0 feet mean?
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Answer:
Sea level elevation is called as 0 feet. All other elevations are measured from the sea level.
For Problems 6-8, graph the numbers on the number line. Then write an inequality to compare the numbers.
Question 6.
-14 and -6
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Answer:
-14 < -6
Question 7.
6 and -1
Answer:
6 > -1
Question 8.
54 and -29
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Answer:
54 > -29
Graph the numbers. Then write the numbers in order from least to greatest.
Question 9.
-1, 1, -4, 0
Answer:
-4 < -1 < 0 < 1
Question 10.
-2, 1, -6, -4
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Answer:
-6 < -4 < -2 < 1
I’m in a Learning Mindset!
What did I learn from Task 2 that I can use in my future learning?
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Lesson 1.2 More Practice/Homework
Compare and Order Integers on a Number Line
Question 1.
Tracy and Maria each choose a card from a deck of cards with positive and negative numbers. Tracy picked -12 and Maria picked -6. Who picked the greater number?
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Answer:
-6 is the greater number.
Explanation:
Tracy picked -12 and Maria picked -6.
-6 < -12
Question 2.
STEM The average temperature on the planet Neptune is -214 °C. The temperature on the south pole of Neptune is thought to be 10 °C. Is this colder or warmer than the average temperature? Write an inequality to support your answer.
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Answer:
10 °C > -214 °C
Explanation:
According to the title,
-214 °C < 0 °C
10 °C > 0 °C
So -214 °C < 10 °C
It is warmer than the average temperature.
Question 3.
An office building uses positive numbers and negative numbers for floors as shown. Nathan is going to floor 1, and Eva is going to floor -1. Who is going to the higher floor?
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Answer:
Nathan is going to the higher floor.
For Problems 4-5, graph the numbers on the number line. Then write an inequality to compare the numbers.
Question 4.
14 and -6
Answer:
14 > -6
Question 5.
-2 and 1
Answer:
-2 < 1
Question 6.
Math on the Spot Graph the numbers. Then write the numbers in order from least to greatest.
5, -3, 2
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Answer:
Test Prep
Question 7.
Tanner, Caleb, Lamar, and Tammy play a game of disc golf, which is similar to golf and played with a flying disc. They record their scores relative to par. Their total scores, after two holes, are shown in the table.
Which choice shows the scores in order from least to greatest?
A. -1, 2, -2, 1
B. -1, -2, 1, 2
C. 2, 1, -1, -2
D. -2, -1, 1, 2
Answer:
D. -2, -1, 1, 2
Question 8.
The temperature in the morning was -2 °F. In the afternoon, a cold front passed and the temperature was -6 °F. Which statements are true? Choose all that apply.
A. It was colder in the morning than in the afternoon.
B. It was colder in the afternoon than in the morning.
C. It was warmer in the morning than in the afternoon.
D. It was warmer in the afternoon than in the morning.
E. The temperature in the morning was greater than the temperature in the afternoon.
F. The temperature in the afternoon was greater than the temperature in the morning.
Answer:
B. It was colder in the afternoon than in the morning.
E. The temperature in the morning was greater than the temperature in the afternoon.
Question 9.
Choose the correct symbol from <, >, and = to compare the numbers.
-6 ___ -8
Answer:
-6 < -8
Spiral Review
Question 10.
What number is ten times as great as 450?
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Answer:
4500
Explanation:
450 × 10 = 4500
Question 11.
Cynthia gave \(\frac{1}{5}\) of her toys to her little sister. If she originally had 25 toys, how many did she give away?
Answer:
Given,
Cynthia gave \(\frac{1}{5}\) of her toys
If she had 25 toys
She gave away = 25 × \(\frac{1}{5}\)
= 5 toys
Question 12.
Laquan has 2 pieces of fabric, each measuring 3\(\frac{1}{4}\) feet long. How many feet of fabric does Laquan have in total?
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Answer:
Given,
Laquan has 2 pieces of fabric
Each measuring 3\(\frac{1}{4}\) feet.
The fabric does Laquan have in total is 2 × 3\(\frac{1}{4}\)
= 2 × \(\frac{13}{4}\)
= \(\frac{13}{2}\)