# Into Math Grade 6 Module 1 Lesson 1 Answer Key Identify and Interpret Integers

We included HMH Into Math Grade 6 Answer Key PDF Module 1 Lesson 1 Identify and Interpret Integers to make students experts in learning maths.

## HMH Into Math Grade 6 Module 1 Lesson 1 Answer Key Identify and Interpret Integers

I Can graph positive and negative integers and find their opposites.

Fergal is recording the number of yards his school’s football team gained or lost on successive plays. How can you model or represent the opposite of each loss or gain shown in the table?

Turn and Talk Write several pairs of your own opposite quantities. Explain how you know they are opposites.
Gain of 4 yards      loss of 4 yards
Gain of 5 yards      Loss of 5 yards
Loss of 8 yards      Gain of 8 yards
Loss of 15 yards    Gain of 15 yards.

Build Understanding
Positive numbers can be written with or without a positive sign (+), but they are usually written without it. Negative numbers are always written with a negative sign (-).

Connect to Vocabulary
A positive number is a number greater than zero.
A negative number is a number less than zero.

1. The results of three football plays are shown in the table.

A. What does 0 represent in this situation?
_____________________
_____________________
The 0 is an integer. The 0 represent in this situation is neither loss nor profit.

B. What do negative numbers represent in this situation?
_____________________
The negative number represent in this situtation is loss.

C. What do positive numbers represent in this situation?
_____________________
The postive numbers that represent in this situation is gain.

D. Complete the number line. Then graph each result from the table on
the number line.
_____________________

Turn and Talk How can you describe a pattern in the positive numbers as you move left to right on a number line? Does the same pattern apply for the negative numbers as well? Explain.

Connect to Vocabulary
Two numbers are opposites if, on a number line, they are the same distance from 0 but on different sides of 0.
Integers are the set of all whole numbers and their opposites.

2. Complete the number line. Then graph the number -2.

A. Graph the opposite of -2. Explain how you used the number distance line to find the opposite.
_____________________________________
_____________________________________
_____________________________________

B. The integer 3 is 3 units from 0 on the number line. Which integer is also 3 units from 0 on the number line? How is this integer related to the integer 3?
_____________________________________
The integer -3 is also 3 units from 0 on the number line. The integer -3 is opposite of integer 3.

C. How many units from zero is 0 on the number line? What is the opposite of 0? Explain.
_____________________________________
_____________________________________
The are no units from zero to 0 on the number line. And the opposite of 0 is same number zero.

D. What is the opposite of the opposite of 5? This is written as -(-5). Explain.
_____________________________________
_____________________________________
5

Explanation:
The number given is 5 and opposite of 5 is -5.
The opposite of the opposite of -5 is 5 and it is written as -(-5) = 5

3. Jesse is the student treasurer for the video game club. She records club expenses as negative numbers and deposits to the club account as positive numbers. She graphed these amounts on the number line.

A. Jesse did not label every tick mark on her number line. What is the distance between each tick mark on Jesse’s number line? Explain.
_____________________________________
_____________________________________
The distance between each tick mark on Jesse’s number line is $2. B. How would she show an expense of$5 on her graph?
_____________________________________
_____________________________________

Turn and Talk Jesse’s number line has 0 in the middle. Does this always have to be the case? Explain.

4. The morning temperature in a large city in Minnesota was recorded each day for seven days. The temperatures recorded were:
-2 °F, 4 °F, 0 °F, 2 °F, -4 °F, -7 °F, and -10 °F

A. Graph the temperatures on the number line at the right.

B. Which pairs of temperatures are opposites? How do you know?
_____________________________________
_____________________________________
_____________________________________
The pairs of temperatures that are opposite is -2 and 2, -4 and 4.

C. What temperature would be the opposite of -7 °F? Explain.
_____________________________________
_____________________________________
7 °F

Explanation:
The temperature that would be opposite of -7 °F is 7 °F.

D. What would a point at 10 represent? What is the opposite of the opposite of 10?
_____________________________________
10.

Explanation:
The opposite of the opposite of 10 is 10.
-(-10) = 10.

E. What does it mean for a temperature to be the opposite of another temperature?
_____________________________________
_____________________________________
The temperature that is opposite of another temperature is increase and decrease in temperature.

Check Understanding

Question 1.
An investment gains $5 in value on one day. The next day, it loses$3 in value. Represent each of these using integers.
+$5, -$3

Explanation:
An investment gains $5 is +$5 and loses mean -$3. Question 2. Iman is playing a game. On one turn she earns 2 points and on the next turn she loses 5 points. Graph her turns on the number line. Answer: Find the opposite of the integer. Question 3. 4 _____________________ Answer: -4 Question 4. -8 _____________________ Answer: 8 Explanation: The opposite of the integer of -8 is 8. Question 5. -25 _____________________ Answer: 25 Explanation: The opposite of the integer -25 is 25. Question 6. 121 _____________________ Answer: -121 Explanation: The opposite of the integer -121 is 121. On Your Own For Problems 7-9, use the following information. Use Structure Every week, Tiana runs 3 miles and records how long it takes to complete the run. She also records the change in time from the previous week. Question 7. Last week, her time spent running decreased by 2 minutes. What integer could represent this change? _______ Answer: Last week her time spent running decreased by 2 minutes. The integer that could represent this change is -2 minutes. Question 8. This week, her time spent running increased by 1 minute. What integer could represent this change? _________________________ Answer: +1 minute. Explanation: The integer that could represent this change is +1 minute. Question 9. In words, what is the opposite of “increased by 1 minute”? What integer represents this opposite? _________________________ Answer: Decreased by 1 minute. Explanation: The integer that represents the opposite of “increased by 1 minute is Decreased by 1 minute. For Problems 10-11, use the following information. The transactions on a bank account are listed as -$15, $10, -$4, and $15. Question 10. What does a transaction of -$4 represent?
A transaction of -$4 represent bank account is lower. Question 11. Which pairs of transactions are opposites? Explain. Answer: -$15 and $15. Explanation: The pairs of transactions that are opposites -$15 and $15. Question 12. The number line shown includes 5 graphed integers. Fill in the labels for the integers. Which graphed integers are opposites? Answer: Question 13. Reason Two integers are opposites of each other. One integer is 3 units to the right of 1 on a number line. What are the two integers? Answer: -30 and 30. 10 and -10. Question 14. Rona starts at the base of a hill that has an elevation of 25 feet below sea level. Then Rona climbs to the top of the hill which has an elevation of 25 feet above sea level. Represent these elevations as integers. How are they related? _______________ Answer: An elevation of 25 feet below sea level of -25 feet. An elevation of 25 feet above sea level of +25 feet. -25 + 25 = 0 they are opposite numbers. On Your Own Question 15. Use Structure The low temperatures on three days are shown at the right. What are the opposites of the three temperatures? Graph the temperatures and their opposites on the number line. Answer: Question 16. Reason Explain how to use a number line to find the opposites of the integers that are 4 units away from -6. _____________________ _____________________ Answer: Question 17. Atoms are made of tiny particles called protons, neutrons, and electrons. Protons and neutrons are in the center of the atom, making up the nucleus. The electrical charges on the proton and electron are exactly the same size but opposite. If a proton has a positive charge of 1, what is the charge of the corresponding electron? _______________ Answer: For Problems 18-20, write the opposite of the integer. Question 18. -6 _______________ Answer: 6 Explanation: The opposite of the given integer is 6. Question 19. -2 _______________ Answer: 2 Explanation: The opposite of the given integer is 2. Question 20. 17 _______________ Answer: -17 Explanation: The opposite of the given integer is -17. Question 21. Graph the integers on a number line: -2, 4, -5, 10. Answer: I’m in a Learning Mindset! What can I apply from previous work to better understand how to find opposites of negative numbers? Lesson 1.1 More Practice/Homework Identify and Interpret Integers Question 1. Mua first stands on a diving board that is 3 feet above the surface of the water. She then dives to the bottom of the pool, to a depth of 10 feet. Answer: She dives 13 feet. 3 + 10 = 13 A. If the surface of the pool is 0, use integers to represent these two locations. ________________________ Answer: The integers to represent these two location us +3 and +10. B. Graph each of the integers on the number line. Then find the opposite of each integer and explain what it represents. ____________________________ ____________________________ ____________________________ ____________________________ Answer: Question 2. Critique Reasoning Hermes says that the opposite of 9 is 9 since each number is 9 units from zero on the number line. Is Hermes correct? Explain why or why not. ________________________ ________________________ Answer: The given statement is wrong. Explanation: Hermes says that the opposite of 9 is 9. But the opposite of 9 is -9. Hence Hermes statement is incorrect. Question 3. The number line shows integers A and B. What are the opposites of these integers? Answer: Given, Integer A in the given graph is – 1 and the opposite integer is 1 Integer B in the given graph is 1 and the opposite of this integer is -1. Question 4. Open Ended There are four integers graphed on the number line. What real-life situation could the integers represent? Answer: The real-life situation could the integers represent is -600, +600, -100 and 200. Math on the Spot For Problems 5 – 7, find the opposite of each integer. Question 5. 2 ________ Answer: -2 Explanation” The opposite of integer 2 is -2. Question 6. -3 ________ Answer: 3 Explanation: The opposite of integer -3 is 3. Question 7. 0 _____________ Answer: 0 Explanation: The opposite of integer 0 is 0. Test Prep Question 8. Jose collects baseball cards. Over the last year, the change in the value of his favorite card is -$7. Which best describes the meaning of this integer?
A. The card is now worth $7. B. The value of the card has increased by$7.
C. The value of the card has decreased by $7. D. The card is now worth -$7.
The value of the card has decreased by $7. Explanation: The value of the card has decreased by$7 best describes the meaning of this integer.

Question 9.
The temperature this morning, measured in degrees Fahrenheit, was eight degrees below zero. What integer represents this temperature?
____ °F
-8 °F.

Explanation:
The integer that represents this temperature is – 8 °F

Question 10.
Match each integer to its opposite.

Opposite of Integer A = 1
Opposite of Integer B = 5
Opposite of Integer C = 0
Opposite of Integer D = -4

Question 11.
Which situation could the integer-50 represent?
A. An increase of $50 in a bank account. B. The temperature on a warm spring day. C. The distance driven on the way to the beach. D. A decrease of$50 in a bank account.
A decrease of $50 in a bank account. Question 12. Which situation can be represented by -8? Choose all that apply. A. a temperature drop of 8 °F B. a depth of 8 meters C. a growth of 8 centimeters D. a time 8 years ago E. a loss of 8 pounds F. a gain of$8

Spiral Review

Question 13.
What is one tenth of 1,850?
________________________
185

Explanation:
Let us solve the given expression
$$\frac{1}{10}$$ × 1850
= 185

For Problems 14 – 16, use >, <, or = to compare the numbers.

Question 14.
0.105 ____ 0.108
<

Explanation:
0.105 < 0.108

Question 15.
0.002 ___ 0.040
0.002 < 0.040

Explanation:
The symbol that is used to compare the given numbers is 0.002 < 0.040.

Question 16.
0.03 ______ 0.017