# Texas Go Math Grade 6 Lesson 1.1 Answer Key Identifying Integers and Their Opposites

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## Texas Go Math Grade 6 Lesson 1.1 Answer Key Identifying Integers and Their Opposites

(A) The table shows the elevations of several locations in a state park.
Graph the locations on the number line according to their elevations. (B) What point on the number line represents sea level?

(C) Which location is closest to sea level? How do you know?

(D) Which two locations are the same distance from sea level? Are these locations above or below sea level?

(E) Which location has the least elevation? How do you know?

Reflect

Question 1.
Analyze Relationships Morning Glory Stream is 7 feet below sea level. What number represents the elevation of Morning Glory Stream?
Because Morning Glory Stream is 7 feet below sea level, the number which represents the elevation of Morning Glory wilt be – 7.
It is – 7 because Morning Glory Stream is 7 feet below sea level and we can let the sea level’s elevation is 0.

Result:
– 7

Question 2.
Multiple Representations Explain how to graph the elevation of Morning Glory Stream on a number line.
Because the elevation of Morning Glory Stream is 7, it is a number which is Less than 0, so, it is negative integer.
So, – 7 will be 7 units left from 0 on number Line.

Result:
It will be 7 units left from 0 on number line.

Question 3.
Justify Reasoning Explain how your number line shows that 8 and -8 are opposites.
From number Line we can notice that 8 and – 8 are the same distance from 0 but also, they are on different sides of 0.
So, according to previous, we can conclude that 8 and – 8 are opposites.

Result:
They are the same distance from 0 and on different sides of 0.

Question 4.
Multiple Representations Explain how to use your number line to find the opposite of the opposite of -6.
First we need to find – 6 on number line. It is 6 units left of point 0. The opposite of – 6 is 6 units right from point 0, it is number 6.
And again, opposite of 6, which is opposite of – 6, is 6 units Left from 0 on number Line.
We get that it is number – 6.
So, conclusion is that the opposite of the opposite of – 6 is – 6.

Result:
The opposite of the opposite of – 6 is – 6.

Question 5.
Analyze Relationships Explain how you can find the opposite of the opposite of any number without using a number line.
From all previous we can conclude that the opposite of the opposite of any number is that number always.

Result:
The opposite of the opposite of any number is that number.

Graph the opposite of the number shown on each number line.

Question 6. Here we need to find the opposite of the number – 1. It is 1 unit from 0 to the right We can conclude that it is number 1. Result:
1

Question 7. Here we need to find the opposite of the number 7.
It is 7 units from 0 to the left. We can conclude that it is number – 7. Result:
– 7

Write the opposite of each number.

Question 8.
10 ___________
The opposite of 10 is – 10, because – 10 is number on number line with the same distance from 0 as 10 and on the opposite side of 0.

Result:
– 10

Question 9.
– 5 ___________
The opposite of – 5 is 5 because 5 is number on number tine with the same distance from 0 as – 5 and on the opposite side of 0.

Result:
5

Question 10.
0 ____________
Here, conclusion is that 0 is its own opposite.

Result:
0

Question 11.
What is the opposite of the opposite of 6?
Like we explain in some previous tasks, the opposite of the opposite of any number is that number.
So, here, the opposite of the opposite of 6 is 6.

Result:
6

Question 1.
Graph and label the following points on the number line.
a. -2
b. 9
c. -8
d. -9
e. 5
f. 8  Graph the opposite of the number shown on each number line. (Explore Activity 2 and Example 1)

Question 2.  Question 3.  Question 4. Note that opposite of 0 is actually 0 Write the opposite of each number. (Explore Activity 2 and Example 1)

Question 5.
4
Opposite of 4 is – 4.
Therefore, we write – 4 on a line.

Question 6.
– 11
Opposite of – 11 is 11.
Therefore, we write 11 on a line.

Question 7.
3
Opposite of 3 is – 3.
Therefore, we write – 3 on a line.

Question 8.
– 3
Opposite of – 3 is 3.
Therefore, we write 3 on a line.

Question 9.
0
Opposite of 0 is 0.
Therefore, we write 0 on a line.

Question 10.
22
Opposite of 22 is – 22.
Therefore, we write – 22 on a line.

Essential Question Check-In

Question 11.
Given an integer, how do you find its opposite?
We will get opposite of integer if we add “—” sign in front of a number(from Left side).

Question 12.
Chemistry Atoms normally have an electric charge of 0. Certain conditions, such as static, can cause atoms to have a positive or a negative charge. Atoms with a positive or negative charge are called ions. a. Which ions have a negative change?
Ions with a negative charge are: A, C, E

b. Which ions have charges that are opposites?
Ions that have charges which are opposite are: B, D, A, E

c. Which ions charge is not the opposite of another ion’s charge?
Ion charge which is not opposite of another ion charge is C

Name the integer that meets the given description.

Question 13.
the opposite of -17 ____________
Opposite number of – 17 is 17.
Therefore, our final solution is: 17

Question 14.
4 units left of 0 _________
Number that is 4 units left from 0 is: – 4
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!
Let’s do it: Question 15.
the opposite of the opposite of 2 ____________
Opposite of the opposite of some number is actuaLLy that same number!
So, in our case the integer that meets the given description is: 2
That is our final solution!

Question 16.
15 units right of 0 ____________
Number that is 15 units right of 0 is: 15
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!

Let’s do it: Question 17.
12 units right of 0 ____________
Number that is 15 units right of 0 is: 15
We can use addition while finding number placed right of another number!
Actually, we could have just drawn a number line for ourselves and have shown the solution through it!

Let’s do it: Question 18.
the opposite of – 19 __________
Opposite number of – 19 is 19
Therefore, our final solution is 19

Question 19.
Analyze Relationships Several wrestlers are trying to lose weight for a competition. Their change in weight since last week is shown in the chart. a. Did Victor lose or gain weight since last week?
Victor gained weight since last week.

b. Which wrestlers weight change is the opposite of Ramsey’s?
Opposite of Ramsey’s weight change is Tino.

c. Which wrestlers have lost weight since last week?
Wrestlers who lost weight since last week are: Tino, Luis.

d. Frankie’s weight change since last week was the opposite of Victor’s.
What was Frankie’s weight change? ____________
Firstly, we conclude that Victor gained 6 pounds!
Now, we can say that Frankie lost 6 pounds
So, Frankie’s weight change from last week is – 6 pounds!

e. Frankie’s goal last week was to gain weight. Did he meet his goal? Explain.
Frankie didn’t meet his goat because he gained 6 pounds since last week and he was supposed to loose weight.

Find the distance between the given number and its opposite on a number line.

Question 20.
6 ____________ Question 21.
– 2 ____________ Question 22.
0 ____________
Please not that the opposite of 0 is 0. Question 23.
– 7 ____________ Question 24.
What If? Three contestants are competing on a trivia game show.
The table shows their scores before the final question. a. How many points must Shawna earn for her score to be the opposite of Timothy’s score before the final question?
We know that the opposite of 18 is – 18
So we calculate distance between – 25 and – 18.
Here is how we do it:
|- 25| – |-17| = 25 – 17 = 8
So, amount of points that Shawna has to earn is: 8

b. Which person’s score is closest to 0?
Here, we calculate lowest absolute value!
|- 25| > |18| >| – 14| = – 14
Absolute value of – 14 is lowest
and therefore closest to 0

c. Who do you think is winning the game before the final question? Explain.
Shawna is in lead before final question since her score is greatest!

H.O.T. Focus on Higher Order Thinking

Question 25.
Communicate Mathematical Ideas Which number is farther from 0 on a number line: – 9 or 6? Explain your reasoning.
Here we can conclude that – 9 is farther from 0 than 6.
That works because the absolute value of – 9 is greater than 6 and therefore it’s distance from 0.

Question 26.
Analyze Relationships A number is k units to the left of 0 on the number line. Describe the location of its opposite.
Since a number is to the Left of 0, that means that it’s opposite
is to the right of O, and aLso means that it starting value is negative
Therefore, its opposite will have value of: – k

Question 27.
Critique Reasoning Roberto says that the opposite of a certain integer is – 5. Cindy concludes that the opposite of an integer is always negative. Explain Cindy’s error.