Download Unit 1 * The Number System: Packet 2 of 3

6th Grade
Unit 1 – The
Number System:
Packet 2 of 3
Mr. Rothdiener
Name: _______________________________________________
Packet Outline, Page 1
 1.9: Dividing Fractions (6.NS.A.1), Pages 2-4
o I can divide fractions by whole numbers and fractions by fractions.
 1.10: Dividing Mixed Numbers (6.NS.A.1), Pages 5-7
o I can divide mixed numbers.
 1.11: Positives and Negatives on the Number Line (6.NS.C.5, 6.NS.C.6a,
6.NS.C.6c), Pages 8-10
o I can use positive integers to locate negative integers, moving in the
opposite direction from zero.
 1.12: Real-World Positives and Negatives (6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c),
Pages 11-13
o I can use positive and negative numbers to indicate a change in
elevation, temperature, and balance in a bank account.
 1.13: Rational Numbers on the Number Line (6.NS.C.5, 6.NS.C.6a,
6.NS.C.6c), Pages 14-16
o I can use number lines that extend in both directions and use 0 and 1
to locate integers and rational numbers on the number line.
 1.14: Order Integers (6.NS.C.7a, 6.NS.C.7b), Pages 17-19
o I can write, interpret, and explain statements of order for integers in
the real-world.
 1.15: Order Rational Numbers (6.NS.C.7a, 6.NS.C.7b), Pages 20-22
o I can write, interpret, and explain statements of order for rational
numbers in the real-world.
 Quiz 1.2 Review (6.NS.A.1, 6.NS.C.5, 6.NS.C.6, 6.NS.C.7), Pages 23-24
o I can divide fractions and mixed numbers.
o I can apply and extend previous understandings of numbers to the
system of rational numbers.
1
1.9: Dividing Fractions (6.NS.A.1)
Bell Work:
Find the greatest common factor of 8 and 10.
Whole-Class:
Find each quotient. Simplify if possible.
1.)
1
4
8
2.)
3 1

4 4
1
2
4.)
9 1

10 10
1 8

3 9
6.)
5 1

9 2
Guided Practice:
Find each quotient. Simplify if possible.
3.) 3 
5.)
2
Independent Practice:
Find each quotient. Simplify if possible.
7.)
1
3
5
8.)
3 1

16 16
9.) 5 
1
3
10.)
1
6
2
11.)
7 1

12 12
12.)
1 1

3 2
13.)
5 7

8 10
14.)
3 5

4 6
15.)
1 3

3 8
3
HOMEWORK 1.9
Find each quotient. Simplify if possible.
1.)
1
5
7
2.)
5 1

6 6
3.) 5 
4.)
1
9
3
5.)
11 1

14 14
6.)
1 1

4 3
7.)
3 15

7 28
8.)
4 6

5 7
9.)
9 4

10 5
4
1
7
1.10: Dividing Mixed Numbers (6.NS.A.1)
Bell Work:
Find the quotient. Simplify if possible.
2 4

9 27
Whole-Class:
Find each quotient. Simplify if possible.
2
1
1.) 2  3
3
4
1
1
2.) 7  2
4
8
Guided Practice:
Find each quotient. Simplify if possible.
3
1
3.) 1  4
4
8
4.) 10  3
5
1
4
Independent Practice:
Find each quotient. Simplify if possible.
1
1
5.) 2  2
5
3
7.) 5  6
1
6.) 5  3
4
2
5
1
4
8.) 4  2
3
5
2
1
9.) 7  5
3
9
3
6
10.) 3  5
7
7
6
HOMEWORK 1.10
Find each quotient. Simplify if possible.
3
1
1.) 1  4
8
8
5
1
2.) 2  6
6
3
3
2
3.) 3  4
4
7
1
2
4.) 5  4
2
5
5.) 1 3
5
9
6.) 8  2
7
2
3
1.11: Positives and Negatives on the Number Line
(6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c)
Bell Work:
List as many opposites as you can that you see in the real world.
Example: hot and cold
Whole-Class:
1.) Construct a horizontal number line. Count by 1’s to label the number line.
2.) Plot your point from your index card on the number line. What is your point?
3.) Show and explain how to find the opposite of your number on the number line.
4.) Mark the opposite on the number line. What is your opposite?
8
Guided Practice:
5.) Below is a list of numbers in order from least to greatest. Use what you know
about the number line to complete the list of numbers by filling in the blanks
with the missing numbers.
−6, −5, ________, −3, −2, −1, _________, 1, 2, _________, 4, _________, 6
Independent Practice:
6.) Complete the number line scale.
2
7.) What is the opposite of 2? __________
8.) What is the opposite of -27? _________
9.) What is the opposite of 0? __________
9
HOMEWORK 1.11
1.) Create a scale for the number line in order to plot the points -2, 4, and 5.
a.) Graph each point and its opposite on the number line.
2
b.) Explain how you found the opposite of each point.
10
1.12: Real-World Positives and Negatives
(6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c)
Bell Work:
Write each word under the appropriate column, “Positive Number” or “Negative
Number”.
Gain
Loss
Deposit
Credit
Debit
Charge
Below Zero
Withdraw
Owe
Receive
Positive Number
Negative Number
Whole-Class/Guided Practice:
1.) Write each individual description below as an integer. Model the integer on
the number line using an appropriate scale.
EVENT
INTEGER
NUMBER LINE MODEL
Open a bank
account with $0.
Make a $150
deposit.
11
Credit an account
for $150.
Make a deposit of
$25.
A bank charge of
$5.
A withdrawal of
$35.
Independent Practice:
Write an integer to represent each of the following situations:
2.) A company loses $345,000 in 2011.
3.) You earned $25 for dog sitting.
4.) Jacob owes his dad $5.
5.) The temperature at the sun’s surface is about 5,600℃.
6.) The temperature outside is 4 degrees below zero.
7.) A football player lost 10 yards when he was tackled.
8.) A diver is 20 feet below sea level.
12
HOMEWORK 1.12
1.) Write an integer to represent each of the following situations:
a. A gain of 56 points in a game.
b. A fee charged of $2.50.
c. A temperature of 32 degrees below zero.
d. A 56 yard loss.
e. 65 feet above sea level.
f. A $12,500 deposit.
For questions 2-3, read each statement about a real-world situation and the two
related statements in parts (a) and (b) carefully. Circle the correct way to
describe each real-world situation.
2.) The elevation of an iceberg with respect to sea level is given as −125 feet.
a. The iceberg is 125 above sea level.
b. The iceberg is 125 feet below sea level.
3.) Alex’s body temperature decreased by 2℉.
a. Alex’s body temperature dropped 2℉.
b. The integer 2 represents the change in Alex’s body temperature in degrees
Fahrenheit.
13
1.13: Rational Numbers on the Number Line
(6.NS.C.5, 6.NS.C.6a, 6.NS.C.6c)
Bell Work:
Complete the number line scale.
3
Whole-Class:
1.) Locate and graph the number
3
10
and its opposite on a number line.
Guided Practice:
7
2.) Use what you know about the points, − and its opposite, to graph both
4
points on the number line below.
On the number line, each segment will have an equal length of
7
fraction − , the numerator is
4
fraction is located between
and the denominator is
and
14
.
. In the
. The
Independent Practice:
3.) The water level of a lake rose 1.25 feet after it rained. Answer the questions
using the diagram below.
a. Write a rational number to represent the situation.
b. What two integers is 1.25 between on a number line?
c. Write the length of each segment on the number line as a
decimal and a fraction.
d. What will be the water level after it rained? Graph the point on
the number line.
e. After two weeks of rain, the water level of the lake is the opposite of the
water level before it rained. What will be the new water level? Graph the
point on the number line.
4.) Use the number line diagram below to answer the following questions.
𝐾
–1
0
1
a) What is the length of each segment on the number line?
b) What number does point 𝐾 represent?
c) What is the opposite of point 𝐾? Graph it on the number line.
15
HOMEWORK 1.13
1.) Locate and graph the number
9
10
and its opposite on a number line.
2.) Use the number line diagram below to answer the following questions.
E
-1
0
1
f. What number does point 𝐸 represent?
g. What is the opposite of point 𝐸?
h. Locate the opposite of point 𝐸 on the number line, and label it point 𝐹.
16
1.14: Order Integers (6.NS.C.7a, 6.NS.C.7b)
Bell Work:
Graph 7 and its opposite on the number line. Graph 5 and its opposite on the
number line.
Order the numbers you plotted from least to greatest.
Whole-Class:
1.) The record low temperatures for a town in Maine for January and February are
-20 and -19 degrees Fahrenheit respectively. Order the numbers from least to
greatest. Explain how you arrived at your answer.
2.) Henry, Jason, and Clark are playing a card game. The object of the game is to
finish with the most points. The scores at the end of the game are: Henry: -7,
Jason: 0, and Clark: -5. Who won the game? Who came in last place? Use a
number line model and explain how you arrived at your answer.
17
Guided Practice:
3.) Henry, Jason, and Clark are playing another round of the card game. Their scores
this time are as follows:
Clark: -1, Jason: -2, and Henry: -4. Who won? Who came in last place?
Independent Practice:
4.) Represent each of the following elevations using a rational number. Then
order, the numbers from least to greatest.
Cayuga Lake
122 meters above sea level
Mount Marcy
1,629 meters above sea level
New York Stock Exchange Vault
15.24 meters below sea level
5.) Order the following from least to greatest: −12, 12, −19, 1 , 5
6.) Order the following from greatest to least: −12, 12, −19, 1 , 5
7.) Jordan, Zach, and Phil are golfing on a Sunday afternoon. The player with the
lowest score in golf wins. Jordan shot a -6, Zach shot a -4, and Phil shot a -9.
Who won their golf match? Explain.
18
HOMEWORK 1.14
1.) Jerry, Kyle, and Mario are playing a card game. The object of the game is to
finish with the most points. The scores at the end of the game are: Jerry: −3,
Kyle: −9, and Mario: −1. Who won the game? Who came in last place?
Explain how you arrived at your answer.
2.) Order the following from least to greatest: −31, 31, −45, 14 , −21
3.) Order the following from greatest to least: −31, 31, −45, 14 , −21
4.) Sean, Derek, and Tim are golfing in a Saturday morning league. The player with
the lowest score in golf wins. Sean shot a -3, Derek shot a -4, and Tim shot a -2.
Who won their golf match? Explain.
19
1.15: Order Rational Numbers (6.NS.C.7a, 6.NS.C.7b)
Bell Work:
Order the following from least to greatest: −4, 8, −9, 7 , −2
Whole-Class:
1.) Mrs. Rodriguez is a teacher at Westbury Middle School. She gives bonus
points on tests for outstanding written answers and deducts points for
answers that are not written correctly. She uses rational numbers to
represent the points. She wrote the following on the students’ papers:
Student 𝐴: −2 points, Student 𝐵: −2.5 points. Did Student A or Student B
perform worse on the test?
2.) Sam has $10 in the bank. He owes his friend Hank $2.25. He owes his sister
$1.75. Consider the three rational numbers related to this story of Sam’s
money. Write and order them from least to greatest.
Guided Practice:
3.) Monica, Jack and Destiny each had their arm length measured for an
experiment in science class. They compared their arm lengths to a standard of
22 inches. The listing below shows in inches how each student’s arm length
compares to 22 inches. Order these rational numbers from least to greatest.
Monica: −
1
8
Jack: 1
3
Destiny: −
4
20
1
2
4.) There are three letters in Ms. Thomas’s mailbox: a bill from the phone
company for $38.12, a bill from the electric company for $67.55, and a tax
refund check for $25.89. (A bill is money that you owe someone and a tax
refund check is money that you receive from someone.) Order these rational
numbers from least to greatest.
Independent Practice:
5.) During their most recent visit to the optometrist (eye doctor), Kate and her
sister Beth had their vision tested. Kate’s vision in her left eye was −1.50 and
her vision in her right eye was the opposite number. Beth’s vision was −1.00
in her left eye and +0.25 in her right eye. Order these rational numbers from
least to greatest.
6.) Jason is entering college and has opened a checking account, which he will use
for college expenses. His parents gave him $200 to deposit into the account.
Jason wrote a check for $85.00 to pay for his Calculus book and a check for
$25.34 to pay for miscellaneous school supplies. Write the three rational
numbers related to the balance in Jason’s checking account in order from
greatest to least.
21
HOMEWORK 1.15
1.) The following are the current monthly bills that must be paid:
$106.00 Cable and Internet
$141.65 Gas and Electric
$138.09 Cell phone
List the rational numbers that relate to the situation in order from greatest to least.
1
2.) Order the following from least to greatest: −4, 4, −7, 3 , 6
5
1
3.) Order the following from greatest to least: −4, 4, −7, 3 , 6
5
22
Quiz 1.2 Review
(6.NS.A.1, 6.NS.C.5, 6.NS.C.6, 6.NS.C.7)
Use your knowledge of math to complete each of the following questions. Show
your work!
1.) Create a scale for the number line in order to plot the points -4 and 2. Graph
each point and its opposite on the number line.
2
2.) Write an integer to represent each of the following situations:
a. A gain of 31 points in a game.
b. A fee charged of $1.25.
c. A temperature of 61 degrees above zero.
d. A three yard loss.
3.) Find the opposite of each number and describe its location on the number line.
a. −9 ______, _________________________________________________
b. 21
______, _________________________________________________
23
4.) Use the number line diagram below to answer the following questions.
G
-1
0
1
a. What number does point 𝐺 represent?
b. What is the opposite of point 𝐺?
c. Graph the opposite of point 𝐺 on the number line and label it point 𝐻.
5-6: Find each quotient. Simplify if possible.
5.)
1
8
9
6.)
7.) Find the quotient. Simplify if possible.
1
1
1 4
5
3
24
2 11

5 20