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

7th Grade
Unit 1 – The
Number System:
Packet 1 of 3
Mr. Rothdiener
Name: _____________________________________
Packet Outline, Page 1
 1.1: Add Integers on the Number Line (7.NS.A.1a-b), Pages 2-4
o I can model integer addition on a number line by using
horizontal arrows.
o I can understand that the sum of a number and its opposite
is zero.
 1.2: Add Integers (7.NS.A.1a-b), Pages 5-7
o I can apply the sign rules for integer addition to fluently
add integers.
 1.3: Subtract Integers (7.NS.A.1c), Pages 8-10
o I can apply the sign rules for integer subtraction, including
double negatives, to fluently subtract integers.
 1.4: Distance Between Two Rational Numbers (7.NS.A.1c), Pages 11-13
o I can apply the distance formula to calculate the distance
between two rational numbers.
 1.5: Addition of Rational Numbers (7.NS.A.1b), Pages 14-16
o I can extend the rule for adding integers to rational numbers.
 1.6: Subtraction of Rational Numbers (7.NS.A.1c), Pages 17-19
o I can extend the rule for subtracting integers to rational numbers.
 1.7: Add and Subtract Rational Numbers (7.NS.A.1b-c), Pages 20-22
o I can add and subtract rational numbers.
 1.8: Apply Properties to Add and Subtract Rational Numbers
(7.NS.A.1d), Pages 23-25
o I can apply the properties of operations to add and subtract
rational numbers.
 Quiz 1.1 Review, Pages 26-27
o I can apply and extend previous understandings of addition
and subtraction to add and subtract rational numbers.
1
1.1: Add Integers on the Number Line (7.NS.A.1a-b)
Bell Work:
Add using the number line: 4 + 5
Whole-Class:
Use the number line to solve each of the following.
1.) 10 + (-4) =
2.) -3 + 2 =
Guided Practice:
Use the number line to solve each of the following.
3.) 4 + (-7)
4.) -7 + 9
5.) -3 + (-6)
6.) 5 + (-5)
2
Independent Practice:
Use the number line to solve each of the following.
7.) 5 + (-6)
8.) -3 + 12
9.) -4 + (-2)
10.) 9 + (-9)
11.) 9 + (-5)
12.) -5 + 4
13.) -1 + (-8)
14.) 3 + (-3)
15.) 6 + (-13)
16.) -4 + 0
3
WORKSHEET 1.1
Use the number line to solve each of the following.
1.) 7 + (-3)
2.) -9 + 15
3.) -8 + (-1)
4.) 4 + (-4)
5.) 1 + (-6)
6.) -7 + 2
7.) -6 + (-1)
8.) -3 + (-3)
9.) 7 + (-11)
10.) -8 + 0
4
1.2: Add Integers (7.NS.A.1a-b)
Bell Work:
Add using the number line: -4 + (-5)
Whole-Class:
Add the following integers using the rule.
1.) 5 + 3 =
2.) -5 + (-3) =
3.) 5 + (-3) =
4.) -5 + 3 =
5.) 6 + 2 =
6.) -3 + (-7) =
7.) 90 + (-90) =
8.) -8 + 1 =
Guided Practice:
Add the following integers using the rule.
9.) 5 + 9 =
10.) -4 + (-2) =
11.) 1 + (-11) =
12.) -20 + 15 =
13.) 12 + 7 =
14.) -6 + (-3) =
15.) 13 + (-13) =
16.) -3 + 8 =
5
Independent Practice:
Add the following integers using the rule.
17.) 15 + 7 =
18.) -4 + (-16) =
19.) -18 + (-64) =
20.) -205 + (-123) =
21.) -10 + 7 =
22.) 8 + (-16) =
23.) -234 + 234 =
24.) -12 + 65 =
25.) 105 + (-126) =
26.) -41 + (-7) =
27.) 15 + (-43) =
28.) -67 + 66 =
29.) 21 + (-32) =
30.) -98 + 98 =
31.) -13 + (-13) =
6
WORKSHEET 1.2
Add the following integers using the rule.
1.) 4 + 17 =
2.) -6 + (-12) =
3.) -5 + 8 =
4.) -2 + 6 =
5.) -4 + 7 =
6.) 6 + (-9) =
7.) -5 + (-5) =
8.) -5 + 5 =
9.) 7 + (-7) =
10.) 67 + (-35) =
11.) -31 + (-55) =
12.) -91 + 92 =
13.) -11 + (-22) =
14.) -77 + 77 =
15.) -77 + (-77) =
7
1.3: Subtract Integers (7.NS.A.1c)
Bell Work:
Add: 4 + (-5)
Whole-Class:
Subtract the following integers using the rule.
1.) 4 – 5
2.) 8 – 2
3.) -9 – (-2)
4.) -3 – 7
Guided Practice:
Subtract the following integers using the rule.
5.) 4 – 9
6.) -2 - (-5)
7.) 11 - (-8)
8.) -5 – 6
9.) 12 – 25
10.) -10 - (-10)
11.) 34 - (-7)
12.) -16 – 9
8
Independent Practice:
Subtract the following integers using the rule.
13.) 15 - 7 =
14.) -4 - (-16) =
15.) -18 - (-64) =
16.) -205 - (-123) =
17.) -10 - 7 =
18.) 8 - (-16) =
19.) -234 - 234 =
20.) -12 - 65 =
21.) 105 - (-105) =
22.) -41 - (-7) =
23.) -15 - (-15) =
24.) -67 – 66 =
9
WORKSHEET 1.3
Subtract the following integers using the rule.
1.) 4 - 17 =
2.) -6 - (-12) =
3.) -5 - 8 =
4.) -2 - 6 =
5.) -4 - 7 =
6.) 6 - (-9) =
7.) -5 - (-5) =
8.) -5 - 5 =
9.) 7 - (-7) =
10.) 67 - (-35) =
11.) -31 - (-55) =
12.) -91 - 92 =
10
1.4: Distance Between Two Rational Numbers (7.NS.A.1c)
Bell Work:
Subtract: 4 - (-5)
Whole-Class:
Use the distance formula p  q to find the distance between each pair
of numbers.
1.) -5 to 8
2.) -8 to -5
3.) -8 to 5
Guided Practice:
Use the distance formula p  q to find the distance between each pair
of numbers.
4.) -4 to 5
5.) -5 to -3
11
6.) 7 to -1
Independent Practice:
Use the distance formula p  q to find the distance between each pair
of numbers.
7.) -3 to 7
8.) -9 to -2
9.) 10 to -4
10.) -41 to 50
11.) -56 to -30
12.) 70 to -15
13.) -24 to 24
14.) -8 to -13
15.) 93 to -4
16.) Berry is the first person to finish a 5K race and is standing 15 feet
beyond the finish line. Another runner, Jeremy, is currently trying to
finish the race and has 14 feet before he reaches the finish line.
What is the distance between Berry and Jeremy?
12
WORKSHEET 1.4
Use the distance formula p  q to find the distance between each pair
of numbers.
1.) -19 to -12
2.) 19 to -12
3.) 10 to -43
4.) -10 to -43
5.) -1 to -16
6.) 1 to -16
7.) Melanie finishes the Boilermaker and meets up with her family 120
feet beyond the finish line. Her sister, Michelle, is still running the
race and has 230 feet before she reaches the finish line. What is the
distance between Melanie and her sister?
13
1.5: Addition of Rational Numbers (7.NS.A.1b)
Bell Work:
Add using the number line: 3 + (-4)
Whole-Class:
Use the number line to solve each of the following.
1
2
1.) 10 + (-4 ) =
2.) -3 + 2.25 =
Guided Practice:
Use the number line to solve each of the following.
1
2
3.) 4 + (-7 )
4.) -7 + 9.75
1
4
5.) -3 + (-6 )
6.) 5.5 + (-5.5)
14
Independent Practice:
Use the number line to solve each of the following.
1
2
7.) 5 + (-6 )
8.) -3 + 12.5
9.) -4 + (-2.75)
10.) 9
1
4
11.) 9 + (-5 )
1
1
+ (-9 )
2
2
12.) -5 + 4.25
13.) Samantha owes her father $7.00. She just got paid $5.50 for
babysitting. If she gives that money to her dad, how much will she
still owe him?
15
WORKSHEET 1.5
Use the number line to solve each of the following.
1
2
1.) 7 + (-3 )
2.) -9 + 15.5
1
4
3.) -8 + (-1 )
4.) 4.75 + (-4.75)
1
2
5.) 1 + (-6 )
6.) -7 + 2.25
16
1.6: Subtraction of Rational Numbers (7.NS.A.1c)
Bell Work:
Subtract: 3 - (-7)
Whole-Class:
Subtract the following rational numbers using the rule.
1.) 4 – 5
1
2
2.) 8 – 2
1
4
3.) -9 – (-2.5)
Guided Practice:
Subtract the following rational numbers using the rule.
4.) 4
1
–9
2
1
4
5.) 11 - (-8 )
17
6.) -5 – 6.25
Independent Practice:
Subtract the following rational numbers using the rule.
7.) 2 – 7
10.) 8
1
2
1
– 15
2
8.) 12 – 5
3
4
9.) -5 – (-4.5)
1
4
11.) 23 - (-4 )
12.) -17 – 2.75
13.) At the start of a trip, a car’s tank contained 9 gallons of gasoline.
During the trip, the car consumed 6
gasoline is left in the tank?
18
1
gallons of gas. How much
8
WORKSHEET 1.6
Subtract the following rational numbers using the rule.
1.) 7 – 9
4.) 11
1
2
1
– 14
2
2.) 10 – 7
1
4
3.) -4 – (-9.5)
1
4
5.) 16 - (-4 )
6.) -8 – 17.25
7.) Suppose a 5th grader turned 10 years old today. How old was she 3
1
2
years ago? Write an equation and use a number line to model your
answer.
19
1.7: Add and Subtract Rational Numbers (7.NS.A.1b-c)
Bell Work:
Subtract: 4 - 5
1
2
Whole-Class:
Add or subtract the following rational numbers.
1.) 10 – 16
1
2
2.) -7 + 8
3.) -7.5 – (-2.5)
4.) -4 – 11
Guided Practice:
Add or subtract the following rational numbers.
5.)
1
– 11
2
9.) -12 + 4
3
- (-3)
4
6.) -0.75 - (-8)
7.) 11
10.) -0.25 - (-0.25)
11.) 0.25 + (-9)
20
8.) -2 – 31
12.) -1 +
1
2
1
4
Independent Practice:
Add or subtract the following rational numbers.
13.) 4 – 7
16.) 11
1
4
1
– 19
2
14.) 27 – 14
3
4
17.) 35 - (-7.75)
15.) -5.25 + (-4.5)
18.) -5.75 – 2.25
1
2
19.) A fish was swimming 3 feet below the water’s surface at 7:00
1
4
AM. Four hours later, the fish was at a depth that is 5 feet
below where it was at 7:00 AM. What rational number represents
the position of the fish with respect to the water’s surface at
11:00 AM?
21
WORKSHEET 1.7
Add or subtract the following rational numbers.
1.) 7 – 8
4.) 45
1
2
3
– 54
4
2.) 31 – 20
1
4
5.) 21 - (-6.25)
3.) -7.5 + (-1.25)
6.) -3.5 – 14.5
1
2
7.) A bird that was perched atop a 15 foot tree dives down six feet to
a branch below. How far above the ground is the bird’s new
location?
22
1.8: Apply Properties to Add and Subtract Rational Numbers
(7.NS.A.1d)
Bell Work:
Simplify: 4 – 15 – 4
Whole-Class:
Use the properties of operations to make simplifying the expressions
easier.
1.) -5 – 12 + 5
{commutative property of addition,
associative property of addition, and
additive inverse}
2.) –(3 + 4) – 21 + 7
{distributive property, commutative
property of addition, associative property
of addition, and additive inverse}
Guided Practice:
Use the properties of operations to make simplifying the expressions
easier.
3.) 4
2
2
- 7.3 + (-4 )
9
9
{commutative property of addition,
associative property of addition, and
additive inverse}
23
1
6
5
6
4.) 2 + 19.7 – (-9 )
{double negative property, commutative
property of addition, associative property
of addition}
Independent Practice:
Use the properties of operations to make simplifying the expressions
easier.
5.) 7
1
1
- (7 - 13)
2
2
{distributive property, associative property
of addition, and additive inverse}
2
9
6.) -7 + 6.5(0) + 8 + 7
2
9
{multiplication property of zero,
commutative property of addition,
associative property of addition, and
additive inverse}
24
WORKSHEET 1.8
Use the properties of operations to make simplifying the expressions
easier.
1.) 4
4
4
- (4 - 10)
7
7
{distributive property, associative property
of addition, and additive inverse}
2.) -5.2 – (-3.1) + 5.2
{double negative property, commutative
property of addition, associative property
of addition, and additive inverse}
3.)
2
3
+ 20.3 + 5
5
5
{commutative property of addition and
associative property of addition}
25
Quiz 1.1 Review
(7.NS.A.1)
Use your knowledge of math to complete each of the following
questions. Show your work!
1-6: Add or subtract the following rational numbers.
1.) 16 – 23
4.) 35
1
2
1
– 83
4
2.) 54 – 13
3
4
5.) 81 - (-21.75)
3.) -64.5 + (-5.25)
6.) -245.5 + 245.5
7-8: Use the distance formula p  q to find the distance between each
pair of numbers.
7.) -7 to 15
8.) -9 to -2
26
9-11: Use the properties of operations to make simplifying the
expressions easier.
9.) 12
6
6
- (12 - 784)
13
13
{distributive property, associative property
of addition, and additive inverse}
10.) -9.8 – (-7.6) + 9.8
{double negative property, commutative
property of addition, associative property
of addition, and additive inverse}
11.)
1
8
+ 31.4 + 14
9
9
{commutative property of addition and
associative property of addition}
27