1. We will add and subtract rational numbers.
Learning Objective
Introduction to Rational Numbers
Unit Two Monday,
We will add and subtract rational numbers.
What are we going to do?
CFU
Activate Prior Knowledge
Add using the number line.
(-3) -1 3 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 5 4 3 2 1 -1 -2 -3 -4 -5 5 4 3 2 1
Students, you already know how to add and subtract positive and negative numbers using a number line. Now, we will add and subtract positive and negative rational numbers without a number line.
Make Connection
7.NS 1.3, 7.NS 1.5
Express Rational Numbers as Decimals.
Express Decimals as Fractions.
Demonstrate Use of Number Line Using Rational Numbers.

2. Same Sign: Different Sign Addition Rules (+Pos) + (+Pos) = +Pos
Concept Development
Addition means to put together.
Subtraction means to add the opposite. Addition Rules can be used to add and subtract rational numbers.
Addition Rules
Same Sign:
When addends have the
Find the Sum and keep the sign.
(+Pos) + (+Pos) = +Pos
(-Neg) + (-Neg) = -Neg
+1 + (+3) = +4
-2 + (-5) = -7
Using Addition Rules, will
be negative or positive? How do you know?
be negative or positive? How do you know?
What is the difference between the Addition Rules for Same Sign and Different Sign?
CFU
Different Sign
When addends have a
Find the Difference and keep the sign of the larger addend.
(+Pos) + (-Neg)
(-Neg) + (+Pos)
+1 + (-5) = -4
-2 + (+3) = +1

3. Skill Development/Guided Practice
Addition means to put together.
Subtraction means to add the opposite.
Rewrite subtraction to add the opposite, if necessary.
Determine1 the addition rule to use.
Apply2 the addition rule.
Interpret3 the answer. “The sum/difference of __ and __ is __.”
Add and subtract rational numbers. 1 2 3 4
How did I/you rewrite subtraction?
How did I/you determine the addition rule to use?
CFU 1 2
(-3)
(-7)
(-4)
(-1)
Same Sign:
Find the Sum and keep the sign.
(+Pos) + (+Pos) = +Pos
(-Neg) + (-Neg) = -Neg
3 + 6
4 + 2 -9 9 6
Same Sign: Sum
Same Sign: Sum
7 - 4
3 - 2
Different Sign
Find the Difference and keep
the sign of the larger addend.
(+Pos) + (-Neg)
(-Neg) + (+Pos) 3 -1 1
Different Sign: Difference
Different Sign: Difference
-2 + (-3)
4 + 7
2 + 3 11 -5 5
Same Sign: Sum
Same Sign: Sum
1 figure out
2 put to use
3 explain (synonym)
Vocabulary
-5 + 4
-2 + 1
5 - 4
2 - 1 -1 1
Different Sign: Difference -1 1
Different Sign: Difference

4. Skill Development/Guided Practice (continued)
Addition means to put together.
Subtraction means to add the opposite.
Rewrite subtraction to add the opposite, if necessary.
Determine the addition rule to use.
Apply the addition rule.
Interpret the answer. “The sum/difference of __ and __ is __.”
Add and subtract rational numbers. 1 2 3 4
How did I/you rewrite subtraction?
How did I/you determine the addition rule to use?
CFU 1 2
(-3.5)
(- )
(-7 )
(- )
(- )
Same Sign:
Find the Sum and keep the sign.
(+Pos) + (+Pos) = +Pos
(-Neg) + (-Neg) = -Neg
-17.2
17.2
2.0
Different Sign: Difference
Same Sign: Sum 1 3 2 3 1 4 3 4 - 2 3 1 + 1 4 3
Different Sign
Find the Difference and keep
the sign of the larger addend.
(+Pos) + (-Neg)
(-Neg) + (+Pos) 1 3 4
Different Sign: Difference
Same Sign: Sum 1 2 1 2 1 3 1 3 1 2 1 3 1
Different Sign: Difference 12 2 3
Same Sign: Sum 2 3 3 5 1 5
5 + 2 3 1 5 3 + 5 2 3
Same Sign: Sum 4 5
Different Sign: Difference

5. At the end of his turn, Jake has 2 points.
Skill Development/Guided Practice (continued)
How did I/you determine what the question is asking?
How did I/you determine the math concept required?
How did I/you determine the relevant information?
How did I/you solve and interpret the problem?
How did I/you check the reasonableness of the answer?
CFU 2 1 3 4 5
17. Jake is playing a math game in class. At the beginning of his turn, he has 7 points. This turn, he earns points. How many points does Jake have at the end of his turn?
_____________________________________________________________________________
18. This morning, the temperature was -2.5 C. By the afternoon, the temperature rose 15 C. What was the temperature in the afternoon?
______________________________________________________________________________ 1 2 1 2
7 + (-5 ) 1 2
Different Sign: Difference 1 2 2
At the end of his turn, Jake has 2 points.
Different Sign: Difference
12.5
In the afternoon, the temperature was 12.5 C.

6. Relevance
Addition means to put together.
Subtraction means to add the opposite.. 1
Adding and subtracting rational numbers helps businesses determine whether they are gaining or losing money.
Lemonade Stand
Sales
Lemonade $20   
Total Sales $20
Cost
Lemons $5
Sugar $3
Cups $2
Total Cost -$10
Total
$10 2
Adding and subtracting rational numbers will help you do well on tests.
Sample Test Question:
73. Choose Yes or No to indicate whether each expression is equivalent to A B C
D 2 - (-4)
O Yes O No
Does anyone else have another reason why it is relevant to add and subtract rational numbers? (Pair-Share) Why is it relevant to add and subtract rational numbers? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?
CFU

7. 10 + 4 -6.4 + 1.3 -14 14 6.4 - 1.3 -5.1 5.1 addition subtraction
Same Sign:
Find the Sum and keep the sign.
(+Pos) + (+Pos) = +Pos
(-Neg) + (-Neg) = -Neg
Addition means to put together.
Subtraction means to add the opposite.
Word Bank
Skill Closure
Rewrite subtraction to add the opposite, if necessary.
Determine the addition rule to use.
Apply the addition rule.
Interpret the answer. “The sum/difference of __ and __ is __.”
Add and subtract rational numbers. 1 2 3 4
Different Sign
Find the Difference and keep
the sign of the larger addend.
(+Pos) + (-Neg)
(-Neg) + (+Pos)
(-1.3)
10 + 4
-14 14
-5.1
5.1
Same Sign: Sum
Different Sign: Difference
Word Bank
addition
subtraction
opposite
sum
difference
Access Common Core
Choose Yes or No to indicate whether each expression is equivalent4 to (-3). A
B 3 - (-7.5) C D
O Yes O No
Summary Closure
What did you learn today about adding and subtracting rational numbers?
(Pair-Share) Use words from the word bank.
4 equal value
Vocabulary

8. Independent Practice
Same Sign:
Find the Sum and keep the sign.
(+Pos) + (+Pos) = +Pos
(-Neg) + (-Neg) = -Neg
Addition means to put together.
Subtraction means to add the opposite.
Rewrite subtraction to add the opposite, if necessary.
Determine the addition rule to use.
Apply the addition rule.
Interpret the answer. “The sum/difference of __ and __ is __.”
Add and subtract rational numbers. 1 2 3 4
Different Sign
Find the Difference and keep
the sign of the larger addend.
(+Pos) + (-Neg)
(-Neg) + (+Pos)
(-1)
(-3)
(-8.3)
(- )
(-6)
5 + 2
8 - 1 -7 7 7
Same Sign: Sum
Different Sign: Difference
-4 + (-7)
2 + -3
4 + 7
3 - 2
-11 11
Same Sign: Sum -1 1
Different Sign: Difference 1 4 2 4 + 1 4 2
Different Sign: Difference 3 4
Same Sign: Sum 6 1 4 1 4 5 6 1 4
+ 6 5 6 1
Different Sign: Difference 5 6
Same Sign: Sum

9. Alisha has $8.75 after paying her mom back.
Independent Practice (continued)
9. Alisha borrowed $8.50 from her mom to buy a new book. On the weekend, she earns $17.25 mowing lawns for her neighbors. How much money does Alisha have after paying her mom back?
_____________________________________________________________________________
Different Sign: Difference
8.75
Alisha has $8.75 after paying her mom back.

10. Periodic Review 1
(-7)
(-1.9) -7 4 2 7 3 7 5 7 - 3
Access Common Core
1. Choose Yes or No to indicate whether each expression is equivalent to -5 - (-3).
A 5 - 3
B -5 + (3)
C 3 - (5)
D 3 - (-5)
O Yes O No
2. Choose Yes or No to indicate whether each expression is equivalent to (-2). A
B 2 + (7.5)
C -2 - (-7.5) D
O Yes O No
3. Choose Yes or No to indicate whether each expression is equivalent to (- ). 3 8 1 7
A -
B (- )
C (- ) D
O Yes O No

11. Explain how you know the expressions are equivalent.
Periodic Review 2
(-9.2)
(-6)
15.9
0.6
-21 5
Access Common Core
For each expression, write an addition and a subtraction expression that is equivalent.
Explain how you know the expressions are equivalent.
(5)
Example: (-5)
(-2.2)
(- ) 7 9 2 9

12. Periodic Review 3
(13)
(-1.1) -1
2.6
Access Common Core
Describe and correct any errors in adding and subtracting rational numbers below.
Name _________________
Manny
(-9)
(-2)
6 + (-9)
7 – 2
8 – 5
9 – 6 5 3 -3
(-2)
(-3)
-11 + (-5)
3 + 2
4 + 3
11 – 5 5 7 -6
EXAMPLE:
# 1 Manny should have cancelled out both negative signs. It should read 6 + 9, therefore the answer should be 15, not -3.