We will add and subtract rational numbers. Learning Objective Introduction to Rational Numbers Unit Two Monday, 9.30.13 We will add and subtract rational numbers. What are we going to do? CFU Activate Prior Knowledge Add using the number line. 1. 2 + (-3) 2. -4 + 7 -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.

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 -3 + -5 be negative or positive? How do you know? -3 + +5 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

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 1. -3 + -6 2. 4 + 2 3. -4 + 7 4. 2 + (-3) 5. -2 - 3 6. 4 - (-7) 7. -5 - (-4) 8. -2 - (-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

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 9. -1.5 - (-3.5) 10. -7.6 + -9.6 11. - + 12. - (- ) 13. -2 + 3 14. 4 - (-7 ) 15. 5 - (- ) 16. - (- ) Same Sign: Find the Sum and keep the sign. (+Pos) + (+Pos) = +Pos (-Neg) + (-Neg) = -Neg -1.5 + 3.5 7.6 + 9.6 3.5 - 1.5 -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 3 - 2 1 2 4 + 7 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

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 -5 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 7 - 5 1 2 2 At the end of his turn, Jake has 2 points. -2.5 + 15 Different Sign: Difference 15 - 2.5 12.5 In the afternoon, the temperature was 12.5 C.

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 -7 + 5. A 8 - 6 B -9 + 7 C 1 - 3 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

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. -10 + -4 2. -6.4 - (-1.3) 10 + 4 -6.4 + 1.3 -14 14 6.4 - 1.3 -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 -7.5 - (-3). A -7.5 + 3 B 3 - (-7.5) C 3 - 7.5 D -3 + 7.5 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

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. -5 + -2 2. 8 + (-1) 3. -4 - 7 4. 2 + (-3) 5. -2.3 - (-8.3) 6. - (- ) 7. -3 + 4 8. - (-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 -2.3 + 8.3 + 1 4 2 8.3 - 2.3 Different Sign: Difference 3 4 Same Sign: Sum 6 1 4 1 4 5 6 4 - 3 1 4 + 6 5 6 1 Different Sign: Difference 5 6 Same Sign: Sum

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? _____________________________________________________________________________ -8.50 + 17.25 Different Sign: Difference 17.25 - 8.50 8.75 Alisha has $8.75 after paying her mom back.

Periodic Review 1 1. -12 + 5 2. 11 + (-7) 3. - - 4. 4.9 + (-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 -7.5 + (-2). A 7.5 - 2 B 2 + (7.5) C -2 - (-7.5) D -2 - 7.5 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

Explain how you know the expressions are equivalent. Periodic Review 2 1. 6.7 - (-9.2) 2. -1.8 + 2.2 3. -13 - 8 4. 11 + (-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. 1. -8 - (5) Example: -8 + (-5) 2. -1.7 + (-2.2) 3. + (- ) 7 9 2 9

Periodic Review 3 1. -14 + (13) 2. 3.7 + (-1.1) -1 2.6 Access Common Core Describe and correct any errors in adding and subtracting rational numbers below. Name _________________ Manny 1. 6 - (-9) 2. 7 + (-2) 3. -8 + 5 6 + (-9) 7 – 2 8 – 5 9 – 6 5 3 -3 4. -11 - 5 5. 3 - (-2) 6. -4 + (-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.