1. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Learning Objective Name _______________________ Today, we will multiply and divide integers. CFU What are we going to do today? Activate (or provide) Prior Knowledge CFU Students, you already know how to multiply and divide whole numbers. Today, we are going to multiply and divide integers. Find the product or quotient below. 1. 4 × 5 = 2. 6 × 2 = 3. 20 ÷ 5 = 4. 12 ÷ 2 = 20 12 4 6 The product is the answer to a multiplication problem. The quotient is the answer to a division problem.

2. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Concept Development Positive integers can be shown with a (+) sign or with no sign at all. Negative integers must be shown with a (-) sign. The multiplication and division integer rules are determined by the signs of the integers used. An integer is a positive whole number or negative whole number. Multiplication and Division Integer Rules +3 and 3 Positive Integer -3 Negative Integer Same Sign The product or quotient will be positive. Different Sign The product or quotient will be negative. (  Pos) × (  Pos)   Pos(  Neg) × (  Neg)   Pos 2 × 3  6  2 ×  3  6 (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos 6 ÷ 3  2  6 ÷  3  2 (  Pos) × (  Neg)   Neg(  Neg) × (  Pos)   Neg2 ×  3   6 2 × 3  62 × 3  6 (  Pos) ÷ (  Neg)   Neg(  Neg) ÷ (  Pos)   Neg6 ÷  3   2 6 ÷ 6  26 ÷ 6  2 CFU On your whiteboards, write a positive integer. How do you know it is a positive integer? On your whiteboards, write a negative integer. How do you know it is a negative integer? Will the product of -2 × -4 be negative or positive ? How do you know? Will the product of 21 ÷ -7 be negative or positive ? How do you know?

3. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Step #1: Use integer rules to determine 1 the sign of the product or quotient. a. Identify 2 the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values 3, ignoring the signs. Step #3: Write the product or quotient with the correct sign. 1 figure out 2 find 3 numbers Skill Development/Guided Practice Multiply and divide integers. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg 1. 4 × 6 = Product: ____ 2. 5 × 3 = Product: ____Quotient: ____ 5. 5 ×  7 = Product : ____ 6. 4 ×  3 = Product : ____ 7. 54 ÷  6 = Quotient: ____ 8. 30 ÷  5 = Quotient: ____ Signs: × = Signs: ÷ = Signs: × = Signs: ÷ = Signs: × = Signs: ÷ = - +++ 24 +++ 15 +++ 3 +++ 4 +- -3535 ++++ --+- -1212 --+- -9-99 --+- -6-66 - 4. 32 ÷ 8 =3. 18 ÷ 6 = The multiplication and division integer rules are determined by the signs of the integers used. CFU (#1a)How did I/you determine the sign of the product or quotient? (#3)How did I/you write the product or quotient with the correct sign?

4. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Skill Development/Guided Practice (continued) Multiply and divide integers. The multiplication and division integer rules are determined by the signs of the integers used. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg 9.  3 × 6 = Product: ____ 10.  5 × 8 = Product: ____ 11.  48 ÷ 6 = Quotient: ____ 12.  42 ÷ 7 = Quotient: ____ 13.  9 ×  5 = Product: ____ 14.  6 ×  1 = Product: ____ 15.  81 ÷  9 = Quotient: ____ 16.  60 ÷  10 = Quotient: ____ Signs: × = Signs: ÷ = Signs: × = Signs: ÷ = Signs: × = Signs: ÷ = -+- 18 - -18 -+- 40 - -40 -+- 8 - -8-8 -+- 6 - -6-6 --+ 45 +--+ 6 +--+ 9 +--+ 6 + CFU (#1a)How did I/you determine the sign of the product or quotient? (#3)How did I/you write the product or quotient with the correct sign?

5. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Relevance 1. Multiplying and dividing with integers will help you solve equations. 2. Multiplying and dividing with integers will help you do well on tests. CFU Does anyone else have another reason why it is relevant to multiply and divide with integers? (pair-share) Why is it relevant to multiply and divide with integers? You may give me one of my reasons or your own. Which reason is more relevant to you? Why?  4 x = 20 The multiplication and division integer rules are determined by the signs of the integers used. -4 x = -5 20 ÷ -4 = -5

6. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. 1. 16 ÷  2 = Quotient: ____ Signs: ÷ = - + - -8-8 8 - 2.  7 ×  4 = Product: ____ Signs: × = -- + 28 + Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Skill Closure Multiply and divide integers. The multiplication and division integer rules are determined by the signs of the integers used. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg Constructed Response Closure Dean is multiplying integers and concludes that a negative integer times another negative integer is always negative. Explain why Dean is incorrect and give an example proving he is incorrect. Summary Closure What did you learn today about multiplying and dividing integers? Day 1 _________________________________________________________________________________________________ _______________________________________________________________________________________________________ Day 2 _________________________________________________________________________________________________ _______________________________________________________________________________________________________ _____________________________________

7. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Independent Practice 1. 7 × 2 = Product : ____ 2. 36 ÷ 4 = Quotient: ____ 3. 2 ×  5 = Product: ____ 4. 18 ÷  6 = Quotient: ____ Signs: × = Signs: ÷ = Signs: × = +++ 14 +++ 9 ++-+- -1010 --+- -3-33 - 5.  8 × 5 = Product : ____ Signs: × = -+- 40 - -40 6.  21 ÷ 3 = Quotient: ____ Signs: ÷ = -+- 7 - -7-7 7.  5 ×  6 = Product : ____ Signs: × = --+ 30 + 8.  63 ÷  7 = Quotient: ____ Signs: ÷ = --+ 9 + Name ___________________________ Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Multiply and divide integers. The multiplication and division integer rules are determined by the signs of the integers used. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg

8. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Periodic Review 1 3. 9 ×  6 = Product: ____ 8. 9 ÷  3 = Quotient: ____ Signs: ÷ = Signs: × = -+- -5454 - -+- -3-33 - 5.  4 × 10 = Product: ____ Signs: × = -+- 40 - -40 4.  8 ÷ 2 = Quotient: ____ Signs: ÷ = -+- 4 - -4-4 7.  3 ×  9 = Product: ____ Signs: × = --+ 27 + 1.  18 ÷  9 = Quotient: ____ Signs: ÷ = --+ 2 + 2.  7 × 6 = Product: ____ Signs: × = -+- 42 - -42 6. 20 ÷  4 = Quotient: ____ Signs: ÷ = -+- -5-55 - Name ___________________________ Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Multiply and divide integers. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg The multiplication and division integer rules are determined by the signs of the integers used.

9. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. 8. 7 ×  8 = Product: ____ 3. 7 ÷  1 = Quotient : ____ Signs: ÷ = Signs: × = - + - -5656 - -+- -7-77 - 5.  6 × 6 = Product: ____ Signs: × = - + - 36 - -36 1.  72 ÷ 9 = Quotient: ____ Signs: ÷ = -+- 8 - -8-8 7.  7 ×  9 = Product: ____ Signs: × = --+ 63 + 6.  50 ÷  10 = Quotient: ____ Signs: ÷ = -- + 5 + 2.  28 ÷  7 = Quotient: ____ Signs: ÷ = --+ 4 + 4. 5 ×  7 = Product: ____ Signs: × = -+- -3535 - Periodic Review 2 Name ___________________________ Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Multiply and divide integers. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg The multiplication and division integer rules are determined by the signs of the integers used.

10. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. 5. 2 ×  6 = Product: ____ 4. 25 ÷  5 = Quotient: ____ Signs: ÷ = Signs: × = - + - -1212 - -+- -5-5 5 - 1.  4 × 1 = Product: ____ Signs: × = -+- 4 - -4-4 6.  24 ÷ 4 = Quotient: ____ Signs: ÷ = -+ - 6 - -6-6 3.  5 ×  12 = Product: ____ Signs: × = --+ 60 + 8.  10 ÷  10 = Quotient: ____ Signs: ÷ = -- + 1 + 2. 32 ÷  4 = Quotient: ____ Signs: ÷ = -+- -8-8 8 - 7.  36 ÷ 4 = Quotient: ____ Signs: ÷ = -+ - 9 - -9-9 Periodic Review 3 Name ___________________________ Step #1: Use integer rules to determine the sign of the product or quotient. a. Identify the signs of the integers. (write) b. Determine the sign of the product or quotient. (Hint: Use integer rules) Step #2: Multiply or divide the values, ignoring the signs. Step #3: Write the product or quotient with the correct sign. Multiply and divide integers. Multiplication and Division Integer Rules Same Sign (  Pos) × (  Pos)   Pos (  Neg) × (  Neg)   Pos The product or quotient will be positive. (  Pos) ÷ (  Pos)   Pos (  Neg) ÷ (  Neg)   Pos Different Sign (  Pos) × (  Neg)   Neg (  Neg) × (  Pos)   Neg The product or quotient will be negative. (  Neg) ÷ (  Pos)   Neg (  Pos) ÷ (  Neg)   Neg The multiplication and division integer rules are determined by the signs of the integers used.

11. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Learning Objective : Today, we will multiply and divide integers. Cognitive StrategiesTeaching Strategies ElaborationDemonstration Targeted vocabulary: integer, determine, identify, values Language Strategies Vocabulary Words Academic determine, identify, values Content integer Support Vocabulary Strategy Multiple-Meaning Synonym identify, values Definition integer, determine Homophone Internal Context Clue Listen, SpeakSimilar Sounds Read Tracked Reading Decoding Rules Write Writing Content Access Strategies Comprehensible Input Cognates Contextual Clues Graphic Organizer Contextualized Definitions Pictures EDI – Cognitive, Teaching and English Learners Strategies

12. DataWORKS Educational Research (800) 495-1550 www.dataworks-ed.com ©2012 All rights reserved. Comments? feedback@dataworks-ed.com 6 th Grade Number Sense 2.3 (6Q) Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Lesson to be used by EDI-trained teachers only. Blank Page