Lesson Rules for Dividing Integers (and Rational Numbers)

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Heather Wells
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1 Lesson: Lesson Rules for Dividing Integers (and Rational Numbers) Supplement Rules for Dividing Integers (and Rational Numbers) Teacher Lesson Plan CC Standards 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing realworld contexts. Objective Students will be introduced to the rules for dividing integers and other signed rational numbers. Mathematical Practices #1 Make sense of problems and persevere in solving them. #8 Look for and express regularity in repeated reasoning. Teacher Input Bellwork: Homework: Introduction: Lesson: Review bellwork. Review important problems assigned the previous night. Today, we will extend upon what we learned during our last class with dividing fractions and decimals. We will learn the rules for dividing integers and other signed rational numbers. Teach as directed in the student notes. Practice Classwork: Page 4 Homework: Page 5 Extra Practice: Teacher selected Closure You can question students about the rules for adding, subtracting, multiplying, and dividing signed numbers. 1) What are the rules for adding signed numbers? Same sign: Add, Keep Sign Different signs: Subtract, Give sign to biggest digit 2) What is different about the rules for subtracting signed numbers compared to adding? Look for double negatives and change them to a positive. 3) How do we multiply signed numbers? Multiply the numbers and then determine the sign by counting the number of negative signs in the problem. If there is an even number of negatives signs your answer will be positive. If there is an odd number of negative signs, your answer will be negative. 4) How do we divide signed numbers? Divide the numbers and then determine the sign by counting the number of negative signs in the problem. If there is an even number of negatives signs your answer will be positive. If there is an odd number of negative signs, your answer will be negative. 1 P a g e

Odd number of negatives: 2 100 20 There are two negative signs! Even number of negatives: 5 27 3 There are two negative signs!

2 Section 1: Rules for Dividing Integers Student Notes In previous lessons you learned the steps to multiply integers. The rules for dividing integers are exactly the same There is one negative sign! Odd number of negatives: There are two negative signs! Even number of negatives: There are two negative signs! Even number of negatives: There is one negative sign! Odd number of negatives: 3 Guided Practice 16 2 = 42 7 = 30 ( 5) = You Try = 81 9 = = 2 P a g e

3 Section 2: Dividing Signed Rational Numbers Follow the rules in section one to find the quotient of these rational numbers. Guided Practice ( 0. 3) The lowest recorded temperature in Wisconsin is -49ᵒF on February 4, Use the expression 5(F 32) 9 to find the temperature in degrees Celsius. Which of the following describes the value of the quotient when a negative integer is divided by a positive integer? A. greater than zero C. equal to zero B. less than zero D. It can be any of the above. You Try Last year, Mr. Engle s total income was $52,000, while his total expenses were $53,800. Use the expression I E, where I represents total income and E represents total expenses, 12 to find the average difference between his income and expenses each month. Then explain the meaning of your answer. Which of the following expressions will NOT produce a negative quotient? A B B. ( 18.8 ) D P a g e

4 Name: Period: Date: Classwork (.61) The boiling point of water is affected by changes in elevation. Use the expression 2A 1000, where A represents the altitude in feet, to find the number of degrees Fahrenheit at which the boiling point of water changes at an altitude of 5,000 feet. 4 P a g e

5 Name: Period: Date: Homework 5 P a g e

6 6 P a g e

7 Section 1: Rules for Dividing Integers Student Notes Answer Key In previous lessons you learned the steps to multiply integers. The rules for dividing integers are exactly the same There is one negative sign! Odd number of negatives: There are two negative signs! Even number of negatives: There are two negative signs! Even number of negatives: There is one negative sign! Odd number of negatives: 3 Guided Practice 16 2 = = 6 30 ( 5) = 6 You Try = = = 6 7 P a g e

8 Section 2: Dividing Signed Rational Numbers Follow the rules in section one to find the quotient of these rational numbers. Guided Practice ( 0. 3) 6. 4 The lowest recorded temperature in Wisconsin is -49ᵒF on February 4, Use the expression 5(F 32) 9 to find the temperature in degrees Celsius. 45ᵒC Which of the following describes the value of the quotient when a negative integer is divided by a positive integer? Answer: B A. greater than zero C. equal to zero B. less than zero D. It can be any of the above. You Try Last year, Mr. Engle s total income was $52,000, while his total expenses were $53,800. Use the expression I E, where I represents total income and E represents total expenses, 12 to find the average difference between his income and expenses each month. Then explain the meaning of your answer. $150 per month; Mr. Engle spends more than he makes a month. Which of the following expressions will NOT produce a negative quotient? Answer: D A B B. ( 18.8 ) D P a g e

9 Name: Period: Date: Classwork Answer Key (.61) The boiling point of water is affected by changes in elevation. Use the expression 2A 1000, where A represents the altitude in feet, to find the number of degrees Fahrenheit at which the boiling point of water changes at an altitude of 5,000 feet. 10ᵒF; The boiling point decreases 10ᵒF at an altitude of 5,000 ft. 9 P a g e

10 Homework Name: Period: Date: Answer Key 10 P a g e

w + 5 = 20 11x + 10 = 76

w + 5 = 20 11x + 10 = 76 Course: 8 th Grade Math DETAIL LESSON PLAN Lesson 5..2 Additional Practice TSW solve equations with fractions and decimals. Big Idea How can I eliminate fractions and decimals in equations? Objective 8.EE.7b