Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Teacher Lesson Plan Lesson: 3.3.1 β Supplement Dividing Fractions and Mixed Numbers 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 real-world contexts. Objective Students will review how to divide fractions and mixed numbers. This was a skill taught in 6 th grade and will get them ready for the rules for dividing signed 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. The 3.3.1 PowerPoint starts with a recap of what students have learned in chapter two and chapter 3. Then the lesson proceeds to a review of dividing fractions and mixed numbers which was covered in 6th grade. This will get them ready to dividing signed number using the rules. Teach as directed in the PowerPoint. Students should follow along in their notes. Practice Classwork: Extra Practice: Homework: Page 4 Page 5 (dividing decimals by decimals) Page 6 Closure 1. What is our strategy for dividing fractions? Keep it, Change it, Flip it (KCF) 2 π 2. What is the reciprocal of ? 3 π 3. How would you change the following division problem to a multiplication problem? 1 2 π π ÷ 3= × π 2 π 5 6 ÷ 4 5 = π π × π π 4. What MUST you do to all mixed numbers when multiplying and dividing? Turn to improper fractions 1|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Student Notes Section 1: Vocabulary Reciprocals β Two numbers are reciprocals if their product = 1. To get the reciprocal of a fraction, just flip it over. The reciprocal of π π isβ¦β¦β¦β¦ What is the reciprocal of 5 8 π 3 π 4 x 4 3 = 12 12 = 1 ? ________ Section 2: Strategy for Dividing Fractions and Mixed Numbers To divide by a fraction, you multiply by its reciprocal! Strategy: Keep, Change, Flip (KCF) Step 1: Convert mixed numbers to improper fractions. π π Step 2: KEEP IT! Keep the first fraction the same. π Step 3: CHANGE IT! Change ÷ to ×. π Step 4: FLIP IT! Flip the numerator and denominator. π Step 5: Multiply as usual. π ÷ ππ π There are no improper fractions. π π π π × × × π ππ π ππ = ππ ππ Simplify π ππ 2|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Section 3: Guided and Independent Practice Guided Practice #1 You Try #1 10 1 ÷ = 8 6 11 4 ÷ = 10 5 Guided Practice #2 You Try #2 4 8 ÷ = 11 3 8 4 ÷ = 9 3 Guided Practice #3 You Try #3 3 7 3 ÷1 = 8 8 1 3 7 ÷2 = 5 5 Guided Practice #4 You Try #4 3 1 4 ÷1 = 7 2 3 13 7 ÷1 = 16 16 3|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Classwork 4|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Extra Practice 5|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Homework Name: ____________________________ Period: _________ Date: ________ Divide the following fractions. Write each answer in simplest form! 1. 2. K C F π π ÷ = π π π π π ÷ = π 3. π ÷ 4. π 5. π π π ππ π π 7. π π π π π = ÷π ÷ 6. π π π π π = = π ÷ π = π π ÷ π = π 1 8. You want to bike 16 miles in 1 hour. What should your average speed per hour be to 3 achieve this goal? π 9. Suzanne has of a cake left after a party. If she divides the leftover cake equally so that 5 π people can take some of it home, what fraction of the original cake will each person receive? 6|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers 7|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Student Notes Section 1: Vocabulary Reciprocals β Two numbers are reciprocals if their product = 1. To get the reciprocal of a fraction, just flip it over. The reciprocal of π π isβ¦β¦β¦β¦ What is the reciprocal of 5 8 π 3 π 4 x 4 3 = 12 12 = 1 ? ________ Section 2: Strategy for Dividing Fractions and Mixed Numbers To divide by a fraction, you multiply by its reciprocal! Strategy: Keep, Change, Flip (KCF) Step 1: Convert mixed numbers to improper fractions. π π Step 2: KEEP IT! Keep the first fraction the same. π Step 3: CHANGE IT! Change ÷ to ×. π Step 4: FLIP IT! Flip the numerator and denominator. π Step 5: Multiply as usual. π ÷ ππ π There are no improper fractions. π π π π × × × π ππ π ππ = ππ ππ Simplify π ππ 8|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Section 3: Guided and Independent Practice Guided Practice #1 You Try #1 10 1 π ÷ = π 8 6 π 11 4 π ÷ = π 10 5 π Guided Practice #2 You Try #2 4 8 π ÷ = 11 3 ππ 8 4 π ÷ = 9 3 π Guided Practice #3 You Try #3 3 7 π 3 ÷1 =π 8 8 π 1 3 ππ 7 ÷2 =π 5 5 ππ Guided Practice #4 You Try #4 3 1 ππ 4 ÷1 =π 7 2 ππ 3 13 7 ππ ÷1 =π 16 16 ππ 9|Page Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Classwork Answer Key 10 | P a g e Lesson 3.3.1 β Dividing Fractions and Mixed Numbers 11 | P a g e Lesson 3.3.1 β Dividing Fractions and Mixed Numbers Name: ____________________________ Period: _________ Date: ________ Homework Answer Key Divide the following fractions. Write each answer in simplest form! 1. 2. K C F π π ÷ = π π π 4 π 5 π 6 ÷ = π 3. π ÷ 4. π 5. 1 π π π ππ π π ÷π ÷ π π π π 1 14 = 9 5 = 16 π π 8 π π 5 6. 1 ÷ π = 7. π π π × 8 = π 19 π 5 ÷ π = 3 × 1 8 3 2 7 ÷ 3 2 × ÷ 1 6 π 12 5 π π ππ = 14 = 9 × 3 7 π = π π = π 8 = 5 ÷ π = 5 × π = 5 × 19 = 5 5 6 × π = 5 12 π = π π π ππ 1 8. You want to bike 16 miles in 1 hour. What should your average speed per hour be to 3 achieve this goal? 1 16 4 16 3 16 ÷ 1 = ÷ = × = 12 miles per hour 3 1 3 1 4 π 9. Suzanne has of a cake left after a party. If she divides the leftover cake equally so that π 5 people can take some of it home, what fraction of the original cake will each person receive? 3 3 1 π ÷ 5= × = 4 4 5 ππ 12 | P a g e
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