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Exploring Inverse and Direct Variation: Real-World Applications in Math

In this lesson, students will learn to compare and contrast inverse and direct variation through practical applications. They will explore how to represent real-world problems mathematically, such as the relationship between cost per person and the number of people in group settings. Students will work on guided and independent practice to reinforce their understanding of these concepts, completing exercises that demonstrate their mastery. This engaging session aims to highlight the importance of mathematical relationships in everyday life.

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Exploring Inverse and Direct Variation: Real-World Applications in Math

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  1. TUESDAY MARCH 25, 2014 SWBAT COMPARE AND CONTRAST INVERSE AND DIRECT VARIATION WITH REAL WORLD APPLICATIONS

  2. SKIP 2 PAGES IN YOUR COMPOSITION NOTEBOOK AND START THE 3RD PAGE LIKE THIS 3/25/14 DO NOW: Learning Target: Homework: y = 3x No relation y = (½)x y = 8/x Learning Target: SWBAT COMPARE AND CONTRAST INVERSE AND DIRECT VARIATION WITH REAL WORLD APPLICATIONS Homework: Finish HW PACKET # 11-15

  3. ANNOUNCEMENTS • 10 MORE WEEKS OF SCHOOL!!! • COMPOSITION NOTEBOOKS DUE TODAY! • SAT HW DUE FRIDAY • mathwithmsdobbs.weebly.com • LUNCH TUTORIALS ON WED ONLY • AFTER SCHOOL TUTORIAL: TUES AND THURS 4:15-6pm

  4. CLASS CORE VALUES • RESPECT • SELF-SUFFICIENCY • PERSEVERANCE • AWARENESS • FLEXIBILITY • SENSE OF URGENCY • EXCELLENCE

  5. CLASS MOTTO • IF I’M TO BE WHO I WANT TO BE, THEN IT’S UP TO ME. BECAUSE THE ME THAT I SEE IS THE ME THAT I WILL BE.

  6. SHARPSTOWN RULES • IDS MUST BE VISIBLE AT ALL TIMES • NO HOODIES ON OVER UNIFORM • NO HATS • NO MUSIC/ NO EARPHONES SHOULD BE SEEN IN MY CLASS • NO HALL PASSES 1ST 15/ LAST 15 MINS • DISMISSAL PROCEDURE

  7. Composition book rules and grading 1 Table of Contents • First page – Write “Table of Contents” at the top • Everyday -Date -Learning target -HW 3/25/14 Learning Target: Homework: • When you see this you must take notes of that slide in your composition book

  8. Composition book rules and grading • First page – Write “Table of Contents” at the top 1 Table of Contents Date Page # Day: Learning Target Summary 3 TUES: DIRECT VS. INVERSE VARIATION 03/25/14 WED: FACTORING REVIEW 03/26/14 THURS: SIMPLIFYING RATIONAL EXPRESSIONS 03/27/14 FRI: SIMPLIFYING RATIONAL EXPRESSIONS PART 2 03/28/14

  9. VS. DEFINITIONS EXAMPLE: EXAMPLE:

  10. GUIDED PRACTICE NEITHER INVERSE INVERSE DIRECT y = 18/x y = 3x y = 12/x DIRECT INVERSE DIRECT INVERSE

  11. GUIDED PRACTICE: ON HANDOUT I.P Complete #’s 6-12 5) Esteban and a few other juniors will be pitching in to buy pizza for lunch. The total cost of the pizza is $40. He wants to figure out the cost per person involved. The relationship between the number of people and the cost per person. Y = cost per person X = the number of people Y = 40/x

  12. 9. Y = # OF PEOPLE X = COST PER PERSON Y =k/x 10. Y = LENGTH X= WIDTH Y= 24/W 11. Y = AMOUNT OF MONET RAISED X = # OF RAFFLE TICKETS SOLD Y=8X 12. Y= # OF RIDE TICKETS YOU BUY X = PRICE OF EACH TICKET Y=18/X I.P. ANSWERS 6. Y= THE AMOUNT OF PAYCHECK X= # OF HOURS WORKED Y = 12.50X 7. Y= DISTANCE TRAVELED X = TIME Y = 60X 8. Y=SPEED X = TIME Y =40/X

  13. INM #2 USING VARIATION FUNCTIONS 2.75 22 119 2.8 K = 3 K = 15 y = 3x Y = 15/ x y = 3(12) =36 Y = 15/ 12 = 1.25

  14. PLOT THE POINTS

  15. GUIDED PRACTICE #2 M = 7.5*16 M = 120 M = k*p 75 = k*10 k = 7.5 R = k/T 168 = k/24 k = 4032 R= 4032/30 R = 134.4

  16. INDEPENDENT PRACTICE # 3-10 • PRACTICE 3-10 WITH SHOULDER PARTNER

  17. EXIT TICKET • LOG ON TO • Socrative.com • ROOM NUMBER 974860

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