ࡱ> CED` bjbjss ., $LLLL$p4$nZ\\\\\\$IhVVV ZVZVV:, ^]L> 0HRw.ww$VX$$$d $$$ $$$ The Study of Gear Ratios: An introduction to Inverse Proportions This lesson combines aspects of Units: 9 & 15 of the Applied Math CORD Curriculum. Unit 9 - Using Ratios and Proportions 1. Read and interpret ratios. 2. Compare ratios. 3. Recognize and write proportions from given information. 4. Distinguish between direct and indirect relationships. 5. Solve proportions in practical, work-related problems.Unit 15 - Using Formulas to Solve Problems 1. Read and write a formula. 2. Rearrange the parts of a formula to fit your problem. 3. Substitute values into the formula and find an answer. 4. Use your calculator as you solve problems with formulas. COLLEGE READINESS STANDARDS Standard Three: Connections The student extends mathematical thinking across mathematical content areas, and to other disciplines and real life situations. 3.1 Use mathematical ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations.a. Compare and contrast the different mathematical concepts and procedures that could be used to complete a particular task. b. Recognize patterns and apply mathematical concepts and procedures in other subject areas and real world situations.3.2 Understand the importance of mathematics as a language. a. Connect mathematical definitions and procedures with underlying math concepts. b. Transfer mathematical vocabulary, concepts, and procedures to other disciplinary contexts and the real world. c. Construct procedures and concepts from mathematical definitions.3.3 Make connections by using multiple representations, e.g., analytic, numeric, and geometric. a. Integrate mathematical content areas by using multiple representations. b. Use multiple representations to demonstrate understanding of links between math and other disciplines, and real world situations. Standard Seven: Algebra The student accurately describes and applies concepts and procedures from algebra. 7.3 Solve various types of equations and inequalities numerically, graphically, and algebraically; interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers. [see GLE 1.5.6, grade 9/10] j. Solve literal equations (formulas) for a particular variable.  The first part of the lesson assesses students understanding of equivalent ratios, introduces terminology associated with working with gears, and explains the inverse proportion for working with gear ratios. Lesson Plan for assessing students understanding of equivalent ratios. The second part of the lesson has students use the inverse proportion formula used when working with gears. Students solve for the different variables (speed in, speed out, number of teeth on input gear, number of teeth on output gear). Student Packet: Gear Ratio worksheets Bonus Question given to students who finish early. Suggestions for enhancement of lesson: Have on-hand, for students to examine, different types of gears and gear trains If you have access to computers, students research different types of gears and gear trains Have students talk in teams of two, then report out to class, why they think the formula is called an inverse proportion Have students examine bicycle gears and make assumptions based on what they know about inverse proportions to determine the gear ratios which ones are used for more power going up hill or more speed on a flat surface be able to justify their reasoning based on what they have learned. ABbfiklmpoW9'#h$hVB*CJOJQJ^JaJph:h$hV5B*CJOJQJ\^JaJfHphq /h0EB*OJQJ\^JfHphq 2h0E5B*OJQJ\^JfHphq 8h0Eh$hV5B*OJQJ\^JfHphq 5h0Eh$hVB*OJQJ\^JfHphq :h$hV5B* CJOJQJ\^JaJfHphq @h0Eh$hV5B*CJOJQJ\^JaJfHphq AB Y wrii 7$8$H$gd0Egd0Exkd$$Ifl0,"LL t0644 la$If$a$gd0E g ۿۿjZI;* h9h0ECJOJQJ^JaJh0ECJOJQJ^JaJ h0E5CJOJQJ\^JaJh9h0E5OJQJ\^J7h0EB*CJOJQJ\^JaJfHphq 5h9h0EB*OJQJ\^JfHphq :h$hV5B*CJOJQJ\^JaJfHphq 7h$hVB*CJOJQJ\^JaJfHphq #h$hVB*CJOJQJ^JaJph#h$hVB*CJOJQJ^JaJphY _   f yxkdL$$Ifl0,"LL t0644 la $7$8$H$Ifgd$hV _   |}LOfg ܹǖ깆ugYgDgDg)h$hVh$hVB*CJOJQJ^JaJphh$hVCJOJQJ^JaJh$hVCJOJQJ^JaJ h$hV5CJOJQJ\^JaJh$hVh$hV5OJQJ\^J)h9h0EB*CJOJQJ^JaJphh0ECJOJQJ^JaJh0ECJOJQJ^JaJ)h9h0EB*CJOJQJ^JaJphh0ECJOJQJ^JaJ)h0Eh0EB*CJOJQJ^JaJph|}Myyyy $7$8$H$Ifgd$hVxkd$$Ifl0,"LL t0644 laMNOg~uul^l $7$8$H$Ifgd$hV $Ifgd$hV 7$8$H$gd$hV 7$8$H$gd0Exkd$$Ifl0,"LL t0644 laӪ|8h0Eh$hV5B* OJQJ\^JfHphq !h0Eh$hVB* OJQJ^Jph5h0Eh$hVB*OJQJ\^JfHphq h$hVCJOJQJ^JaJ7h$hVB*CJOJQJ\^JaJfHphq h$hV6CJOJQJ]^JaJ'Z[.{{ & F & Fxkd0$$Ifl0,"LL t0644 la. & F,1h/ =!"#$% J$$If!vh5L5L#vL:Vl t65LJ$$If!vh5L5L#vL:Vl t65LJ$$If!vh5L5L#vL:Vl t65LJ$$If!vh5L5L#vL:Vl t65LJ$$If!vh5L5L#vL:Vl t65L@@@ NormalCJ_HaJmH sH tH DA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No Listj@j  Table Grid7:V0 ,ABY_f|}MNOg   ' Z [ . 0000 0 0 000000 00 0 00 000 0 00 00 0 0000 h00 0 000 0000 0 000 0 0 0 0000Y_|}MNOg j00j00j00K0 0j00K0 0j00j0#0j0$0j0#0K00K00j0,0 j0,0j0*0+<I00K00h020 h020h0/0 I00I00h00I00h00 h00h00h00K00K00  Y M.   3i @@filmg !Cw\S5v6hhh^h`OJQJo(hHh88^8`OJQJ^Jo(hHoh^`OJQJo(hHh  ^ `OJQJo(hHh  ^ `OJQJ^Jo(hHohxx^x`OJQJo(hHhHH^H`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHhhh^h`OJQJo(hHh88^8`OJQJ^Jo(hHoh^`OJQJo(hHh  ^ `OJQJo(hHh  ^ `OJQJ^Jo(hHohxx^x`OJQJo(hHhHH^H`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hH!C5v                  f0E$hVY}MN @%@{ @@Unknown Gz Times New Roman5Symbol3& z ArialUTimesNewRomanPS-BoldMTKTimesNewRomanPSMT?Times-RomanYTimesNewRomanPS-ItalicMT;Wingdings?5 z Courier New"hF2F   !24d  2QKP ?fAThe Study of Gear Ratios: An introduction to Inverse Proportions JEFF LEVYJohn  Oh+'0, <H h t DThe Study of Gear Ratios: An introduction to Inverse Proportions  JEFF LEVYNormalJohn3Microsoft Office Word@d@]@] ՜.+,0, hp  HOME  BThe Study of Gear Ratios: An introduction to Inverse Proportions Title  !"#$%&'()*+,-/012345789:;<=@Root Entry Fe]BData 1TableWordDocument.,SummaryInformation(.DocumentSummaryInformation86CompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89qRoot Entry FH@Data 1TableWordDocument.,  !"#$%&'()*+,-/012345GF$, SummaryInformation(.DocumentSummaryInformation8CompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89q՜.+,D՜.+,p, hp  HOME  BThe Study of Gear Ratios: An introduction to Inverse Proportions Title4