P@HH(FG(HH(d'@xxxxC APPPLIED MATHC UNIT 14 REVIEWL L  1. KEY CONCEPTSL S The key concepts are found on pages 29 and 30 and are listed as the SUMMARY.L L L ) 2. VOCABULARY (UNIT EMPHSIS)L # All the glossary pages 54,55L 2 Noninteger bases-TN =(teachers notes) -p. 7L  Noninterger exponentsL  Negative exponentsL " Binary- exer.39 p. 52L 0 3. PRACTICAL EXAMPLES (VIDEO)L-H   Video WorksheetL-H  Unit 14 Powers and RootsL-H L-H  Nmae__________________L-H  Period_________________L-H  Date __________________L-H L-H j 1. Math is used at the ___________________of the design and during the ___________________for boats.L-H L-H 6 2. List 3 occupations that use powers and roots.L-H 3 ___________________________________L-H 3 ___________________________________L-H 3 ___________________________________L-H L-H D 3. Which of these occupations might you be interested in? Why?L-H 3 ___________________________________L-H 3 ___________________________________L-H 3 ___________________________________L-H L-H 0 4. Wattage = _______________ x resistance.L-H L-H 1 5. Area of a sphere = ____________________.L-H L-H  L-H  VIDEO PROBLEM:L-H ] Given: Inverse square law = 1/d 2 . d= ratio of change of distance.L-H W Example if d is reduced by half then the formula is 1/0.5 2 =4L-H L-H P Find: What would happen if the distance is reuced 1/4 instead 1/2?L-H L-H L L - 4. STUDY GUIDE (WORKSHEET)C (STUDY GUIDE BEGINING UNIT 14L  L * 1. In the example (5) 3L  5 is the __________.L  3 is the __________.L A 2. 5 to the 3rd power can be written as "five ________",L 7 or five raised _____ _____ _______ ___________.L L E 3. When looking for the square root of 49, you are looking forL : _______ __________ __________ __________ that,whenL  mltiplied, give 49.L L " READING AND WRITING POWERSL ? 4. The formula for the area of a circle is___________.L = The radius "r" is squared. Is pi squared?__________L L C 5. Use your calculator to carry out the multiplication andL . write the corect answer on your paper.L , A=pi(20.5/2) 2L L A What answer do you get if you leave the parenthesis out?L L 6 6. Write the formula for the volumn of a cube.L L L  7. Study Activity Page 9L A Use the Y to the x key on your calculator to find a valueL  for these powers.L  a. (16) 4 L  b. ( 5) 9L  c. (2) 15 L  d. (1) 99 L 8 Powers Involving Noninteger And Negative Numbers L > 8. 3 raised to a noninteger power between 2and 3 givesL + a result between _____ and _____.L  9. Study Activity L @ Estimate the values of the following numbers, by tellingL > which two intiger numbers (endpoints) the value falls L  between.L  a. (4) L > b. (2) 3.9  c. (2)   2.5 L L @ 10. Now use the Y to the x key on your calculator to getL @ the correct values-rounded to one or two decimal places.L  L K 1. Read and follow the instructions for example 1:L f 2. Explain the difference in how the calculator is keyed for squaring and cubing a base number.L a 3. Read and follow the instructions for example 2: including the study activity on page 9.L 9 4. Do the next 2 study activities on pages 10 & 11L  5. Due to the importance of this foundation of roots and powers, all the examples and keyed icons should be worked and/or a substitution of similar problems.L X 6. When all are complete give students a photo copy of the summary pages 29 & 30.L L D 5. LAB USEFULNESS/ APPLICABILITY (MATERIALS LIST)L  Lab 1 has a potential question =Whats the point? The answer is to change a curved line on a graph to a reasonable straight one for better approximations.L z Lab 2 shows a greater increase in volume when the base that is squared is doubled rather than the non squared base.L Lab 3. Prerequisite: Knowledge of how a framing square is layed out. Some parts of the square are in twelfths of an inch, some eigths, and some sixteenths. Also a framing square is not the same width on both legs; therefore be sure that you measu re both end points of the hypotenuse from either the inside or the outside in order for the proof to work. Use to layout a baseball diamond, house foundation,parking lot,any large item that needs a square corner,etc.L  Lab 4. Exponential Notation  Exponential growth is a very rapid increase in value. The following example illustrates the rate of increase and how it can be described in "mathematical shorthand", or exponential notation.L PROBLEM You are given a sheet of paper that is .002 of an inch thick. The paper is to be folded 20 times. How thick will the paper be? Now 50 times. Can you physically perform the folding? Have the students try it. All labs shou Eld have worksheets, and handed in at the completion of the lab.L , 6. RESOURCE PERSON (TYPE)L  Boat builderL  RadiologistL + Engineer- p.u.d., county, electricalL  SurveyerL D 7. GAPS (MISSING INFORMATION) - NEEDED RESOURCESL O Exercise 12 check w/Ag. instructor for updated info. on pig ear notchingL } Teachers page 14 The last step on the bottom of the page 14 in some manuals is transfered incorectly. Check it out.L  Teachers manual exer. 15 ans. to 5yrs. should be $375,000. Some books are corrected. If you assign this ex. it will be super helpful to write out the step by step procedure. Otherwise students will likely get lost in the double ( 2( 4)) L \ Teachers m. exer. 40 sq. root sign is extended to far. The student manual is correct.L 5 8. RECOMMENDED STUDENT EXERCISES L  note L Because graphs are used and they are ususlly to show a curve and that curveis to have a specific rotatation dependant on input. Particular attention as to the location of axis items is necessary. For example. Inf stops vs distance the distance is %to be located on the horizontal axis.L  Ex. 1,2,3,4,5,6,7,8,9L F Ex. 4 warning cm/ sec squared is all allowed for in the formulaL 8 9. TEACHING SCHEDULE USE AS DESIREDL :Before day one, assign pp 3-4 for students to read. L  DAY ONE: Lab activity in class. Students in groups. Use acculine to estimate the area of a pipe with a 20.5 inch diameterL  DAY TWO: Discuss pp 3-4. Use writing on paper or board or overhead to help explain info. Watch video and answer video questions, and work the video problem. ( use the prepared handout.L ?study guide 14) note you may wish to use this in day 3-6L M DAYS THREE - SIX:  follow this general guide. L ] 1. Read and follow the instructions for example 1: lab 4L f 2. Explain the difference in how the calculator is keyed for squaring and cubing a base number.L  3. Read and follow the instructions for example 2: including the study activity on page 9. Do lab 1 also found in unit 1L 9 4. Do the next 2 study activities on pages 10 & 11L  5. Due to the importance of this foundation of roots and powers, all the examples and keyed icons should be worked and/or a substitution of similar problems.L X 6. When all are complete give students a photo copy of the summary pages 29 & 30.L a DAY SEVEN: Read through "summary of examples". Review video. Assign exercises 1-5 L : DAY EIGHT: Lab 2  need worksheetL @ DAY NINE:  Review exercises 1-5 Lab 3 L Q DAY TEN: Assign exercises 6-9, have students select two moreL = DAY ELEVEN: summerize, review, late work .L % DAY TWELVE: Test.L 1 10. TEACHING SCHEDULE OPTION BL L-H 'Unit 14 - Powers and Roots.L-H L-H = Before Day one, assign pages 3-4 for students to read .L-H L-H  Day One: Lab activity in class. Students in groups. Use acculine to estimate the area of a pipe thats 20.5 inch in diameter.L-H L-H  Day Two: Discuss page 3-4. Use butcher paper from previous units to help explain information needed to complete this unit. Watch video and discuss.L-H n Review example #1, using lab homework as a comparison. Students need to be in groups during example.L-H L-H  Day Three: Read pages 7-12. Do: Example 2, leading students through. Have students do study activity to be handed in at the end of the period. Have extra assignments prepared ahead of time, both verbally and written.L-H L-H  Day Four: Refresh and Reinforce. Review previos work. Using calcs, have additional activites for students. Lead students thru examples 3,4,5 and study activities. Assign general exercises 1-5 to be handed in on Day Five. Individual work.L-H L-H w Day Five: Hand in exercises 1-5. Read page 20. Do examples 6,7,8,9,10,11,12. Reinforce objectives using calcs.L-H L-H  Day Six: Read thru "Summary of Examples". Review video and do problem sheet. Assign exercises 13-18, 31-35 to be done in groups in class.L-H L-H _ Day Seven: Review 13-18, 31-35 in class by calling on one person randomly from groups.L-H L-H z Day Eight: Lab. Page 34, Pythagorean Theorem. Need worksheet, equipment and designated groups. Hand in worksheet.L-H L-H { Day Nine. Lab. Page 33. Volumes and Diameters. Need worksheet, equipment and designated groups. Hand in worksheet.L-H L-H  Day Ten: Lab. Page 31. Pendulum Length and period. Need worksheet, equipment and designated groups. Hand in worksheet.L-H L-H K Day Eleven: Test. Add 2 story problems, exercices #24 and #30.