INQUIRY PHYSICS A Modified Learning Cycle Curriculum by Granger Meador, 010 inquiryphysics.org Unit 0: Measurement Teacher s Guide these TEACHER S GUIDES are copyrighted and all rights are reserved so you may NOT distribute them or modified versions of them to others However, the STUDENT PAPERS, SAMPLE NOTES, and any PRESENTATIONS for each unit have a creative commons attribution non-commercial share-alike license; you may freely duplicate, modify, and distribute them for non-commercial purposes if you give attribution to Granger Meador and reference http://inquiryphysics.org
0 Measurement Teacher's Guide Inquiry Physics Key Concepts Algebra skills are essential for physics. Measurements need to be accurate, precise, and avoid parallax. They should be expressed with appropriate SI prefixes and significant figures. Many physics relationships are linear, inverse, or quadratic (linear, hyperbolic, or parabolic in shape) and dem onstrate different proportionalities. Experim ental results can be analyzed for percentage error and/or percentage difference. Student Papers Algebra Tips Algebra Remediation Introduction I call this Unit 0 because it is remedial in nature. Students should have been exposed to all of this material in prior science and math classes, but it is essential to remind them of these basics so that they are m ore successful and less frustrated. I only have two handouts, which are not related to the sample notes. The first is an Algebra Tips sheet where students are reminded of basic algebraic rules and complete a few problems. I assign these on the first day of class and grade them on completion. I give a brief quiz after we complete the notes which covers algebra and the other concepts. Any students who miss an algebra problem are assigned the Algebra Remediation worksheet and receive a bonus point for any of those remediation problems they work correctly. If they still miss a problem on that sheet, I have them come in for one-on-one tutoring to assess if they have the pre-requisite math skills for the course. Here are the missing answers on the Algebra Rem ediation sheet: 4. 5. INQUIRY PHYSICS TEACHER'S GUIDE FOR UNIT 0: MEASUREMENT PAGE OF
INQUIRY PHYSICS A Modified Learning Cycle Curriculum by Granger Meador Unit 0: Measurement Student Papers inquiryphysics.org 010 these SAMPLE NOTES, the STUDENT PAPERS, and any PRESENTATIONS for each unit have a creative commons attribution non-commercial share-alike license; you may freely duplicate, modify, and distribute them for non-commercial purposes if you give attribution to Granger Meador and reference http://inquiryphysics.org however, please note that the TEACHER S GUIDES are copyrighted and all rights are reserved so you may NOT distribute them or modified versions of them to others
ALGEBRA TIPS Name We often need to rearrange an equation to solve it for the variable we are interested in. When doing so, remember these rules:! Addition reverses subtraction and vice versa.! Multiplication reverses division and vice versa.! What you do to one side of the equation must be done to ALL of the terms on that side as well as the other side.! Here is the order of operations when solving for a variable: 1. First get rid of any added or subtracted terms on the same side of the equation as the variable which you are solving for. (Assuming your variable is not part of a fraction; if it is, you can only get rid of added or subtracted terms separate from your variable s fraction.). Next get rid of any multiplied or divided terms that are with your variable. (If your variable was in a fraction, after this step it may still have some lingering added or subtracted terms; you can now get rid of them.) 3. Finally take any square roots or raise to powers as needed to simplify your variable. a b d Example: Solve + = e + f for a. c 1. Get rid of the added term +d/ first, by subtracting d/ from both sides: a b d d d a b + = e + f becomes c c d = e + f. Now get rid of the c by multiplying ALL of the terms on BOTH sides by c: a b d cd c = ( e + f ) c becomes a b = ce + cf c 3. Now get rid of the b by adding it to both sides: cd cd a b + b = ce + cf + b becomes a = ce + cf + b 4. Finally get rid of the square by taking the square root of both sides: a cd cd = ce + cf + b becomes a = ce + cf + b Try these problems for practice. Check your results with the answers on the reverse. 1. Solve for r: r + t = 5t + 7 3. Solve for p: qp + 3t = u u t 3. Solve for u: a+ c = b Unit 0: Measurement, Algebra Tips 008 by G. Meador www.inquiryphysics.org
Answers: 1. Method: 1. First we need to isolate the term with the r in it by subtracting t from each side: which simplifies to. Now get rid of the fraction by multiplying both sides by 3. Remember, EVERY term on a side gets multipled by 3: 3. And distributing the 3 on the right side yields the final answer:. Method: 1. First we need to isolate the term with the p in it by subtracting 3t from each side:. Now divide both sides by q to isolate the p: and we get the answer. 3. Method: 1. We cannot simply add t to each side, because we have not cleared away the fraction. So first multiply both sides by b to get rid of that fraction that contains the u: becomes or. Now we need to isolate the u term by adding t to each side: and then we get the u by itself by dividing both sides by : 3. Finally you take the square root of each side to get the answer:
ALGEBRA REMEDIATION Name You missed one or more of the algebra problems on the quiz. Work out the following algebraic problems and return this paper, fully completed with all work shown, at the beginning of class on the date specified below. You will receive bonus points for correct answers to problems 4 and 5 if problems 1-3 are also completed. Remember these rules:! Addition reverses subtraction and vice versa.! Multiplication reverses division and vice versa.! W hat you do to one side of the equation must be done to ALL of the terms on that side as well as the other side.! Here is the order of operations when solving for a variable: 1. First get rid of any added or subtracted terms on the same side of the equation as the variable which you are solving for. (Assum ing your variable is not part of a fraction; if it is, you can only get rid of added or subtracted term s separate from your variable s fraction.). Next get rid of any multiplied or divided terms that are with your variable. (If your variable was in a fraction, after this step it may still have some lingering added or subtracted terms; you can now get rid of them.) 3. Finally take any square roots or raise to powers as needed to simplify your variable. 1. Rearrange and solve the following equation for c: Answer:. Rearrange and solve the following equation for a: Answer: 3. Rearrange and solve the following equation for c: Answer: 4. Rearrange and solve the following equation for c: 5. Rearrange and solve the following equation for a: Unit 0: Measurement, Algebra Remediation 008 by G. Meador www.inquiryphysics.org
Unit 0: Measurement Notes Meador s Inquiry Physics Page 1 of 8 INQUIRY PHYSICS A Modified Learning Cycle Curriculum by Granger Meador Unit 0: Measurement Sample Notes I recommend that you always write out notes, by hand, on the board for each class. That allows you to control the pacing and focus, rather than having students ignore you while they simply copy down the content of a slide. It also controls your pacing, so that you don t race ahead but instead focus on student understanding. Unit 0 is simply a remedial unit on measurement to ensure all students have some basic skills and information needed to analyze data from the laboratories and solve problems. inquiryphysics.org 010 Ask frequent questions of students to check their grasp of the material, and call upon students to provide the next step when working examples. My rule for students is that if I write it on the board, they must write it in their notes, and I grade their notes each quarter and take off for any units with incomplete notes or examples. Trigonometry-Based Physics (AP Physics B) These notes apply to both traditional algebraonly Inquiry Physics and to the more advanced trigonometry-based physics used in Advanced Placement Physics B. these SAMPLE NOTES, the STUDENT PAPERS, and any PRESENTATIONS for each unit have a creative commons attribution non-commercial share-alike license; you may freely duplicate, modify, and distribute them for non-commercial purposes if you give attribution to Granger Meador and reference http://inquiryphysics.org however, please note that the TEACHER S GUIDES are copyrighted and all rights are reserved so you may NOT distribute them or modified versions of them to others
Unit 0: Measurement Notes Meador s Inquiry Physics Page of 8 Sample Notes for Unit 0: Measurement Unit 0: Measurement accuracy: how close a measurement is to the actual value (the right number) precision: how reproducible a measurement is or how many places or significant figures it has Example 0-1: Three students measured elapsed time. The actual value was 14.030 s. Student 1: 13.980 s < most precise Student : 14.0 s < most accurate Student 3: 14.1 s < least accurate & least precise Mnemonics (memory tricks): ACcuracy is the ACtual value Precision is Places One can be accurate but imprecise, and precise but inaccurate. Don t just write out these answers. Tell the students to decide silently which student was the most precise, for example. Then have them all simultaneously raise their hands to signal the answer, showing 1,, or 3 fingers to indicate which student. This allows you to check each person s understanding at a glance. parallax: error due to point of view when reading analog scales Have the students stick out a forefinger at arm s length, peering at it through only one eye, then the other. It will appear to shift against the background. That is parallax, and not good if the finger were a meter s needle and the background the markings for an analog scale.
Unit 0: Measurement Notes Meador s Inquiry Physics Page 3 of 8 SI Prefixes (SI = international system /metric system) Power Meaning Prefix Abbreviation 10-9 one billionth nano- n so nm = nanometer 10-6 one millionth micro- μ so μs = microsecond 10-3 one thousandth milli- m so ml = milliliter 10 - one hundredth centi- c so cm = centimeter 10 3 one thousand kilo- k so kg = kilogram 10 6 one million mega- M so MV = megavolt Significant Figures The answer to a calculation cannot be more precise than the input measurements. billionth of a goat = nanogoat millionth of a mouthwash = microscope thousandth of a pede = millipede ten millipedes = centipede 000 mockingbirds = kilomockingbirds millon phones = megaphone ----------------------------------------------------- I like to show the great Powers of Ten video by Charles and Ray Eames here. http://www.powersof10.com Counting sig figs: decimal point shown: don t count zeroes on left end no decimal point: don t count zeroes on right end 79,030.0 has 7 significant figures but 79,030 has 5 sig figs 0.0050040 has 5 sig figs and 0.500 has 3 sig figs, but 500 is only 1 sig fig. So how can we make 500 have two sig figs? Either write it in scientific notation as 5.0 x 10 or cheat by underlining the final significant zero: 500 I avoid using lines over the final significant zero, as that notation typically means a repeating decimal, but you may want to skip this entirely, as students will tend to overuse this notational trick. In addition and subtraction the answer is rounded off so that only completed columns after a decimal point are included: 46.706 cm +.07 cm 68.776 cm which rounds off to 68.78 cm (last column was incomplete)
Unit 0: Measurement Notes Meador s Inquiry Physics Page 4 of 8 In multiplication and division the answer is rounded off so it has the same sig figs as the worst input:.4 m x 0.7 m = 16.18 m which rounds off to 16 m (0.7 has only sig figs) Example 0-: 35.63 m 4 sig figs x 0.003 m sig figs 0.114016 m rounds off to 0.11 m to have sig figs in answer Example 0-3: 756 s 0.83 s +_37. s 794.03 s rounds off to 794 s since none of the columns after the decimal point were complete I write almost all of my problems and examples with three significant figures to keep things simple. But I do insist all year long that students follow the rules of significant figures on their calculations and in laboratory work. Many textbooks falter on this, not applying the rules to their examples nor to the answers they provide to problems. Since most physics work involves multiplication or division, the rule of rounding off to match the worst input is usually sufficient.
Unit 0: Measurement Notes Meador s Inquiry Physics Page 5 of 8 Math relationships NAME FULL EQUATION SIMPLE FORM PROPORTION EXAMPLE Linear ax + by = c y = mx y α x y = 3x (Linear fit) or y = mx + b where m=slope or m=(y f y i )/(x f x i ) while b=y-intercept (line goes through origin) y is directly proportional to x 1 3 6 3 9 Parabolic y = ax + bx + c y = ax y α x y = x (Quadratic fit) (quadratic because there are four terms) y is directly proportional to x squared 1 8 3 18 Hyperbolic xy = c y α 1/x y = 4/x (Inverse fit) or y = c / x y is inversely proportional to x 1 4 3 4/3 4 1
Unit 0: Measurement Notes Meador s Inquiry Physics Page 6 of 8 Students are typically very weak on identifying the proper proportion and what that means, so I use the t-tables in the above examples to stress these concepts. When two variables are directly proportional, if one variables doubles then the other doubles: 1 3 6 3 9 While if one variable triples the other triples: 1 3 6 3 9 But if they are inversely proportional, if one doubles the other one halves: 1 4 3 4/3 4 1 While if one variables triples the other now becomes one-third of its previous value: 1 4 3 4/3 4 1
Unit 0: Measurement Notes Meador s Inquiry Physics Page 7 of 8 Typical parabolic/quadratic relationships have the parabola opening upward, so if x doubles, y quadruples: 1 8 3 18 While if x triples, y nonnuples (goes up by a factor of 9): 1 8 3 18 You may wish to have advanced students note that a parabola can open sideways instead of upward, such that x is directly proportional to y squared. For example, consider y = x. In that case, y equals the square of x. So if x doubles, y changes by the factor of the square root of two: 1 1 3 and if x triples, y changes by the factor of the square root of three: 1 1 3
Unit 0: Measurement Notes Meador s Inquiry Physics Page 8 of 8 Calculating Error Percent error compares an experimental value to a known or accepted value. experiment al known experiment al difference accepted value x 100 measured theoretical theoretical x 100 x 100 In labs they ll sometimes have a theoretical value and calculate percent error. Pick your poison here any version of the formula still leads to questions from students when applying it as to what values to plug in where. Percent difference compares two values when an accepted value is not available. largest smallest average x 100 Sometimes they won t yet have any idea of what value to expect in a lab, and have to rely on percent difference.