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What is not to like about this volume and the curriculum? It provides students with real—life challenges about real—world problems. Students use high order thinking skills to solve a medical mystery of sorts. All the activities are student—centered and their success depends on their hard work and making connections.

The lessons, as the author states, fit into classes that are 45 minutes to 90 minutes. Preparation for this curriculum is designed to reduce the amount of work an educator has to do. A student workbook can be purchased so a teacher would not have to spend their life at a copier.

How many inches are there in 3 meters? How much time would it take for light to travel 10, feet? How many inches would light travel in 10 fs? Refer to Table 1 for the unit prefix related to factors of How many newtons of force do you need to lift a 34 pound bag? Intuitively, just assume that you need exactly the same amount of force as the weight of Rounding off numbers Ask the students why one needs to round off numbers. Possible answers may include reference to estimating a measurement, simplifying a report of a measurement, etc. Discuss the rules of rounding off numbers: a.

Know which last digit to keep b. This last digit remains the same if the next digit is less than 5. Increase this last digit if the next digit is 5 or more. A rich farmer has 87 goats—round the number of goats to the nearest Round off to the nearest , , , , Round off to the nearest tenths: 3. Evaluation 20 minutes Conversion of units: A snail moves 1cm every 20 seconds.

Decide how to report the answer that is, let the students round off their answers according to their preference. In the first line, 1. By strategically putting the unit of cm in the denominator, we are able However, based on the calculator, the conversion involves several digits. In the second line, we divided 1. The final answer is then rounded off to retain 2 figures.

In performing the conversion, we did two things. We identified the number of significant figures and then rounded off the final answer to retain this number of figures. For convenience, the final answer is re-written in scientific notation. This allows one to write only the significant figures multiplied to 10 with the appropriate power.

As a shorthand notation, we therefore use only one digit before the decimal point with the rest of the significant figures written after the decimal point. How many significant figures do the following numbers have? Perform the following conversions using the correct number of significant figures in scientific notation: It takes about 8. How far is the sun from the earth in meters, in feet? Let students perform the calculations in groups people per group. Let volunteers show their answer on the board.

Part 2: Measurement uncertainties Motivation for this section 15 minutes 1. Measurement and experimentation is fundamental to Physics. To test whether the recognized patterns are consistent, Physicists perform experiments, leading to new ways of understanding observable phenomena in nature. Thus, measurement is a primary skill for all scientists. To illustrate issues surrounding this skill, the following measurement activities can be performed by volunteer pairs: a. Body size: weight, height, waistline From a volunteer pair, ask one to measure the suggested dimensions of the other person with three trials using a weighing scale and a tape measure.

Ask the class to express opinions on what the effect of the measurement tool might have on the true value of a measured physical quantity. What about the skill of the one measuring? Is the measurement Scientific notation and significant figures Discuss that in reporting a measurement value, one often performs several trials and calculates the average of the measurements to report a representative value. The repeated measurements have a range of values due to several possible sources.

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For instance, with the use of a tape measure, a length measurement may vary due to the fact that the tape measure is not stretched straight in the same manner in all trials. So what is the height of a table? Should this be reported in millimeters? The choice of units can be settled by agreement.

However, there are times when the unit chosen is considered most applicable when the choice allows easy access to a mental estimate. Thus, a pencil is measured in centimeters and roads are measured in kilometers. How high is mount Apo? How many Filipinos are there in the world? How many children are born every hour in the world? Discuss the following: a. When the length of a table is 1. This is how we report the accuracy of a measurement. The maximum and minimum provides upper and lower bounds to the true value. The shorthand notation is reported as 1.

The number enclosed in parentheses The measurement can also be presented or expressed in terms of the maximum likely fractional or percent error. Discuss that the uncertainty can then be expressed by the number of meaningful digits included in the reported measurement. For instance, in measuring the area of a rectangle, one may proceed by measuring the length of its two sides and the area is calculated by the product of these measurements.

The side that is a little above 5. However, for this example only we will use 5. The area cannot be reported with a precision lower than half a millimeter and is then rounded off to the nearest th. Review of significant figures Convert Note that since the original number has 3 figures, the conversion to cubic inches should retain this Review of scientific notation Convert km to mm: 4.

Reporting a measurement value A measurement is limited by the tools used to derive the number to be reported in the correct units as illustrated in the example above on determining the area of a rectangle. Now, consider a table with the following sides: Note: The associated error in a measurement is not to be attributed to human error.

Here, we use the term to refer to the associated uncertainty in obtaining a representative value for the measurement due to undetermined factors. A bias in a measurement can be associated to systematic errors that could be due to several factors consistently contributing a predictable direction for the overall error.

We will deal with random uncertainties that do not contribute towards a predictable bias in a measurement. How does one report the resulting number when arithmetic operations are performed between measurements? Addition or subtraction: the resulting error is simply the sum of the corresponding errors.

The estimate for the compounded error is conservatively calculated. Hence, the resultant error is taken as the sum of the corresponding errors or fractional errors. Thus, repeated operation results in a corresponding increase in error. However, a less conservative error estimate is possible: For addition or subtraction: For multiplication or division: 6. Statistical treatment The arithmetic average of the repeated measurements of a physical quantity is the best representative value of this quantity provided the errors involved is random.

Systematic errors cannot be treated statistically. The standard error can be taken as the standard deviation of the means. Given a function f x , the local slope at xo is calculated as the first derivative at xo. Example: Graphing relations between physical quantities. Distance related to the square of time for motions with constant acceleration. The acceleration a can be calculated from the slope of the line.

And the intercept at the vertical axis do is determined from the graph. The simplest relation between physical quantities is linear. A smart choice of physical quantities or a mathematical manipulation allows one to simplify the study of the relation between these quantities. Figure 3 shows that the relation between the displacement magnitude d and the square of the time exhibits a linear relation implicitly having a constant acceleration; and having no initial velocity.

Another example is the simple pendulum, where the frequency of oscillation fo is proportional to the square-root of the acceleration due to gravity divided by the length of the pendulum L. The relation between the frequency of oscillation and the root of the multiplicative inverse of the pendulum length can be explored by repeated measurements or by varying the length L. And from the slope, the acceleration due to gravity can be determined. The previous examples showed that the equation of the line can be determined from two parameters, its slope and the constant y-intercept figure 4.

The line can be determined from a set of points by plotting and finding the slope and the y-intercept by finding the best fitting straight line. Fitting a line relating y to x, with slope m and y-intercept b. By visual inspection, the red line has the best fit through all the points compared to the other trials dashed lines. The slope and the y-intercept can be determined analytically. The assumption here is that the best fitting line has the least distance from all the points at once.

Legendre stated the criterion for the best fitting curve to a set of points. The best fitting curve is the one which has the least sum of deviations from the given set of data points the Method of Least Squares.

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More precisely, the curve with the least sum of squared deviations from a set of points has the best fit. From this principle the slope and the y-intercept are determined as follows: The lab report Explain that in performing experiments one has to consider that the findings found can be verified by other scientists. Below lists the sections normally found in a Lab report which is roughly less than or equal to four pages : Objectives - a concise and summarized list of what needs to be accomplished in the experiment.

Background - an account of the experiment intended to familiarize the reader with the theory, related research that are relevant to the experiment itself. Methods - a description of what was performed, which may include a list of equipment and materials used in order to pursue the objectives of the experiment.

Results - a presentation of relevant measurements convincing the reader that the objectives have been performed and accomplished. Discussion of Result - the interpretation of results directing the reader back to the objectives Conclusions - could be part of the previous section but is not intended solely as a summary of results. This section could highlight the novelty of the experiment in relation to other studies performed before. Scalars 2. Motivation: 5 minutes Choose one from: scenarios involving paddling on a flowing river, tension game, random walk 3.

Enrichment: 10 to 15 minutes 5. Give examples which of these quantities are scalars or vectors then ask the students to give examples of vectors and scalars. Vectors are physical quantities that has both magnitude and direction Scalars are physical quantities that can be represented by a single number Motivation 5 minutes Option 1: Discuss with students scenarios involving paddling upstream, downstream, or across a flowing river.

Allow the students to strategize how should one paddle across the river to traverse the least possible distance? Do the same for the next volunteer then draw an arrow connecting the two subsequent dots with the previous one as starting point and the current dot with the arrow head. Do the same for the rest of the volunteers. This vector is the sum of all the drawn vectors by connecting the endpoint to the starting point of the next.

Figure 1. Summing vectors by sequential connecting of dots based on the random walk exercise. If option 3 above was performed, use the resulting diagram to introduce displacement as a vector. Otherwise, illustrate on the board the magnitude and direction of a vector using displacement with a starting point and an ending point, where the arrow head is at the ending point.

Geometric sum of vectors example. The sum is independent of the actual path but is subtended between the starting and ending points of the displacement steps. Illustrate the addition of vectors using perpendicular displacements as shown below where the red vector is the sum : Vector addition illustrated in a right triangle configuration. Explain how to calculate the magnitude of vector C by using the Pythagorian theorem and its components as the magnitude of vector A and the magnitude of vector B. Explain how to calculate the components of vector C in general, from its magnitude multiplied with the cosine of its angle from vector A theta and the cosine of its angle from vector B phi.

Use the parallelogram method to illustrate the sum of two vectors. Give more examples for students to work with on the board. Vector addition using the parallelogram method. Illustrate vector subtraction by adding a vector to the negative direction of another vector.

Compare the direction of the difference and the sum of vectors A and B. Indicate that vectors of the same magnitude but opposite directions are anti-parallel vectors.

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Figure 5. Subtraction of Vectors. Geometrically vector subtraction is done by adding the vector minuend to the Note: the subtrahend is the quantity subtracted from the minuend. Discuss when vectors are parallel and when they are equal. Part 2: The unit vector 1. Explain that the direction of a vector can be represented by a unit vector that is parallel to that vector. Using the algebraic representation of a vector, calculate the components of the unit vector parallel to that vector.

Figure 6. Unit vector. Indicate how to write a unit vector by using a caret or a hat: Part 3: Vector components 1. Discuss that vectors can be written by using its components multiplied by unit vectors along the horizontal x and the vertical y axes. Discuss vectors and their addition using the quadrant plane to illustrate how the signs of the components vary depending on the location on the quadrant Extend discussion to include vectors in 3 dimensions.

Discuss how to sum or subtract vectors algebraically using the vector components.

Tips —In paddling across the running river, you may introduce an initial angle or velocity or let the students discuss their relation. An intuition on tension and length relation can be discussed if necessary. Vectors can be drawn separately before making their origins coincident in illustrating geometric addition. Enrichment 10 or 15 minutes 1. Illustrate on the board how the magnitude of the components of a uniformly rotating unit vector change with time.

Note that this magnitude varies as the cosine and sine of the rotation angle the angular velocity magnitude multiplied with time. Calculate the components of a rotated unit vector and introduce the rotation matrix. This can be extended to vectors with arbitrary magnitude. The two equations can then be re-written using matrix notation where the For now, it can simply be agreed that this way of writing simultaneous equations is convenient.

That is, a way to separate vector components into a column and the 2x2 matrix that operates on this column of numbers to yield a rotated vector, also written as a column of components. This can be generalized by multiplying both sides with the same arbitrary length.


Thus, the components of the rotated vector on 2D can be calculated using the rotation matrix. Rotating a vector using a matrix multiplication. Evaluation 10 or 15 minutes Seatwork exercises using materials include some questions related to the motivation; no calculators allowed Sample exercise 1: involving calculation of vector magnitudes Sample exercise 2: involving addition of vectors using components Sample exercise 3: involving determination of vector components using triangles Differentiate average velocity from instantaneous velocity 3.

Introduce acceleration 4. No furor actually ensued until long after Copernicus's death, when Galileo's run-in with the church landed De Revolutionibus on the Inquisition's index of forbidden books see 4, above. Copernicus, by arguing that Earth and the other planets move around the sun rather than everything revolving around Earth , sparked a revolution in which scientific thought first dared to depart from religious dogma. While no longer forbidden, De Revolutionibus is hardly user-friendly. The book's title page gives fair warning: "Let no one untrained in geometry enter here.

Physica Physics by Aristotle circa B. By contrast, Aristotle placed Earth firmly at the center of the cosmos, and viewed the universe as a neat set of nested spheres. He also mistakenly concluded that things move differently on Earth and in the heavens. Nevertheless, Physica, Aristotle's treatise on the nature of motion, change, and time, stands out because in it he presented a systematic way of studying the natural world—one that held sway for two millennia and led to modern scientific method.

You cannot overestimate his influence on the West and the world. In , the same year that Copernicus's De Revolutionibus appeared, anatomist Andreas Vesalius published the world's first comprehensive illustrated anatomy textbook. For centuries, anatomists had dissected the human body according to instructions spelled out by ancient Greek texts.

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Vesalius dispensed with that dusty methodology and conducted his own dissections, reporting findings that departed from the ancients' on numerous points of anatomy. The hundreds of illustrations, many rendered in meticulous detail by students of Titian's studio, are ravishing.

Albert Einstein's theories overturned long-held notions about bodies in motion. Time and space, he showed, are not absolutes. A moving yardstick shrinks in flight; a clock mounted on that yardstick runs slow. Relativity, written for those not acquainted with the underlying math, reveals Einstein as a skillful popularizer of his ideas. To explain the special theory of relativity, Einstein invites us on board a train filled with rulers and clocks; for the more complex general theory, we career in a cosmic elevator through empty space.

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As Einstein warns in his preface, however, the book does demand "a fair amount of patience and force of will on the part of the reader. The Selfish Gene by Richard Dawkins In this enduring popularization of evolutionary biology, Dawkins argues that our genes do not exist to perpetuate us; instead, we are useful machines that serve to perpetuate them. So is a related notion: that altruistic behavior in animals does not evolve for "the good of the species" but is really selfishness in disguise. One Two Three.

Infinity by George Gamow Illustrating these tales with his own charming sketches, renowned Russian-born physicist Gamow covers the gamut of science from the Big Bang to the curvature of space and the amount of mysterious genetic material in our bodies DNA had not yet been described.

No one can read this book and conclude that science is dull. Who but a physicist would analyze the atomic constituents of genetic material and calculate how much all that material, if extracted from every cell in your body, would weigh? The answer is less than two ounces. Krauss, Case Western Reserve University. The Double Helix by James D. Watson James Watson's frank, and often frankly rude, account of his role in discovering the structure of DNA infuriated nearly everyone whose name appeared in it, but it nonetheless ranks as a first-rate piece of science writing.

The Double Helix takes us inside a pell-mell race whose winners were almost guaranteed fame and a Nobel Prize. Her X-ray crystallography images showed the molecule to be a helix, crucial data that Watson and his collaborator Francis Crick "borrowed" to construct their DNA model.

Franklin died of ovarian cancer in , losing out on the Nobel Prize for the discovery. Perhaps to atone, Watson noted her key contribution in the epilogue to his book. What Is Life? Long a classic among biologists, this volume describes, from the perspective of a Nobel Prize—winning physicist, how living organisms differ from inanimate objects like crystals.

The Cosmic Connection by Carl Sagan At a time when NASA was reeling from the end of the Apollo program, Sagan reacquainted both the public and his colleagues with the majesty of the universe, starting with the oft-overlooked worlds of our own solar system. He also championed the search for extraterrestrial life and argued for the likelihood of planets around other stars two decades before they were discovered. The TV series Cosmos brought Sagan to the masses, but the adventure began here.

The Insect Societies by Edward O. Wilson The patriarch of modern evolutionary biology explores the lives of everyone's favorite creepy crawlies—ants, termites, bees, and wasps—in this page treatise unmatched in scope and detail by any other work on the topic with the possible exception of his own volume, The Ants. It also lays the groundwork for his classic, Sociobiology: The New Synthesis, which explores the then-controversial idea that the social behavior of animals, including humans, has a deep biological basis.

The book is a labor of love, infused with the author's boundless fascination for his tiny subjects. Wilson openly acknowledges the quirkiness of his obsession; the dedication reads, "For my wife Irene, who understands.