Sally B Chemistry | The teacher of teachers



Teaching for meaning and understanding:The International System of UnitsWhen we understand, we learn. Teaching the metric system for meaning and understanding gives the student the grounded theory behind the international system of units. When students understand why prefixes are used, then there is no problem measuring and manipulating the quantities of measurement. When tricks are taught for the moment, the student may answer a question correctly on a standardized exam, but two weeks later…. Forget about it. Teachers need to do their homework too. Teachers should be grounded in the theory behind concepts before attempting to teach them. Teaching is not about memorizing, although, sometimes, facts do need to be rehearsed so that understanding can take place at a later time. Associating facts together can bring understanding. Lincoln: Nebraska, penny, automobile, beard, top hat,….. now associate it with the five dollar bill. How the brain works; it associates all of these facts together, gets the RAM going in the brain, and now, I can begin a lesson on the Emancipation Proclamation. You can teach science concepts in the same way. Bring familiar thoughts together with novel learning. I use social studies, English, art, mathematics, business, physical fitness, etc… in all of my lessons dealing with my content in science. Let’s begin with explaining: What is a quantity and how can we express quantities?word notationnumber notationexpanded notationscientific notationengineering notationmetric notationother notation using exponentsWhat is a prefix?Units of measurement in the International System of Units (SI)coherence – one unit for each type of mecombining prefixes with units Changing PrefixesWhy would you want to change a prefix?Different methods of changing prefixes-multiplicative identity method-exponent method-Dimensional analysis (often what is in a chemistry textbook)-Proportional reasoning (how math teachers teach conversions)-Mnemonics 5. Calculations in science involving prefixesAnomalies of some measurements: Angstrom and MicronArea and Volume – problems students haveTeaching Notes:In English class, a prefix is morpheme, the smallest grammatical unit, which is placed before the stem of a word. A prefix such as the letter a, can negate a word such as symmetrical causing it to become asymmetrical or not symmetrical. Think of the metric system as a series of prefixes (bound morphenes) with units (free morphenes) The prefix is an affix, a bound morphene that should only be used in conjunction with another word. (Some people use metric prefixes incorrectly and say, I make 72 kilo at work, or I am running a 10 k today.) In the metric system, the prefix is a symbol, representing a quantity or a fraction of a quantity. In other words, a prefix used in the metric system is just a number. Think of it this way: the prefix is part of the quantity, not part of the unit. I know this sounds different, but open your mind and you will see.This may be different in English class for the definition of a prefix, but this is how prefixes are used in the metric system. Think of the prefix as an affix, and then think of the unit of measurement as the stem. (there is one exception in the metric system and that is the kilogram, the base unit of mass. There is a special reason for this and there is a great video to explain why this base unit uses a prefix to define itself…. We just wish this weren’t the case, but it is, and it is too late to change it at this point)Here is an example: The word notation is three hundred millionWord notation: Write it out with wordsNormal notation or number notation for this quantity “3 hundred million” is 300,000,000. Expanded notation: (some math classes teach this with Common Core) The number is broken down into the groups it comes from such as 303 would be 3 hundreds + zero tens + 3 onesStudents quickly and eagerly learn a system called scientific notation can be applied to this quantity by using two numbers and exponents to express the quantity as 3 x 108. Scientific notation preserves the quantity and expresses it as a number one or greater but less than 10 times the base 10 raised to an exponent. This makes the number easier to write, to say, and to manipulate in a mathematical equation. -Scientific notation is great when expressing the number of significant figures in a measurement.-Scientific notation was used extensively after the invention of the slide ruler. When using a slide ruler, a non-electrical calculator, the quantities that were going to be multiplied or divided were placed into scientific notation first, the exponents taken out leaving just the number before the 10 raised to the power, and the numbers left over were inputted into the slide ruler, the calculation done, and then answer was given. The laws of exponents were used on the powers taken out and the final answer was easy to see. I think we have come a long way since slide rulers…… and yet, we keep drilling students to put their answers into scientific notation. You should be familiar with scientific notation, you love it, because you understand how to do it. You learned it in 7th grade, you mastered the technique of moving the decimal point over and placing the quantity in “proper scientific notation”. But I say, why not teach more in 7th grade? Teach them to express quantities in all powers of exponents, open their minds. With the invention of calculators, we need to move on and open our minds to something more powerful, something called engineering notation. Your calculators have a button in it labeled ENG and yet, most people have not a clue as to what it means. (when teaching your students about engineering notation, do not tell them what it means, lead them to discovery of what the button on their calculator does for them…. More later) I will come back to this in just a minute.I explained normal notation, scientific notation, but introduced you to engineering notation. Do you know what it is? Have you ever used that little button on your calculator? (show a calculator screenshot of ENG on the display off of mode). Lesson #1 Quantities and NotationsThe idea of quantity – we are going to discuss quantity as a magnitude. How much?How do we express quantities in science? We can use numbers for counts and numbers for amounts when we have units of measurement associated with the use of instruments.When we use numbersCount – I have 2 applesMeasurement – I have 500 mL of waterWrite a very large quantity – they will use commas after groups of 3. Write a very small quantity – teach them to use spaces between groups of 3 (most will write a number as .000000000032, teach them to start with 0.000 000 000 032) When writing small numbers use spaces in groups of three. The reason is that it is easier to count the zeroes and to place into engineering notation quicker)Objectives:-to express numbers in as many different ways as possible and open the mind to an infinite number of ways to express the same quantity-to define the different types of notation (let the students develop the definitions with you, but make sure you get on the board what you want them to remember)-to understand that the form of the number can be changed to suit what ever purpose needed at the time. Use of prefixes are great sometimes, but other times, a different form is easier to use.Example given: Three hundred million WORD NOTATIONNormal Notation: 300,000,000Scientific Notation: 3 x 108Engineering Notation: 300 x 106Prefix (Metric) Notation: 300 MAny notation: to suit the situation 0.3 x 109 or 300,000 x 103Now go back to the notations and come up with a definition (see teacher notes)When you get to engineering notation, many have never heard of this. To develop this concept, have them get out their calculators and find the mode button for ENG and have them try some numbers and write down what the calculator says. If you don’t have calculators, then put a series of numbers on the board and give them the first couple of ways to express ENG notation. Keep the number the same, but keep adding zeroes. When they get the idea of large numbers in ENG mode, try some smaller numbers.Normal NotationScientific NotationEngineering Notation33 E 03 E 0303 E 130 E 03003 E 2300 E 03,0003 E 33 E 330,0003 E 430 E 3300,0003 E 5300 E 33,000,0003 E 63 E 630,000,0003 E 730 E 6300,000,0003 E 8300 E 6Have your students look at the patterns. Give them time to discover what ENG notation is and hopefully you can develop the notation that engineering notation places a quantity into a number between 1 and 1000 times ten raised to a coefficient divisible by 3.Now try some smaller numbers:Say 0.000 000 000 032 (say it: 0 point 000 pause 000 pause 000 pause 032)Most will write 0.000000000032Teach them to put a space between groups of three, it is easier to see the zeroes.Ask them to express this quantity in word notation: They can’t, it is difficult. Now write this quantity in SCI 3.2 x 10-11Now write this quantity in ENG 32 x 10-12After you get this in ENG notation, it is easier to put into word notation: 32 trillionthsGive them the Prefix notation: This will be developed in the next lesson. You are planting a seed here. Engineering Piece:This is the time to give the application of the use of different notations. I am going to write you a check for 300 million dollars. Draw a check on the board: Teach your students how to write a check (this is a life skill that is going away, but still important)How will I express the quantity on the two different lines?Do they mean the same thing?Have them conclude that quantities can be expressed different ways for different reasons. You have to have all different tools in your tool kit to solve the problem. Lesson #2 What are the prefixes of SI? Objectives:-to allow for prior learning (see how many they already know)-develop those they don’t know by guiding them to the proper prefix-proper substitutions in and out of quantitiesTeaching Notes:Start with a prefix used in English class such as isoList all of the words you can that begin with that prefix. Then come up with a meaning of the prefix in each group. Now share the meaning. Hopefully they come up with iso means same.Examples of words: Isoceles, isotope, isomer, isometric, isotherm 2. Understanding prefixes used in SI, do you know them? Understand that a prefix is just a symbol for a quantity (number) Go through them with the students, see how many they already know. Where are they commonly used? This is written out 10-12 all the way to 1012Fill them all in. Use this sheet for all of your exercises.3. Working with NotationsDeveloping an understanding of Engineering notation and other notations using only numbers and exponents. Conclusion: there are an infinite number of ways to express a quantity.Plan: Stop teachers from insisting on scientific notation. Use the appropriate notation for the appropriate situation. -Express the following quantities using proper engineering notation:-Then have them do all 3 notations-Then take a number and express it using 103, 106, 10-3 just for practice.Now place all of your quantities in Prefix notation. Lesson #3 Units of MeasurementNIST has a beautiful publication that is printed on A3 paper with the history of the measurement systems and the proper base units of SIUse this sheet to introduce the base units of measurement.They are familiar with:Length – meterTime – secondsMass – kilogram (note again, we wish there wasn’t a prefix used here, but deal with it)The ones they are not so familiar with Temperature – KelvinCurrent – AmpereAmount of substance – MoleLuminosity – CandelaLesson #4 Changing Prefixes1. Teach why you would want to have a prefix or to change a prefix. Answers would include: when quantities become large or small, an appropriate prefix makes the number easier to express. Or changing prefixes help when comparing two measurements.2. Proper Prefix (Metric) Notation: A term that I coined. This is when you substitute the appropriate symbol (prefix) for the quantity it represents.2 x 103 becomes 2 km Give an example such as 35,000 ps, the proper metric notation would become 35 ns“Proper Prefix Notation” is when the quantity is placed into ENG notation and then the appropriate prefix is substituted in for the power of 10.Changing Prefixes for comparisona. Why would you do it? B. How do you do it? NOTE and Point out often: separate the prefix from the unitThe prefix is part of the quantity, the unit is coherent. One unit, one type of measurement. Different methods of manipulating the prefixMultiplicative identity method (see other handouts)Exponent substitutionDimensional analysisproportional reasoningmnemonicsENGINEERING PIECEHere’s where it gets exciting: write great problems having students change prefixes for different purposes and use all notations, then select which form to use for different purposes. -conclude: texting is easier using prefix notation for quantities Lesson #5 Calculations using SI prefixes Which is the appropriate representation of the quantity in an equation?If you have a wavelength of 750 nm, what is the frequency of the light? Substitution of the number for the symbol when plugging into equations.c = = c/ = 3 x 108 m/s / 750 x 10-9 m Just substitute in the meaning for the prefix.Lesson #7 Area calculations-don’t use prefixes with squared quantities, instead, substitute in the numbersinstead of cm2 use 10-4m2-Use multiplicative identity methodLesson #8 Volume CalculationsInstead of using cm3 use 10-6m3TAKE HOME LESSONSPrefixes are symbols, they represent a quantityChange prefixes, don’t call it conversionsPlease don’t test SI, use it, allow your students to become comfortable with it.Get rid of centi as a prefix. You can bring it back later after there is confidence in using the metric system. It does have an application when converting mL to cubic centimeters.Use sound mathematical principles when using the metric system or changing prefixes. No tricks.Use your engineering skills as often as you can. Give students challenges and problems to solve whenever possible.Operational define definitions and continue to do this as the year progresses. Allow your students to come up with the definitions. Don’t tell them definitions.Always do your homework as a teacher. Know more than the students, and find applications of your lessons.Use points of references when designing your exercisesLet me teach you something right now:TEACH WITH IMPORTANT POINTS OF REFERENCETake your left index finger, point it, know bend it like this. Take the second bone in, this one right here and look at it. Now compare it to the people around you. Notice, in general, most of you will have the same length of that bone. Whose bone is longer than most out there? Whose bone is shorter than most out there?Did you know, back in the early 1920’s (check the date) when scientists were trying to find unique features about a person they tried many different measurements and collected data. They finally decided to use fingerprints as the identity of an individual, but the data was in, and someone noticed that most of the people had the same length of this bone. And the ones who bones were longer, had really really long arms. And people whose bones were shorter had really really short arms compared to the rest of the population. And then….. manufacturers were able to make shirts for the mass population and sell them in retail stores as: Small, medium, and large instead of neck size and shirt length. But if your bone wasn’t 30 millimeters long (yes, I just gave you another point of reference) then you had to go to a mr big and tall store to buy your long sleeve shirt. (Hand out the metric millimeter-only rulers) Now you try it, measure that bone.I ask myself why hasn’t the rest of the USA caught on? Is it because they were not as fortunate enough as me to have the most awesome kindergarten teacher? I have been on a mission to find out why, and I think I have the answer. Why? Because our teachers do not understand the ease and simplicity of the metric system. Our teachers from physical education, to English, social studies, science, mathematics, technology, art, the list goes on and on, should first understand it. When the USA decided to go metric, it was taught incorrectly, we held onto the gallon, the inch, the miles and the pound. Why, because that is what we had learned. Remember, “A child learns what we teach them.” If we teach kilograms for mass, they learn kilograms. If we teach gallons for volume, they learn gallons.****Don’t teach conversions back and forth between the metric system and the inch-pound system, move forward with great instruction instead. Teach a normal size candy bar is 50 grams in mass. Teach a child in 6th grade that they have a mass of 52 kg. Put yourself on a balance and learn what you are. Compare mass to known masses.Let me demonstrate:I love telling you my mass, I love telling you my mass. Why? Because you don’t understand. I am over-massive, I really am, but I am not embarrassed to tell you that my mass is 100 kg. I would like this system to only be 60 kg of mass, so I would like to take some of my mass that is in the form of stored energy, you may call it fat, and convert it over to carbon dioxide and water and release this mass to my surrounding. I can do that efficiently by taking in oxygen and exercising, controlling how much food I consume, and mess with this open system. I can use my knowledge of thermodynamics and explain how the whole system works. I can teach my students to relate everyday things to science.Look at all of the seeds I just planted, I just taught you a different concept in thermodynamics by relating it to something you may want to manipulate. You are listening, you are learning, I am teaching you with meaning and for understanding. ................
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