Lesson Plan 1

These are the resources I used and referred to throughout the text:

resource1 #1 (.pdf file)

resource1 #2 (.doc file)

resource1 #3 (.pdf file)

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Lesson Plan: Fundamental Units and Dimensional Analysis of Electricity

Grade Level: 9th Grade (Freshman High School), 1st semester

Context: Electricity through Chemistry and Mathematics

Estimated time: 3×80 minutes

(NB: although the Stage 3 is essentially designed for 3 consecutive 80 minutes long classroom meetings, the lesson is flexible and easy to be modified so that 6×40 minutes long sessions take place)

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BIG IDEA: In order to completely understand the Ohm´s low including Electric Power, initial introduction of other concepts is necessary. Students will understand mathematics behind Electric Current, Voltage and Resistance so that later explanation of Electric Power and the Ohm’s Law (following units) seems natural.

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STAGE ONE: DESIRED RESULTS


ESTABLISHED GOALS: The students should leave the classroom with clear understanding of Electric Current, Voltage and Resistance – i.e. their concepts, meaning and mathematical relationships of multiplication, division, exponents and functions with two unknowns. The state standards of Vermont DoE are:

  • Standard 7.8: Functions and Algebra Concepts

MHS: 20 Demonstrates conceptual understanding of linear relationships and linear and nonlinear functions (including f(x) = ax2, f(x) = ax3, absolute value function, exponential growth) through analysis of intercepts, domain, range and constant and variable rates of change in mathematical and contextual situations.

MHS: 21 Demonstrates conceptual understanding of algebraic expressions by evaluating, simplifying, or writing algebraic expressions; and writes equivalent forms of algebraic expressions or formulas (d = rt—> r = d/t or solves a multivariable equation or formula for one variable in terms of the others).

UNDERSTANDINGS:

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-electric current as flow of charge per unit time

( I=Dq/Dt, [A] )

-electric voltage as electromotive force causing the charge flow and so electrical current

( V=I×?, [A])

-electric resistance as a factor requiring voltage to be bigger in order to keep some current constant (+ materials causing it: i.e. conductors & insulators)

( R=V/I, [W])

-thus we have had V=IR

ESSENTIAL QUESTIONS:

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Where can we see effects of electricity?

How would we describe them?

What causes them?

How would you define electricity?

Does electricity have more variables?

What do you think I, V, R are?

Are they related to each other? How?

Why are some materials more resistant than others?

Could you think of a feasible explanation?

KNOWLEDGE:

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-energy conversions & transmission of electric energy

(chemical à electrical,

electrical à mechanical e.g. electric motor,

or electrical à radiant e.g. light bulb, toaster)

-prefixes of metric multipliers and their numerical values

retrieved from the resource1 #3, page 2 (or 49):

-( I ) Current is what flows on a wire or conductor like water flowing down a river. Current flows from points of high voltage to points of low voltage on the surface of a conductor. Current is measured in (A) amperes or amps.

-( V ) Voltage is the difference in electrical potential between two points in a circuit. It’s the push or pressure behind current flow through a circuit, and is measured in (V) volts.

-( R ) Resistance determines how much current will flow through a component. Resistors are used to control voltage and current levels. A very high resistance allows a small amount of current to flow. A very low resistance allows a large amount of current to flow. Resistance is measured in ohms.

SKILLS:

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By the end of this lesson, students should be confident about physical meanings of I, V, R and their units.

Also, students should have gained fair skills of multiplication, division, use of fractions and composite numbers, cancelation rule, basic exponential functions, solving equations with one variable and two unknown variables.

Most of this should not be new though as the first four concepts had already been introduced by the end of the eighth grade. This lesson should provide a good start to the new school year (fist semester) as a refresher of the previous concepts taught. We would, however, introduce a few other ones as well so that once they are learning about them in a traditional math class (with more time and details supported), they would already have an idea of their real-life application (e.g. basic exponential functions as 10n for expressing different magnitudes)

COMMON MISCONCEPTIONS:

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Moderate conductor such as zinc heats up because electrons move too fast. But why good conductors such as metals do not heat up so much? Think of a car driving through a bumpy road in comparison of a highway (insulator would then be a car in front of a wall).

ESSENTIAL VOCABULARY:

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-current & ammeter

-voltage & voltmeter & batteries/generators

-resistance & insulator/conductor

-metric multipliers and exponential multiples (e.g. milli- vs. kilo-)

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STAGE TWO: ASSESSMENT EVIDENCE


PERFORMANCE TASK (S): (STUDENTS DEMONSTRATE BY SATISFACTORY, INDEPENDENT)

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-solving classroom examples (e.g. questions 12-15 on the resource1 #1 from http://www.allaboutcircuits.com/pdf/worksheets/ohm_law.pdf) – notice that only computational questions investigating the clear understanding of mathematical relationships are selected for this lesson at first since the students are going to be introduced to the concepts of Power, Ohm´s Law and electric circuits subsequently; afterwards, they will be able to pick up on more complex ideas involving less technical computation and diagrammatic expression of circuits (following later through this unit)

-answering homework questions (e.g. all but questions 6, 7, 8 on the resource1 #2 from http://radue.wiscoscience.com/Electronics%201/Ohms%20law%20worksheet.doc)

-answering true false statements and providing their reasoning

-calculating with metric multipliers (see examples of questions provided)

-finding solutions to functions with two unknown variables (e.g. “If we know that the magnitude of R is 3 times the I and that the actual V is 12, what are R and I?”)

-participating in the final quiz requiring both mathematical skills and contextual reading skills

(again, see the resources1 #´s 1, 2, 3 for some inspirations about I, V, R questions)

OTHER EVIDENCE: (FORMATIVE, SELF-ASSESSMENT)

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-ongoing classroom evaluation based on student reactions, questions and answers

-initial discussion (to asses prior knowledge and learner types represented in the class by providing first 15 minutes for an opened discussion yielding space to express ideas of any kind about electricity and student´s thoughts/experiences with it)

-students write down their ideas/definitions before the discussion (during the first classroom meeting) and right after the first lesson in order to see the development of their understanding

-writing a homework paragraph explaining their understanding of I, V, R and their relations (so that the teacher can see the type of learners – e.g. “word-to-word memorizers” rewriting definitions from the class, “conceptual-realizers” interpreting the knowledge through their own words or “misunderstood-thinkers” being already confused about meanings of I, V, R)

-students start the last (third) classroom meeting with a quick write up of the I, V, R definitions (the teacher would then see whether the students kept their original ideas, and have then a chance for the last-minute correction, or the students changed their minds – if they did so, did they memorize definitions or reinterpreted them?)

KEY CRITERIA:

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Do students recognize real-life applications and importance of electricity (e.g. electricians or construction workers using “the formulas to install the correct gauge of wire to carry the load“ – resource1 #1, page 1)?

Have the students shown any progress and development of their ideas?

Are the students doing their tasks responsibly and actively participating in the class?

Can the students distinguish I, V, R one from each other?

Do the students make calculations intuitively without trial-error approach, i.e. trying to calculate either through division or multiplication and guessing more likely answer (thence, some numerical examples should include numbers too big or too small – to uncommon – to be observed in the natural world)?

Are the students able to solve more complex tasks such as exponential functions and functions with two unknown variables?

Do students have fun, enjoy the class and are they engaged?

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STAGE THREE:  LEARNING PLAN

(LESSON SEQUENCE + LEARNING ACTIVITIES, “WHERETO”)

CLASS # 1: (Days/classroom periods __1×80min__ ) Prior knowledge + Introduction:

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Since the students would meet with me, the teacher, for the first time during that school year, the lesson would start with a classroom discussion assessing students’ prior knowledge, concepts of electricity and learning preferences (Are they more likely to be listening quietly as introverts or speaking permanently as extroverts?). The students would get first 5 minutes to note down any thoughts/connotations they have about electricity. Then they would spend other 10 minutes with an opened discussion yielding space to express ideas of any kind about electricity and student´s thoughts/experiences with it. The students should contemplate on where they could have seen effects of electricity and how it all happened, while I would work around and peak in the sheets in order to see what the students wanted to share.

Then I would show them a complex picture of electrical network circuit (see below)

Diagram of the commercial Electricity current

as the final destination of our knowledge acquisition, scheduled for a few weeks/months ahead. The students should express their observations and confess what they have no clue about in the following 10 minutes. By this time, I would have noticed any reticent speakers and could ask them to brainstorm out loud. If they would be still reluctant, I could bring up my own personal experience stressing that nobody is born knowing stuff but anyone can try to learn it: “Once I also had no clue and was confused about electricity but, after I discussed my ideas with others, I managed to understand it all.” In case of shy students, I could ask to continue writing down the ideas on the sheet from the beginning of the lesson (the sheets would be collected on the end). We would eventually find out that in order to decode the schematic diagram, we have to know meanings of dimensions, their units, abbreviations of their magnitudes and vocabulary terms. Thus we would actually construct our own Know-Want-Learn framework that would help us to guide our intellectual seeking.

Then we would move towards formal explanations and definitions of electric current, voltage and resistance, mentioning insulating and electricity conducting materials. I would ask the students constructive questions (see Essential Questions in the Stage 1, third one onwards) trying to achieve student´s own informal understanding that would be close enough to the formal definitions provided afterwards (see the Understandings in the Stage 1). For the Resistance part, we would speculate a bit about conductors and resistors, trying to recall differences in their internal chemical structure (already mentioned by Vijaya earlier in the unit).

Finally, time allowing, we would finish the lesson with some basic calculations of one unknown variable (either I, V or R) through fractions and composite numbers. Some really basic homework problems would be assigned too. For examples of classroom and homework problems, see some of the handout questions suggested in the Performance Tasks and Other Evidence homework paragraph mentioned in the Stage 2.

CLASS # 2: (Days/classroom periods __1×80min__ ) Consolidation:

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The students would start this lesson asking about unclear homework problems and then they would continue with further calculations practicing multiplication and division of fractions. They would also hand in the paragraph homework paragraph explaining their understanding of I, V, R and their relations so that I could quickly assess the type of learners. My classification would be something like “word-to-word memorizers” who rewrote definitions from the first class, “conceptual-realizers” who interpreted the knowledge through their own words and “misunderstood-thinkers” who got already confused about meanings of I, V, R. Especially for the lastly mentioned ones, I would make a quick 5 minutes long revision lecture about the main ideas behind I, V, R, finishing up with a clear table expressing units and relationships of all three variables (something like the information from the page 19, or 57, in the resource1 #3, so far excluding the information about Electrical Power though).

We would then expand our computational skills by adding up on some basic exponential functions by mentioning metric multipliers and theirs prefixes. We would clearly distinguish 10 to different negative and positive powers

SI_Prefix_Table The lesson would continue with solving examples that would consolidate the mathematical relationship among I, V, R concepts and their units, and expand their mathematical knowledge of 10n notation and naming/vocabulary system. This would take up the major part of our lesson. We would work through examples including multiplication and division (e.g. 103/10-3=10(3-[-3]) =106=mega).

In general the questions in this lesson should be simple and not requiring the use of a calculator. All the numbers in examples used should be multiples of each other so further simplification (cancellation rule) is possible. For example, if a question is “find R if V=15 and I=3”, the process should be identifying the proper formula from V=IR (i.e. divide both sides by I and end up with V/I=R) and then calculating R=V/I=15/3=5×3/3=5×1=5. Of course, the level of difficulty would quickly progress into recognizing three digit numbers as squares of two digit ones (e.g. 625=25×25). The use of a calculator would be required as soon as possible the students start the next lesson about the electrical power.

The students would be encouraged to pose questions at any time of unclear thoughts in order to solidify their knowledge or clarify lacking concepts. I want the classroom to have home-like feeling and therefore the environment would be set up untraditionally with small groups of students sitting around bigger round/rectangular desks instead of all students facing the blackboard and starting at the teacher. Also I would keep moving around the classroom in order to help out with problems and establish closer teacher-pupil relationship.

CLASS # 3: (Days/classroom periods __1×80min__ ) Application + Revision/Assessment:

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We would start this classroom meeting with a quick 1-2 minute write up of the I, V, R definitions. I could then see whether the students kept their original ideas, and have a chance for the last-minute correction. And again, if the students changed their minds from previous lesson, did they memorize definitions or reinterpreted them? My aim is to try to make as many students as possible to be “conceptual-thinkers”.

Finally, the students would learn how to read all the new knowledge out of the context in order to solve mathematically complicated tasks such as those of functions with two unknown variables. See the complex question suggested in the Performance Tasks in the Stage 2 and think of it as being formulated in a sentence which would not explicitly say “electric current I” but express its true meaning “flow of charge”, for example.

Students would compute some examples right in the classroom and, according to the level of their performance, a short quiz is possible to be done during the lesson. If the students would need more practice, the quiz could be postponed for the beginning of the next lesson or assigned as take-home homework. Anyway, it would provide formative assessment of student´s abilities and their level of understanding before the crucial change of the topic – lesson on Electrical Power.

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I believe I made it clear that my potential students should take active part in the class (discussion, questions, answers, tasks) and that they have a space for clarifications at any time. Also, it is also crucial to convey the message/topic (teacher to student direction) and at the same time check on the way the message was received – the students’ interpretations (student to teacher direction).

I decided to include clear characterization of current, voltage and resistance concepts, possibly compartmentalized to a table on the beginning of the second lesson so that students clearly see what I am asking them to know (as I have wrote above, the table would be something like the information from the page 19, or 57, in the resource1 #3, so far excluding the information about Electrical Power though). However, in order to provide the freedom of cognitive thinking to all students at the same time, their reasoning should be first asked to be written down in a paragraph (homework from the first lesson). Then the table on my mind would become rather a helpful tool to some students than a dogmatic approach of understanding these topics.

At this stage of me being a new teacher in the classroom, I decided not to include any group work yet. I want to make sure that students are respectful of each other at first and that they see me as an authority who does not allow them too much of freedom so far. Later, however, I would certainly include many examples of group work in order to spin cooperation and further creation of positive learning environment. So far, the learning environment would be positive in a secure way fulfilling personal learning needs individually by considering different learning styles.

I am aware that visual diagraphs and pictures would be necessary in order to make sure that visual learners understand the concepts by using their imaginative applications. It is easier to draw a chart of flowing electrons instead of trying to describe it in several different metaphors. But, at the same time, I am aware that those metaphoric explanations (e.g. fish swimming down the river) shall be used if some students are not visual learners. Mentioning too many different approaches, however, may confuse students and so I would rather go with less is more (quality of ideas instead of quantity) – mentioning only one of each kind.

Yes, I mentioned electrons in a paragraph above. Vijaya and I are cooperating on a cross-curricular unit and thus we decided to teach ninth-graders the concepts of electricity through chemic and mathematical points of view. She would start with atomic structure, describing elements capable of transferring electricity and thinking of moving charge (that would become immediate prior knowledge for students of my unit) while I would join later with this particular unit of dimensional analysis and fundamental units. Our aim is to work the students towards complete understanding of electrical circuits, reading electrical bills and making practical decisions in their life to positively change their electricity use.

Furthermore, I believe that I provided a variety of assessments, which are reasoned in the Stage 2 and 3. The continuous assessment style would provide me with enough information to revise and change next teaching strategies. If students are failing to understand what I am trying to tell them, I am not doing my job properly. The quick write-up of V, I, R definitions on the beginning of the third lesson (while all the books are closed and nothing has been mentioned that day) would allow me to see what and how students have learnt about current, voltage and resistance so far. If they still have problems distinguishing among these three concepts, there is no point to move on more complex calculations with two unknowns.

Lastly to mention, I am aware that teaching a class of ninth-graders in a public school (that is Vijaya’s and my decision about the grade level) means teaching a mixture of young adolescents with diverse social background defining their knowledge and skills. I am anticipating some degree of confusion about the topic, misconceptions (e.g. about conductors), no interest or emotional distress, or possibly satisfactory prior knowledge causing the class to appear boring. In the last case, I am sure I would come up with some more advanced individual learning plan including extra computational tasks and/or investigation about real values for I, V, R for domestic electric devices (for homework) so that also that particular student learns/explores something new in our classroom.

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