Competition Under Price And Quantity Postponement - Free Essay Example

Sample details Pages: 14 Words: 4062 Downloads: 2 Date added: 2017/06/26 Category Statistics Essay Did you like this example? This paper studies competition under price and quantity postponement where product substituability is included. Supplier who operates as market leader and two retailers who act as follower produce two differentiated products according to the same product family. Price postponement is taken into consideration from a motivation to anticipate product variety while quantity postponement to anticipate demand changing. Don’t waste time! Our writers will create an original "Competition Under Price And Quantity Postponement" essay for you Create order Game theory is applied to this competition in order to compare between price and quantity postponement effectiveness according to Bertrand and Cournot Stackelberg game. Furthermore product substitutability degrees are included in order to show its effect to postponement competitiveness and as guidance to product development. Demand stochasticity is overcomed by differential game application to both of Bertrand and Cournot Stackelberg game. The first and second simulation results show that Cournot game is superior to highly differentiated product while Bertrand game for product which shares common platform. Moreover the results show that product substitutability gives antipode effects (price, quantity and profit) to Cournot and Bertrand game. The final part of the paper concludes the results and outlines future research direction is discussed. Keywords: price postponement, quantity postponement, Stackelberg game, Cournot game, product substitutability 1. INTRODUCTION For many years, it has been a common policy for manufacturers to produce in a large batch to keep production cost and ordering cost low. Unfortunately, the current trend in consumer requirements does not support this idea. Consumers wish to be served according to their own à ¢Ã¢â€š ¬Ã…“special needsà ¢Ã¢â€š ¬? and for this reason the variety of products is increasing. Obviously, it makes production lines become busier with frequent setup and down time due to higher product variety. Inline with this idea, a manufacturer needs to make a closer relationship with his opponents in order to keep their market share. Mass customization now has been to be an order qualifier to supply chain. Kreps and Scheinkman (1983) show that if the firms choose capacities before engaging in Bertrand-like price competition then the Cournot outcome eventuates if the given capacities are at Cournot levels or it should be rationed when the capacity cannot meet market demand. On the contrary, Davidson and Doneckere (1986) argued this investigation and show that alternative rationing rule can eliminate idle capacity because players agree to compete at higher equilibrium capacity. Either Kreps and Scheinkman or Davidson and Doneckere rationing rule however is difficult to be observed in the real world. One motivation is there are no manufacturers produce homogenous products because all firms are equally placed around a circle which represents a consumer taste spectrum (Salop, 1979). Thus, this paper proposes product substitutability degrees (Spence, 1976) to represent consumer taste spectrum. Lower product substitutability degree describes wider spectrum and vise versa. Product substitutability inclusion into Cournot and Bertrand-like price competition gives a chance to explore the possibility of cooperation in long-term relationships, such as cooperation between firms in join product development. Lambertini and Cellini (2002) show that join product development. The effectiveness of the different game strategies has been studied in the context of equal cost function-product firm without product substitution degree (Fujiwara, 2006). Two interesting research questions then arise: (1) how does product substitution degree affects the different game strategy? (2) How does different game strategy affect the optimal price and quantities? These questions are the focus of this paper. Specifically, we consider a supply chain whiches consist of three parties they are one supplier and two buyer firms whose operate in a monopolistic setting. With regards to both postponement types, Cournot model uses linear quantity function while Bertrand applies linear price function. Supply chain needs to make two sets of decisions: production prices and quantities. Follower can postpone his production decisions to a later time when information on market leader is obtained. Furthermore at the final discussion we can observe both of Bertrand and Cournot Stackelberg games simultaneously by comparing their profit, price level and output (quantity). The following sections first introduce postponement competition (section 2), where it focuses on features of competition application and game theory. Section 3 describes on postponement modeling with dynamic stackelberg, which is benchmarked against Cournot Stackelberg. Section 4 exhibits results and discussion from problem example. Finally Section 5 explores the opportunity for future research. 2. LITERATURE REVIEW The objective of this section is to give common perception on supply chain strategy and specifically postponement competition application by game theory. In addition to Pine (1993) definition of mass customization, Davis (1987) drives readers to an argument that supply chain strategy for mass customization should be focused on the entity properties. For instance modularity is intended to components standardization while postponement is subjected to reduce lead times by move point of differentiation closer to delivery point (Lee, 1996). Shortly if entities have wide variety so that modularity should be done in order to reduce process variation. In other side, postponement is delivered while components have slime variety in order to reduce lead times. Furthermore Ernst and Kamrad (2004), Mikkola (2004) and Salvador et al (2004) propose a flexible strategy that is reflected by combination of modularization and postponement. In conclusion, product modularity should support postponement p olicy as well as reduce uncertainty (Swaminathan and Lee, 2003). 2.1 POSTPONEMENT COMPETITION Zinn and Bowerzox (1988) differs postponements according to product and process redesign point of view (Lee, 1996). On the contrary Miegham and Dada (1999) proposed six postponement types according to three factors they are capacity, price and quantity. In their paper demand is assumed a function of price so that in that case price can control demand. Meanwhile Biller et al (2005) investigate price postponement effect to quantity and flexibility investment decision according to demand elasticity. The first paper considers to fixed quantity and the second emphasizes on flexible quantity. In addition to both papers, Gilbert and Cvsa (2003) add innovation effort to revenue maximization by postpone quantity or price decision. Similarly, another postponement model is dedicated to product substitutability effect to price and quantity postponement (Bish et al, 2007). This paper considers supply flexibility as a tool to overcome demand uncertainty and keep quantity flexibility. All of those suppose demand can be drawn according to certain functions which is emphasize on price/quantity competition and aside other factors such as decoupling point in push-pull strategy. Push pull strategy needs not only demand information but more emphasize on internal efficiency or costs minimization. In conclusion, two research forts envisage postponement from different perspectives these are operations management (Zinn and Bowerzox, 1988) and economic perspective (Miegham and Dada, 1999). From all above literature review, this paper studies postponement competition according to both of economic perspective as final goal (price and quantity) and supply chain management perspective by develop a cooperation networks among one supplier and two buyers via game theoretic approach. Previously Miegham and Dada (1999) avoid game theory application because Nash equilibrium does not exist whenever demand is stochastic. On the contrary, game theory is applied in this paper because even demand is stochastic but in this case dynamic Stackelberg game solves this problem by using optimal controlled pricing policy or in other words the effect of demand uncertainty is also considered by this game. 3. MODEL DEVELOPMENT In this section, we propose a study of economic impact of adopting postponement to price and capacity. The objective is to derive findings that will allow us to illustrate results for selecting decision sequence between price and capacity. In what follows we provide a simple analytical framework for evaluating different postponement strategies on revenue basis. The advantage of this approach, in addition to providing comparative results, is that it allows for incorporating decision sequence influencing profit. However, in this research, we only regarding to the development a general framework upon which future work can be based. To focus discussion, consider a supplier that sells a modular component to two retailers who operate based on customized product. From this reason, trade off between service level and efficiency is emphasized on how to decide product quantity and prices according to product standardization degrees. So that how many production quantity and how much its price i s the main topic in this research. To gather general understanding for this concept, both postponement concepts will be discussed separately and then general concept will be developed. The following section discusses competition according to Bertrand and Cournot rule. 3.1 BERTRAND GAME COMPETITION DECSRIPTION Consider two competition conditions. Firstly, downstream (retailers) compete according to static Bertrand and Cournot game and secondly downstream and upstream compete according to two stages Bertrand and Cournot game so we can use a duopoly model. It is also assumed that followers are downstream and supplier is the leader. Furthermore follower costs function is assumed equal because they order from the same supplier. Different with previous postponement models this paper intends to compare decision sequence between price and quantity so that the outcome of this paper is in what situation price or quantity postponement is enable. Game rules This two stages Bertrand game adopts backward induction where follower is analyzed first and leader later. In stage 2 suppose followers determine their price as a function of market leader price so that he maximizing his own profits. (1) In the first stage, supplier (leader) determines his quantity and price. (2) Equation (1) and (2) represent our game as backward induction so at first stage Nash equilibrium will be. The intuition behind this situation is simple, market leader of course like to be a monopolist. However, in Bertrand Stackelberg game total profit is calculated from equilibrium price so that quantity tend to be higher if both players agree to increase their product commonality and the consequence is players cooperation desire will increases. At the first stage leader tries to determine his own price based on market situation (this game is a competition with perfect information) for instance market share, competitor capability to handle market demand. The intuition behind this situation is in backward induction outcome does not involve non-credible threats. Leader anticipates that follower react optimally to any action of leader might choose while leader has no any reason to threat because stage 2 is not leader self interests to threat follower. Obviously, this situation will be subgame perfect. Notations Equilibrium quantity, market leader, follower and leader price Compound and discount factor for dynamic stackelberg game, product commonality Here it is the form of this game that represents First game is rounded by Stackelberg game for quantity postponement Second game is dedicated to price postponement Profit comparison between quantity and price postponement. Bertrand game model Consider a Bertrand duopoly model with price function for retailers given by (see Gibbons, 2002) (3) Whereandis time and form postponements prices from both of market leader and follower respectively and ideally they should be produce in equal amount. This game put Bertrand dupoly model with the following reasoning. Naturally, customization process may want to choose different (and presumably higher) price because of variety. Supplier, on the other hand should take advantage from the above situation by serves inventory in order to reduce selling price and finally either inventory reduction or higher customization price are however risky for customer loose. One solution that is usually adopted is keep steady and optimum production output by considering market fluctuation and competition. The following model can be one of solutions for previous problems. Stackelberg model is taken because in this case supply is the most dominant problem so supplier as a market leader more comfort with his position so he emphasizes his strategy to keep his position ahead of others by product availability in market while follower ussualy more innovative in order to fullfil customer requirement. It is also assumed that between leader and follower can observe their manufacturing performance each other so that this is a dynamic game with perfect information. This assumption is adopted because between supplier and retailer employ vertical integration so that both of them can access demand and supply data. In conclusion, this game applies commonality degree in order to attract cooperation between leader and followers. Bacward induction Bacward induction is used to analyze equilibrium price and capacity in order to guarantee Nash equilibrium so that we move first from stage 2 as follow Stage 2 Follower decide his price according to leader price (4) The first order condition is (5) Similarly, the FOC from second product variant is (6) Solving these two equations simultaneously, one obtains (7) Stage 2 explores price equilibrium between two buyers. This equation shows effort to maximize standard platform utilization by increasing product substitutability value. Furthermore both buyer and supplier can take advantage from this problem because whenever supplier increases his selling price, buyer product price also increases. Price equilibrium from stage 2 then is used to decide supplier price as follow Stage 1 Leader decide his own profit function At the first stage we can find as (8) Find c by insert (7) into (8) so we get (9) (10) Stage 1 describes that product substitutability influences supplier price considerably. We can see that supplier price is a concave function of product substitutability (g). Shortly innovation between two buyers increases supplier price also. Finally price decision is used to decide capacity which is postponement until price is issued. Capacity postponement decision Capacity postponement is assumed because Bertrand game players will not try to steal their opponent customer by lower price because their price will simply fall to zero. Moreover they must consider their own capacity and customer demand. Furthermore in economic theory demand is a function for a firmà ¢Ã¢â€š ¬Ã¢â€ž ¢s product (or service) relates the quantities of a product that consumers would like to purchase and it quantities also might be a function of its price (Truett and Truett, 1984). From this point on, this game is developed according to Fershtman and Kamien (1987) and Fujiwara (2006) but quantity is variable rather than price. ;; (11) In equation (11) we recognize s as speed of quantity to go to its optimal value and it is eligible to both followers according to Bertrand duopoly quantity function. Because we assume that both followers have same cost function then both players must have equal quantity. To solve (11), let us set up a current-value Hamiltonian as (12) S.t (11) ,, Whereis costate variable that is associated with the quantity dynamics and at the following derivation we will recognize s and as compound factor and discount rate. (13) (14) Steady state quantity can be found from (14) as (15) We can see that equilibrium quantity is a concave function of price. In conclusion quantity postponement gives significant impact to supplier-buyer supply chain whenever both buyers agree to improve their product commonality. Below price postponement is given in order to do comparative study between quantity and price postponement. 3.2 COURNOT GAME COMPETITION DECSRIPTION In this model we consider a Cournot duopoly model with price function for retailers given by (16) Whereis product variant 1 and 2 quantity respectively and ideally they should be produce in equal amount. This game put Cournot dupoly model with the following reasoning. Naturally, price is not a competitiveness objective but market share. For this game, both buyers effort to produce common product is undermined. One solution that is usually adopted is product differentiation in order to get larger market so that cooperation between two product variants at certain commonality degree is recomended. The following model can be one of solutions for this problem. Stackelberg model is taken because mostly market leader in this game is modular component supplier and they tend to produce standard product platform in a large batch. It is assumed that between leader and follower can observe their manufacturing performance each other so that this is a dynamic game with perfect information. Game rules This two stages Cournot game adopts backward induction where follower is analyzed first and leader later. In stage 2 suppose followers determine their price as a function of market leader price so that he maximizing his own profits. (17) In the first stage, supplier (leader) determines his quantity and price. (18) Equation (1) and (2) represent our game as backward induction so at first stage Nash equilibrium will be. The intuition behind this situation is simple, market leader of course like to be a monopolist. However, in Cournot Stackelberg game total profit is calculated from equilibrium quantity so that price tends to be higher if both players compete according their own unique feature and the consequence is player cooperation desire decreases. Game 2: Price postponement This game will decide equilibrium capacity first before price and it will be run under backward induction as follow Stage 2 Follower decide his capacity according to leader capacity (19) By assuming equal costs function and both players try to cooperate by produce products with a certain commonality degree so (19) can be modified according to Cournot duopoly inversion (Spence, 1976) as follow (20) Equation (20) describes that total revenue consists of total profit for two followers minus their total costs then the first order condition for (20) is (21) Similarly the FOC for second product variant is (22) We can solve (21) and (22) simultaneously to be (23) Stage 1 Leader decide his own profit function At the first stage we can use (23) in order to calculate leader profit as follow (24) FOC of (24) according to c then we have (25) Then (25) can be rewritten as (26) Price postponement decision Price postponement is taken by an assumption that Cournot game players trust to their opponent that they will keep their capacity at constant value (Trett and Truett, 1984). There are some ctirics for this method such as it is hard to believe Cournot assumption and in duopoly players should get together their price and quantities. The result of this game usually higher price with lower equilibrium output and this paper investigates their opportunity to be improved by an assumption that at infinite time both players will achieve a steady state price. From this point on, this game is developed according to Fershtman and Kamien (1987) and Fujiwara (2006) as follow ;; (27) In equation (27) s is a speed value of price to go to its optimal value. Equation (27) also eligible to both suppliers (leader and follower) because Cournot duopoly price definition is a function of its constituents quantities they are leader and follower. In other words, both players adopt equal price policy. Finally price dynamic can be derived by insert (26) into (27) as follow (28) To solve (28), let us set up a current-value Hamiltonian as (29) S.t (28), Whereis costate variable that is associated with the price dynamics and at the following derivation we will recognize s and as compound factor and discount rate. (30) (31) Solve (30) and (31) simultaneously then equilibrium price is finally founded as (32) Result and Discussion Previous section discusses about how to optimize quantity and price according to two different postponement strategies. It is quiet different with previous approaches by assuming identic costs function (Fujiwara, 2006; Fershtman et al, 1987) according to price postponement without product substitutitability degrees while in this paper we differ both players according to quantity and price postponement. Moreover both postponement strategies are also treated with different solutions, Cournot and Bertrand game. Firstly, we intend to compare between common Stackelberg and dynamic stackelberg game to see their unique feature. (Please attach table 1 approximately here) (Please attach figure 1 approximately here) (Please attach figure 2 approximately here) Those figures and table will be used to answer our previous research questions as follow Question 1: how does product substitution degree affects the different game strategy? Analysis Figure 1 and 2 exhibits comparison between Cournot stackelberg versus Bertrand stackelberg from quantity and price at various substitutability degrees. Generally, it is shown that product substitutability degree gives reverse effect to Bertrand and Cournot game. Moreover Cournot game is better in highly differentiated products than Bertrand game and on the contrary this game ineffective at highly compatible product. Furthermore Cournot game gives higher profit to retailers while lower to supplier. In conclusion, Cournot game is better to be applied whenever supplier is not a part of supply chain or common platform does not exist. Conclusion Product substitution degree gives different significant impact to both of Cournot and Bertrand game. Figure 1 and 2 depict lower substitutability gives advantage to Cournot and on the contrary higher substitutability is preferred by Bertrand game. Cournot game can be explained as if customer has more options for product variant then they will deal with a product based on product configuration. Price postponement had better to be applied at highly differentiated products because they split market sharply according to each product unique features. Different case if product variants does not exist then consumerà ¢Ã¢â€š ¬Ã¢â€ž ¢s decision will depend on product availability so that producer bargaining position will decrease and finally producer should postpone his production quantity until he receives exact demand information because market is differentiated just according to product availability. Question 2: How does different game strategy affect the optimal price and quantities? Analysis Question 2 is figured out through figure 1 and 2 which show how different game strategies influence price and quantity decisions. Bertrand game gives more opportunity to leader and follower to gain more profit through higher product and material price at higher product substitutability degrees while Cournot game gives the reverse effect as it depicted by figure 1 and 2. Furthermore figure 2 exhibits Cournot game affects more significantly to price and quantities than Bertrand game. In short, both games should be applied according to product design in order to get optimal price and quantities. Conclusion Cournot and Bertrand game give reverse effect to aggregate profit. Figure 1 and 2 depicts how we should apply both games according to our product design in order to achieve optimal profit. Bertrand game gives more advantage to the entire supply chain because among two retailers and supplier share more equal profit than Cournot game. On the contrary Cournot game gives significant profit to retailers and less to supplier. This situation can be explained as Cournot game traditionally is a quantity competition so retailers will order as much as possible in order to dominate market share and as a consequence this situation will reduce product price in market. On the contrary Bertrand game is a price competition so retailers will decide their order according to price equilibrium even they cannot flood market with their products. Furthermore product substitutability also gives additional consideration to retailer decision. In conclusion, Cournot game is better to be applied to unique produc t because it can maintain its price higher while Bertrand game is intended to common product for price stability. 5. Further research and conclusion This paper proposes an alternative method to apply Bertrand and Cournot game to quantity and price postponement according to profit maximization. Both postponement types are explored in order to investigate their compatibility to product differentiation and standardization. This paper proposes dynamic Bertrand and Cournot Stackelberg games with regards to product substitutability degree. It is shown that the generic model derived is consistent with research questions and important from academic perspective as it utilizes a generic model of multistage price and quantity postponement competition. Particularly, this paper offers a comprehensive solution of both types of postponement according to Dynamic Stackelberg game. Even this paper just proposes a theoretical modeling it is also possible to apply at real situation because this paper accommodates common demand function as it is widely used in economic theory. Furthermore there is a great chance to improve it by moving from duopoly to opligopoly competition where there are more than two monopolists. For management implication point of view, this paper gives an insight about coordination mechanism for both of market leader and follower. In real business situation there is no pure competition but some degree of cooperation that is so called coopetition. Example for Bertrand game is join production between Cakra Kembar and Kereta Kencana wheat flour for some markets. Both products are manufactured by Bogasari Flour Mills Surabaya Indonesia which is the biggest wheat flour mills in the world. Both products share common wheat grain contents. Kereta Kencana and Cakra Kembar share their market in order to keep their price so in this case they are managed as Bertrand game. On the contrary, Semar which is produced by Bogasari Surabaya fights with Pena Emas which is produced by Sriboga Ratu Raya Semarang according to Cournot game. Both products have much different product features and produce as much as possible wheat flour to market even they must suffere from price reduction. For future research direction, oligopoly model is considered to be developed according to future market demand that is determined by how close customer requirements is meet so that in future oligopoly model quantity and price can be replaced with some parameter such as inventory and lead times. From this result, a sequence between lead times and inventory can be determined and the outcome will be a decision which one more important for a company, agility or efficiency so that the outcome can be used by top management to compose their business strategy. Finally, the future research should accommodate strategic and tactical level alligment in order to develop comprehensive decision analysis.

History Is Taken From The Patient Essay - 899 Words

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Piano and Mozart free essay sample

First Movement In this paper, I will go In depth and analyze the first movement of Mozart Plano sonata In C major, K. 330. Will follow the gulden by Jan C. Large titled Guldens for Style Analysis*. I will look in depth at the different factors that facilitate our ability in recognizing music in general. The five factors are Sound, Harmony, Melody, Rhythm, and Growth. My goal is to clarify and facilitate what it was that Mozart intended to do in this piece, as well as simply describe some of the different configurations that he implemented in this particular first movement.It is important to describe styles from different composers since we need to develop our ability in using our ears so we can differentiate music from different composers. Overall, however, It is my goal to achieve a higher degree of understanding of this piece from the readers point of view. First, however, I think it is important to understand some of the historical background that took place when this music was composed. Unlike our current time, musicians were seen as low middle class individuals during the eighteenth century. They were usually employed by churches and royalty since they were in need of individuals that could produce a lot of works for their continuous events, yet they were usually underpaid. Another option was being a freelance musician, but that was risky since they would make even less income since they would not be stable. Mozart is an example of someone that attempted being a freelancer, but it wasn’t great for him since he was in debt and always in need of money. Regardless, Mozart was able to produce an overwhelming amount of music that influenced future generations. During his time, one of the musical styles that was prevalent was the â€Å"Style Galant†, which was light and frivolous music that was simple and pleasing to listeners, almost like entertainment music. Mozart was very much indulged in this style and wrote some prominent music that, in my opinion, best represents this style, such as his piano sonata in C major, K. 330. It has a very homophonic texture, with occasional ornamentation that fits the characteristics of Galant music and overall Classical simplicity. Also, it is important to note that this sonata, along with most of Mozart’s works, very much differ from the complex harmonic tonicizations of the Baroque period in the seventeenth century. This sonata was composed among the three other works. It is in a cycle of piano sonatas, from K. 330, to K. 332. The K. 330 sonata was composed in 1783, at a time when Mozart was twenty-seven years old. When one hears this sonata, the sound is very different: the Alberti bass-like configurations in the left hand with a consistent melody in the right hand stick out and makes us wonder and curious to know more. Actually, when looking at the score, it strikes me that the writing is rather simple writing, but only that himself Mozart could execute. All he does is have a nice opera-like melody in the right hand, while the left hand has a â€Å"new† kind of accompaniment that gives the piece a different kind of flow that hasn’t really been heard that often before in Classical piano music. The amalgamation of a nice melody and new kind of left hand accompaniment is one aspect of the music that is interesting, which, of course, creates a new sound. This texture is light, frivolous, and very much in the Galant style that Mozart was so fond of. This kind of timbre belongs only to Mozart and it is what differentiates his music from the rest. For example, measure eight has ascending sixteenth notes, and in measure nine, the right hand melody imitates that previous measure, except it’s the melody, and not the accompaniment. In measure 13, we finally get eight notes staccatos in the left hand with thirty two second notes in the right hand. This is nice since all we’ve been getting is rapid sixteenth notes in the left hand. Harmonically, everything is rather straight forward. There is a prevalent relationship between the tonic of C major and the dominant of G major. Most of the chords Mozart has implemented are in root position and are very much predictable: there isn’t any harmonic ambiguity that makes the piece hard to follow or understand. Once in a while, however, a strong presence of some seventh chords will appear and be felt in the development, and they will usually be in syncopated motion with the motivic configurations taking place in the left hand bass. And for tonicization, which happens from measure 71, they take place based on the resolution of previous keys, which is to be expected of Mozart. But overall, there is a sense of very organized tonality that sometimes feels as if we’re being deviated somewhere else, when in reality, Mozart is simply applying simple harmonies. For the melodic characteristic in this piece, I feel that this particular factor is what differentiates Mozart from every other composer. First of all, his melodies are very operatic, and it is obvious he got this influence from the keyboard works of C. P. E. Bach; actually, Mozart once said that C. P. E. Bach â€Å"Bach is the father, we are the children! †. Mozart was referring to Bach’s ingenious melodic writing, and only that. C. P. E. Bach was in the style of â€Å"Empfindsamer Stil†, which is very different from the Galant style. Regardless, what makes this piece special is not only the beautiful and long melodies, but also how he manages to add accompaniment in the left hand that gives it a fluidity that is hard for anyone else to emulate. The melodies themselves are mostly in stepwise motion, are within a narrow compass, and have a clear diatonic organization. The accompaniment, however, is rather simple, but ingenious. It consists primarily of sixteenth notes, staccato and legato eight notes, sixteenth triplets, and occasional quarter notes. They sound ordinary and vapid, but what the way in which Mozart juxtaposed them, along with the melodies in the right hand, is what makes everything pretty neat. The melodies also change in notes values: eight notes, sixteenth notes, and thirty two second notes. This being said, all he did was combine notes values in a way that gives it a different sense of flow, but we have to remember that the melody is what dictates most of everything. As I kind of already mentioned, the rhythm is varied between eight notes, sixteenth notes, thirty two second notes, and very few quarter notes. The piece is in a 2/4 time signature, with a tempo of â€Å"Allegro Moderato†. The beats are grouped normally, meaning that they are easily felt on both the down and up beats. Regarding rests, they are usually placed before the beginning of a new phrase on either the right or left hand. Ornaments and trills are clearly used, but they are executed rapidly so they won’t interfere with the consistency of the tempo. Measures two, four, and seven are examples of the rapid execution required for the ornaments and trills. As I’ve already implied, since this piece is in the Galant style, the music will most likely stay simple in every sense, including rhythm, which is exactly what we get in this first movement. The growth of the piece is definitely interesting. First of all, most phrases are eight to nine bars long, and are architecturally symmetrical. Also, there are constant two bar sequences with slight ornamentation that gives it some contrast. In the first theme there are motifs and melody played on right hand while left hand takes role in accompanying. Diatonic bass with descending patterns take place right before the first bridge passage from measure 13 through 17, unlike the second theme, but that tends to happen in other Mozart piano sonatas. Another thing he does is that he uses functional pivot chord diatonically where transition from C major to G major occurs in measure 18. The Perfect Authentic Cadence defines the tonality, and he modulates to the related key theme one, which is in C major, and theme two is in G major in Exposition in the development section it continues the ideas in the key of G major, with Adagio beginning. In the Recapitulation section starting at measure 88 both themes one and two are in C major. He later developed more melodic (melody and accompaniment, too) section within a structure that is mostly based on the circle of key. A brief coda provides the harmonic and tonal resolution of the tonic (C major) and relative keys that he pivots in the themes. I believe that his experiment of providing the repeat (the beginning of development section in coda) with tonic presentation of primary material makes this composition unique and so significant that he usually provides off-tonic or relevant key in the coda to end the piece in most music he worked. As James says â€Å"seeming resolution is better understood as a convenient by-product of a larger governing idea: that of thematic rotation, or the architectural propensity within the style to recycle arrays of thematic material in relatively the same order† (P. 110)*, in this piece, he emphasizes the importance of â€Å"recycle† based on the circle of the key by pedal points frequently represented throughout the piece. For example, alberti bass-like part (m. 1~m. 7), which I analyzed as part of pedal point, is relatively modulated in the different key in development, is repeated in recapitulation, and lastly modulated in home key in the coda. Consequently, overall thematic structure is fully supported by this idea, and it is strongly legible that this was something Mozart would need to pertain several sonatas to compose. Another point of view of this piece that I have is that I think Mozart might have even written this sonata based on the operatic style he had already been writing in. He was definitely also influenced by J. C. Bach’s simple and elegant writing, but there is an intense vocal sense in Mozart’s writing that is not felt anywhere else, which is one of the reasons he was idolized as perfection ever since the beginning of the Romantic era; this is still common, even to this day. Regardless of my point of view, what gives this movement its unique timbres are the harmonies, clever use of rhythms, interesting development, soothing and beautiful melodies, unique growth of entire first movement, and overall achieved sound. I hope my analysis was clear and provided a higher degree of understanding and clarification. Mozart is not easy to understand, but he is definitely an interesting composer that makes the listener interested in knowing more about him and his music. Jan C. LaRue’s five essential elements in music are helpful and has made listening to music an easier experience since I have my listening skills have been solidified.

The Self Assessment Of College Students Essay Example For Students

The Self Assessment Of College Students Essay College students are very impressionable when it comes to how to act in the workplace. In high school we develop habits, like how to study and how to write properly, but we are not fully prepared to go into the working field. The self-assessments, provided by Professor Whitten, gave students a chance to know what they need to improve or maintain. Also, it allowed us to explore our values, opportunities, and strengths, something that I have never done before. Although some of my self-assessments gave me results that I expected, they revealed many things about myself that were surprising. Based on my self-assessments I am an ethical person that enjoys a diversified workplace. I have many strengths such as internal locus control and handling facts, however, I have opportunities such as time management Ethics in the workplace is to behave in a manner consistent with what is right or moral (O Brien 1). Morality changes over time to support current events. For example, the United States was once a country that allowed slavery and only allowed men to vote. Now we live in a country where women can vote and open their own businesses; something that other countries would frown upon. My Individual Ethics self-assessment gave me a high ethics rating. We will write a custom essay on The Self Assessment Of College Students specifically for you for only $16.38 $13.9/page Order now As a supervisor for Best Buy, I always have to ensure that I am making the right decisions and behaving ethically in order to cultivate a positive work environment. It has been seen across businesses that having an ethical work environment leads to less observed misconduct at work; greater overall satisfaction with their organizations; and a greater likelihood of feeling valued (Joseph 2). Therefore, representing a good example of an ethical behavior is personally important because I know . .2014) while being ethical and having empowering employees by giving them the proper training to do their job. Currently I enjoy teaching my line-level associates how to do different tasks in order to prepare them for better positions. It is a great feeling taking part in someone s career path and seeing a positive outcome. My self-assessments taught me many things about myself, such as the importance of ethics in the workplace and my time management skills. When I started going to college I knew very little of how to behave in a business setting as a manager. Personal experiences have given me a lot of knowledge. However, after going through this course and really speaking about different situations that can occur, I feel as though I have a lot of things to learn and bad habits to dispose of in order to be a better management and to guarantee success in my future.

pagal bnana Essays

pagal bnana Essays pagal bnana Essay pagal bnana Essay November 2010 Table of Contents Section 1: Section 2: Section 3: Section 1 Introduction and Background Project Concept and Design Project Financial Profile Introduction Introduction and Background to the assignment The project is to design a sustainable multi-storey apartment complex in Islamabad. The site for this project is located in Chak Shazad, opposite CllT campus on Park Road. The relatively flat site measures approximately 3. 91 acres and falls under the jurisdiction of CDA . Water table was encountered at a depth of 180+1- below existing ground level. Due to limits of the soil bearing capacity, the findings in the report recommend that a raft foundation be designed for a multi-storey building as have been the foundation design of other multi-storey buildings built in this area. The site is accessed by the 2-lane Park Road, which is a high speed road. Considerations should be given to a deceleration lane prior to entry to the site. ould be apartments for middle class to upper class type clientele with individual apartments to be for sale on an ownership basis. However, the developer, while wishing to maximize his profits, also recognizes that the housing complex should be istinctive, spacious, airy, daylight, convey an open feeling, a green/sustainable building and contribute to good living. The complex offering these valuable amenities contributing to good living, among other facilities, could be priced higher than other normal housing complex . In this area the setting is mostly rural but this is as a result more of it being undeveloped thus so far. In time to come, this area would convey an urban feeling due to the various educational and institutions and other buildings that would be added to the existing buildings. As designers, need to create a rural/urban feeling ithin the individual housing units. Special attention needs to be paid to designing a sustainable building design with respect to environment in Islamabad. One of the mainstays of sustainability and green buildings is the location of the building site. This site is located in the suburbs of the city, and is unfavorable to sustainability due to the impact of transportation energy required to access this site from other areas. The availability of public transportation in this area is very limited and this site is mostly accessible by cars and a very limited and inadequate public transportation. As compensation the developer envisages that this building would accommodate the owners commercial/community facilities such as a community hall, meeting rooms, gym, swimming pool, shops, a daycare center, gymnasium, common open outdoor spaces and an outdoor walking/running track, all of which would reduce the need to spend transportation energy on a daily basis. As architect/designer, need to develop a building program to include functional spaces, facilities and amenities. As developer, have to conduct a market pre- feasibility study which would ensure a good potential investment and rate of return. Objective As designer and developer a blue print of the project needs to be designed. In particular following needs to be delivered: A pre-feasibility economic study to be included in the design brief. A building program outlining no. of housing units, size of units (one-bed, two-bed, three- bed, etc. and square footage) and all other amenities to be provided. Include also green/ sustainable features, which you would incorporate in your design. Key emphasis will be placed on the functional spaces and green effect of the project. This will include community hall, meeting rooms, gym, swimming pool, shops, a daycare center, ymnasium, common open outdoor spaces and an outdoor walking/running track, all of which would reduce the need to spend transportation energy on a daily basis. The nature of this assignment required conducting surveys with the professional construction companies and developers. For this purpose I short listed 3 of the prestigious organizations currently engaged in similar projects. These included; 1. pak Gulf (PVt) Ltd. 2. Chaudhry Enterprises Real Estate and Developers 3. A1-Ghurar . ak Gulf (PVt) Ltd. Chaudhry Enterprises Real Estate and Developers F-7 Jinnah super Ibrahim Javed ( concern person) A1-Ghurar . Short questioners were designed which included the following The market price of land per yard in the vicinity Cost of construction for 1 5 stories Labour cost and availability Dual access to the location from Islamabad and Rawalpindi Social cultural aspect of target market Travel time Market growth Investor interest Assumption used: The blue prints to the project design are based on few fundamental assumptions. These include the following; 1 . The approval for the construction / NOCS will be issued without any technical or financial delays 2. The material is easily available at a competitive pricing 3. Buys and nvestors are readily available 4. There is a constant demand in the market for apartment complexes Section 2 Project Concept Design Project Concept and Objectives A Multi-storey apartment complex needs to be designed keeping in mind that family space needs vary according to family needs and other requirements, the development of this housing complex should have a mix of size of apartments. It is up to the designer to include units of varying combinations such as I-bedroom, 2- bedroom, 3-bedroom, 4-bedroom, etc. Also incorporate within the design community spaces offering various activities such as a community hall, meeting rooms, gym, wimming pool, shops, daycare center, common open outdoor spaces and an outdoor walking/running track. 2. 2 Components and Facilities at the Apartments The Apartments will comprise of following 8 main divisions; 1 . Deceleration Lane 2. Parking space 3. Outdoor landscaping 4. Security complex 5. Community halls 6. Recreational areas- Indoor and out door 7. Shopping arcade 8. Apartment complex building Each division is addressed in detail in the following sections. The complex is planned as a mixture of different size apartments. This includes 1- bedroom, 2-bedroom, 3-bedrooms, and 4-bedrooms apartments. The apartment acility is proposed to encompass the following units with the following bed allocation: sr. NO. Facility Qty Deceleration lane- as per by-laws of CDA 2. Parking space- Minimum of 2 for each residential unit 3. Outdoor landscaping 4. Security complex 2 5. Recreational unit 5. 1. Gym 5. 2. Swimming pool 5. 3. kids play area 5. 4. Common open outdoor space 5. 5 walking / running tracks 6. Community halls / Meeting halls 7. 1. Shopping arcade 5 7. 2. Beauty salon 8. Multi size apartments 45 2. 3 By Laws applicable on the site: The construction site fall in the Jurisdiction of the CDA and therefore the by-laws of CDA will be applicable on this site. Some of the salient feature included in the said by-laws is stated as under ZONING AND OTHER REQUIREMENTS: -Building setbacks: Front 60, Rear 40, Sides 30 -Max. site coverage = 40% -Max. no. of floors = 15 -Max building height = 190-0 from road level at entry/exit point whichever is higher. A 4-0 parapet is permitted above the 190-0 height limitation. -Max. mumty area/ height = 4,000 sf/9-0 -Max. plinth height = 5-0 -Rainwater retention area on site of 20% of site area to a depth of 5-0. -Max. 3 projection in setbacks permitted above openings windows, doors, etc. and/or for building aesthetics only). -Basements permitted for parking and services only DRIVEWAY AND PARKING REQUIREMENTS: A deceleration lane off Park Road to be incorporated prior to entry to site. -Ingress and egress driveways to be minimum of 20-0 for one-way traffic and 30-0 for two-way traffic. 9x17 right-angled parking space with 23 perpendicular back up space. -5x 17 landscaping island after every 10 parking spaces max. in open areas. -Min of 2 parking spaces per residential unit. -Parking for commercial/amenity areas based upon occupant load. 5% of parking spaces to be 12x 17 accessible spaces for the physically challenged with a 5x 17 wheelchair loading area. One loading area may be shared by 2 acces sible car spaces. -Van spaces of 10 x 19 as required for services. -Visitor parking: 10% of total no. of residential units parking spaces. -Vehicle circulation to be in forward motion only. Motorcycle spaces, 2 per each dwelling unit plus 50% additional motorcycle spaces for visitors and other amenities. -No stacked parking permitted for vehicles and motorcycles. -A 20-0 wide fire truck access lane with a minimum inside turning radius of 30-0. Fire truck movement to be in forward motion only or a cul-de-sac turnaround radius of minimum 30-0. The fire truck access lane to be not more than 100-0 from the apartment complex perimeter wall. -Landscaped area of minimum 15% of the site area. -Landscaping setbacks: Front 30-0, Sides 15-0, Rear 20-0 (driveways excepted). No parking permitted in landscaping setbacks 2. 4 Number of apartment complex: Based on my survey and discussion with the interviewed parties, I propose the following plan. This plan caters the needs of the project as are s tated in the objectives. Description One Bedroom apartment (12th, 13th and 14th Floor) 15 Two Bedroom apartment (8th, 9th, 10th floor) 12 Three Bedroom apartment (7th , 6th and7th floor) 9 Four Bedroom apartment (3rd, 4th and 5th floor) Total The first two floors will accommodate for the meeting halls and recreational activities such as Gym and common outdoor area. . 5 Target Market The target market for these apartments is for upper and middle class. Initially we intended to cater both the middle and upper class but after meeting with the companies in this field, such as Pak Gulf, I have resolute to go with middle class ostly, people who are looking to upgrade their status from middle case to upper The one bed room (pent house / studio style) will provide for the need of working couples and also for international students. Where as the 2, 3 and 4 bed room will be located in the middle of the complex and will provide for families. All the apartments will be designed with an independent look and feel to enhance their privacy and provide a posh feeling. Why Come Here From Urban Areas ? These apartments will be luxurious apartments like those in urban areas but here , cost of living is different, its lower than those . People will have to pay lesser amount for the same facilities , The cost of the land here is 20-27 Lac/kenal whereas its 80 Lac/kenal in urban areas . They would be able to get luxurious apartments by paying Just one crore as compare t03. crores price of apartments in silver oak. Here the Travelling time is Shorter , As if we consider Zero point or Convention centre as hub, the traveling time is about 20 minutes , Airport is at the traveling distance of about 15 minutes , would be able to get to Islamabad or Rawalpindi within 30 minutes. Educational institutes are nearby , as CllT and schools are Just opposite to the site , Beacon in Banigala etc. lts a facility for the students over here and for t he overseas students as well who will accommodate in these apartments . Will provide a security systems. Section 3 Project Financial Profile This basically is the process of developing a financial model for the proposed apartment complex. The financial assessment incorporate various options which are under consideration viz-a-viz the ownership, management governance and operating structure of the proposed project (see Operational Model Assumptions below). Key variables that are needed to be presented in the model provide links etween capital expenditure, debt, and Complex operating expenses. Moreover, the model will also highlight the impact of expected demographic trends and market forces on the financial viability and sustainability of the project. The financial assessment is done in three stages which include (i) Development of Project Capital Cost Model; Determining the projects Operational, Managerial, Maintenance Costs and integrating the financial model to include all cost aspects; and (iii) Determining the financial sustainability of the project based on various Operational Models. These costs are one off costs that have to be incurred to make the project perational. The estimated project cost is PKR 239,800,000. This includes the cost of Land, Building, Civil Electrical Works, Project consultancy fee and Other Miscellaneous cost. Land Cost has been estimated on the basis of average market price of land per acre which can be evaluated through consultation with the local real estate agents. An average estimate land based on the 3 interviewed companies is estimated to be Rs 20-27 Lac per Kennel. This translates into Rs 95 million. The Building Civil Works comprises of cost to be incurred for developing the main infrastructure of each facility. Item cost PKR A. Land Scraping and deceleration lane B. Building and Civil Works c. Elevators D. Civil Work, Electrical Works and Communication System Fire Sighting System Generators G. Tube well Waste Water Treatment Plant Management Fees and Other Pre Operating Expenses including booking 5,000,000 Interest During Construction (Optional) TOTAL PROJECT COST *The above figures are based on initial survey with the shortlisted companies and purely estimate and approximation based on Consumer Price Index of 2010. These fgures should be broken down over the life of the project and be subject to inflation s well for accurate results. Operating Cost Operating costs are the routine costs required to keep the facility operational at pre- defined standards. These costs can be divided into direct operational costs and indirect operational costs or overheads. Direct Cost Direct Costs are those costs which are directly attributable to operations of the facility. Salaries Wages cover the salaries of staff such as architect and builders and Thakadar (Construction Company) directly engaged in providing the construction. Daily salaries include a base salary as well as the consultancy fee harged based on the number of visits. Other Direct Costs Other direct cost for the project includes the repair and maintenance costs of plant and equipment such as water treatment plant etc, in order to maintain operational efficiency and provide green effect. These costs will be low in the initial years as new plant will require less maintenance and will increase in accordance to the useful life. Indirect Cost These costs include all other costs that are not directly attributable to the complex operations. Such costs are normally fixed in nature and include security and marketing.

Green Surname Meaning and Origin

Green Surname Meaning and Origin GREEN Surname Meaning Origin: The Green surname can have one of many possible derivations. It was commonly used to describe someone who dwelled at, or near, the village green, or other grassy ground. Other possible origins include someone who favored the color green (from the Old English grene), or someone who was immature or inexperienced. Green may also have been used as the surname of somone who had played the part of the Green Man in May Day celebrations. Green is the 37th most popular surname in the United States and the 19th most common surname in England. Surname Origin: English Alternate Surname Spellings: GREENE Famous People with the Surname GREEN: Pat Green - American country music starEva Green - French actressNathanael Green - General in the Continental Army during the American Revolution Genealogy Resources for the Surname GREEN: 100 Most Common U.S. Surnames Their MeaningsSmith, Johnson, Williams, Jones, Brown... Are you one of the millions of Americans sporting one of these top 100 common last names from the 2000 census? GREEN / GREENE Surname DNA ProjectMales Greens from anywhere, including alternate spellings of Greene, MacGreen, MacGreene, McGrane, McGreen, McGreene, can join this Y-DNA project which is attempting to sort out various GREEN families. GREEN Family Genealogy ForumSearch this popular genealogy forum for the Green surname to find others who might be researching your ancestors, or post your own Green query. There is also a separate forum for the GREENE variation of the Green surname. FamilySearch - GREEN GenealogyFind records, queries, and lineage-linked family trees posted for the Green surname and its variations. GREEN Surname Family Mailing ListsRootsWeb hosts several free mailing lists for researchers of the Green surname. Cousin Connect - GREEN Genealogy QueriesRead or post genealogy queries for the surname Green, and sign up for free notification when new Green queries are added. DistantCousin.com - GREEN Genealogy Family HistoryFree databases and genealogy links for the last name Green. Looking for the meaning of a given name? Check out First Name Meanings Cant find your last name listed? Suggest a surname to be added to the Glossary of Surname Meanings Origins. - References: Surname Meanings Origins Cottle, Basil. Penguin Dictionary of Surnames. Baltimore, MD: Penguin Books, 1967. Menk, Lars. A Dictionary of German Jewish Surnames. Avotaynu, 2005. Beider, Alexander. A Dictionary of Jewish Surnames from Galicia. Avotaynu, 2004. Hanks, Patrick and Flavia Hodges. A Dictionary of Surnames. Oxford University Press, 1989. Hanks, Patrick. Dictionary of American Family Names. Oxford University Press, 2003. Smith, Elsdon C. American Surnames. Genealogical Publishing Company, 1997. Back to Glossary of Surname Meanings Origins

A Shift in the Balance of Power from the USA to China Essay

A Shift in the Balance of Power from the USA to China - Essay Example This paper illustrates that while China balances precariously between the free market and an edgy military regime, the nation is surfacing as a formidable contender in the economic sector and an impending challenger for technological advantage. From the benchmark of Tiananmen Square in 1989 well into the first tender years of the Twenty-first Century, many in the West continue to view China with unease and distrust. From the appalling crackdown on the visionary expectation of the ardent student protesters some16 years ago to the subsequent repression of all political dissidence, Communist leaders have time and again tended to reassert a blind obeisance to a dogged system of harsh and mechanical one-party rule. Equally alarming is the ostentatious display of military power in response to Taiwanese aspirations for independence over the last two decades, along with the troubling detection of furtive deliveries of military know-how to unstable areas in the Middle East, the Persian Gulf, and South Asia. These measures scarcely serve to improve international confidence in the Chinese bid for a responsible position on the world stage of the new century. Admittedly China has recently begun to evince a new, less menacing and forward-looking stance toward proving itself as a responsible collaborator in global interaction as the nation begins to assume a substantial position in the world economy. By assisting in negotiations on the Korean Peninsula, China, in effect, was able to take advantage of her influence in the region in the service of broader international concerns. Domestically, the Peoples Republic of China has taken steps to free a token number of leading political dissidents in response to Western appeals, and, in diverse rural villages, elections for local leaders have been authorized. Chinese rulers also seem to be dealing moderately with the lately re-annexed regions of Hong Kong and Macau, and so far seem to be restricting intimidation tactics to verbal pos turing and a display of military muscle in response to Taiwanese desires for independence.  

The Case Marbury V. Madison Essay Example | Topics and Well Written Essays - 2250 words

The Case Marbury V. Madison - Essay Example Thus, this historic case created the concept of Judicial Review or the capability of the Judiciary declaring a law unconstitutional. The court case hence resulted to the Judiciary, Legislative & Executive branches of the government is on an evener power basis ultimately setting the precedent for an infinite number of future historic decisions (Marbury versus Madison, 1803). On the last day in office, Adams the president commissioned sixteen new justices for the circuit court and forty-two peace justices for the Columbia district in his last day in office under the Organic Act, which was meant taking control of the Judiciary of the Federal government by the Federalists before Thomas Jefferson took office. The commissions were consequently signed by President John Adams & sealed by the then acting State Secretary, John Marshall (author of the opinion of this case) before he becomes the Court of Supreme Chief Justice. However, the commissions were not submitted before the end of John Adams’s term as the president of the U.S. resulting to rejection of the appointments by Thomas Jefferson who termed them as invalid on grounds that they were not submitted before the end of John Adams’s term as the president (Marbury versus Madison, 1803). Therefore, this prompted William Marbury one of the appointees filing a writ of mandamus before the Court of Supreme, which had original jurisdiction issuing writs of mandamus to any persons holding office or courts under the U.S. authority, to compel Madison, the Stare Secretary delivering the new appointments. However, supreme led by John Marshall rejected on grounds that the move was unconstitutional under some part of the Judiciary Act of 1789 (Marbury versus Madison, 1803). Â  

Cebu Province Division Essay Example for Free

Cebu Province Division Essay Introduction DAMATH, a patent-pending mathematical board-game invented by five-time national awardee Jesus L. Huenda, is coined from the popular Filipino checkerboard game of dama, (or lady in Spanish) and mathematics. It started in a Sorsogon National High School class in Sorsogon, Philippines and its popularity spread quickly and resulted in the first national DAMATH competitions held at Legaspi City in 1980. He initiated this competition with the support of the Science Foundation of the Philippines. He hopes to introduce DAMATH to secondary math teachers as part of a requirement of his work as PASMEP Fellow at Curtin University / WACAE, Western Australia. Thus if this material, or part of it, is used commercially or otherwise (except for classroom instruction purposes), permission must be secured in writing from him. By the way, DAMATH is part of the inventor’s position paper, Non-formal mathematics education: the Sorsogon National High School experience, delivered at the 1978 First Southeast Asian Conference on Mathematical Education, PICC, Manila; 1979 and 1980 MTAP national conventions at Legaspi City and Quezon City, respectively. 1981, 1983 and 1988 Philippine Expositions, PHILTRADE, Manila; conference, Mandurah, WA; Australian Association of Mathematics Teachers 13th biennial national conference, Hobart. Rationale It is becoming a growing classroom practice in many school subjects, including mathematics, to use games to promote the understanding of concepts and skills. This practice is supported by child psychologist Piaget and Inhelder (1969) and Kohlberg (1969) who are convinced that affective, cognitive, and social development strongly influence one another and develop along parallel lines. There are data to support this statement. Thus, the use of socially interactive mathematical games in learning and teaching mathematics is credible. Objectives 1. To integrate the Filipino checkerboard game of dama into the teaching of mathematical concepts and skills. 2. To encourage the utilization of recycled materials in constructing damath board set (for classroom use only). 3. To analyze damath as a possible subject of mathematical investigations. 4. To enhance wholesome interpersonal relations among learners. 5. To promote mathematical consciousness among, family members in particular and the community in general through the mathematics club’s community outreach damath competitions. 6. To promote awareness of girls in mathematics [as king is to the game of chess, so dama (or lady) is to damath ] ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 2 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Teacher’s Notes: Any game can be trivial or worthwhile. It all depends on the players of the game and when and why. Feedback from teachers who have tried damath is encouraging because they have found it appropriate, fun, and useful in their classes. All 12 games are to be played in pairs. Students learning mathematics in this way have been found to associate mathematics with wholesome and purposeful work. These games may introduce, supplement, reinforce or refresh concepts, skills and attitudes. To get the most out of damath, read the accompanying guide sheet and list of materials needed. Determine what extra work can be assigned to pairs of students who will carry out the activity. As a follow-up activity, some mathematical investigations concerning damath may be assigned to small groups of students, or mathematics club may conduct community-outreach damath competitions highlighting awareness of girls in mathematics. In doing so, observe student’s performance and reactions and record them in a cognitive skill checklist and attitude respectively. This, together with your assessment, will provide you with significant data for future reference. The inventor welcome suggestions from teachers in the field by sending it to: Jesus L. Huenda, Curriculum Development Division, Bureau of Secondary Education, Department of Education, Culture and Sports, Palacio del Governador, Intramuros, Manila. Suggestions and input can be mailed to him using the following form: (See next page). TO THE STUDENTS In DAMATH, there are 12 games to play. All of these games are original especially designed for you to make you do and play mathematics, have fun with it in thinking, making a game plan, and using your common sense, honesty and fair play. Do them and learn mathematics. Do them and enjoy yourself, too. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 3 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Name of the game: ___________________________ School:____________________________ Sender’s Name (Optional):_____________________ Address:___________________________ What I like in the game Areas for improvement Guide Sheet Title Damath the Teeny Integer Countess Damath Damath-in-a-Whole Damath Over U Busy Deci Damath Damath the Old Prime Madonna Damath the Fibo Nutty Lady Byte-a-Damath Damath a la Mod Trig-a-Damath Sci-No-Damath Log-a-Damath Concept Integers Counting numbers Whole numbers Fractions decimals Prime numbers Fibonacci sequence Binary numbers Modulo 12 Trigonometric Functions Scientific Notation Logarithmic function Place in the Curriculum Review activity for Units 3 – 8 List of Materials Damath board set (See attachment A) Enrichment activity for Units 3 – 8 Enrichment activity for Unit 2 Introductory activity for Unit 5 Enrichment activity for Unit 6 ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 4 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ DAMATH: 12 games for High School Mathematics Contents Of This Package †¢ Activity sheets for students for each of the following titles: Activity Activity Activity Activity Activity Activity Activity Activity Activity Activity Activity Activity †¢ Teacher’ Manual 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Damath the Teeny Integer Countess Damath Damath-in-a-Whole Damath Over U Busy Deci Damath Damath the Odd Prime Madonna Damath the Fibo Nutty Lady Byte-a-Damath Damath a la Mod Trig-a-Damath Sci-no-Damath Log-a-Damath Rules: How to S T A R T 24 chips should be placed first on the following squares on the DAMATH board Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 5 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ How to make a move 1. Toss a coin to decide who moves first. 2. The first player moves a piece by sliding diagonally forward to an adjoining vacant square (no chip is to be placed on colored squares). Record your move in the scoresheet. Example: Red player moves â€Å"-1† to an adjoining vacant square ( 5 , 4 ), thus, to the scoresheet the player writes on the first column under the heading â€Å"Move† with [-1 (5,4) ] to mean â€Å"-1† goes to a square located 5 on its x-axis and 4 on its y-axis. 3. The two players alternately take turn in moving a piece. How to take a piece (Ka-on) 1. In the example above, Red player with piece â€Å"-1† is required (pass is not allowed) to take a piece â€Å"2† of Blue side by jumping over the piece to be taken and landing on the latter’s adjoining vacant square, which, also, determine the symbol of operation to be used. Example: â€Å"-1† takes â€Å"2† by jumping over it (player gets the piece â€Å"2†) and finally lands on a square (7,2) which has minus sign on it. Thus, on the scoresheet, the player writes on the first column with â€Å"-1 – 2†. Moreover, on the second column under the heading â€Å"Score†, the player writes the answer as â€Å"-3†. While on the third column under the heading â€Å"Total Score†, the player writes the total score by adding whatever points in it, thus, â€Å"-3†. Round off numbers, if necessary. 2. A player can take one chip or more than one chip with the required option to take the greater number of chips. 3. A Red chip is declared as â€Å"dama† if it reaches any of the following squares: ( 1, 0 ) (3,0) (5,0) (7,0) Similarly, for Blue Chip as follows: ( 0, 7 ) (2,7) (4,7) (6,7) 4. Once a piece is declared as â€Å"dama† it could slide diagonally forward or backward in any vacant square provided no opposing piece blocks it. It could take a piece or pieces and have the privilege of doubling its scores. 5. The game is ended it (a.) a player has no more piece to move; or, (b.) it is impossible for any or both players to go on because of repeated move. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 6 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ In (a) or (b), the remaining piece or pieces are added to the total score. Finally, the player with the greater accumulated total, wins the game. How to score Shown below is a Damath Scoresheet. Initial entries on it were taken from the above examples of player’s move and in taking piece or pieces. DAMATH SCORESHEET Red Player Move -1 (5,4) -1 2 Score -3 Total 2 -3 Player Move (9,3) Score Total Blue Player’s Signature: Player’s Signature: Signature of Teacher / Parent: Signature of Teacher / Parent: Win Loss Win Loss ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 7 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 1: DAMATH the Teeny Integer A game for two players. What you need * †¢ DAMATH board ( 8 squares by 8 squares ) 24 chips in two colors: ( 12 of each color, thus, 0, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11 ) For illustration, see attachment A of this Package. What it is about It is a game of addition, subtraction, multiplication and division of integers, rounding off numbers, and point plotting. Aim of the Game The player with the most points wins. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 8 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 2: Countess DAMATH A game for two players. What you need Same materials as in Activity 1, but on the reverse side of chip no. â€Å"0† write chip no. â€Å"12†. What it is about It is a game of adding, subtracting, multiplying, and dividing counting numbers; rounding off numbers, and point plotting. Aim of the Game The player with the most points wins. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 9 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Rules Same rules as in Activity 1,but the â€Å"0† chip is replaced by â€Å"12† [ â€Å"12† is on the reverse side of â€Å"0† chip]; and, negative signs have to be disregarded. Thus, initial positions of the chips are as follows: Chip Number 1 2 3 4 5 6 7 8 9 10 11 12 Position of Blue Chip (1,2) (3,2) (5,2) (7,2) (0,1) (2,1) (4,1) (6,1) (1,0) (3,0) (5,0) (7,0) Position of Red Chip (6,5) (4,5) (2,5) (0,5) (7,6) (5,6) (3,6) (1,6) (6,7) (4,7) (2,7) (0,7) In taking a chip or chips, addition, subtraction multiplication, and division of counting numbers are used. Round off numbers, if necessary, in making entries on the scoresheet. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 10 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 3: DAMATH – in – a Whole A game for two players. What you need Same materials as in Activity 1 What it is about It is a game of adding, subtracting, multiplying and dividing Whole numbers ; rounding off numbers, and point plotting. Aim of the Game The player with the most points wins. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 11 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 _____________________________________________________________________________ _ Rules Same rules as in Activity 2, but the â€Å"12† chip is replaced by â€Å"0† [ â€Å"0† is on the reverse side of â€Å"12† chip]; and, negative signs have to be disregarded. Thus, initial positions of the chips are as follows: Chip Number 0 1 2 3 4 5 6 7 8 9 10 11 Position of Blue Chip (1,2) (3,2) (5,2) (7,2) (0,1) (2,1) (4,1) (6,1) (1,0) (3,0) (5,0) (7,0) Position of Red Chip (6,5) (4,5) (2,5) (0,5) (7,6) (5,6) (3,6) (1,6) (6,7) (4,7) (2,7) (0,7) In taking a chip or chips, addition, subtraction multiplication, and division of whole numbers are used. Round off numbers, if necessary, in making entries on the Scoresheet. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 12 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 4: DAMATH Over U A game for two players. What you need Same materials as in Activity 1, but the positive and negative numbers should have â€Å"10† as denominator (use reverse side of chips). What it is about It is a game of adding, subtracting, multiplying and dividing fractions; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity1, but adding, Subtracting, multiplying and dividing fractions are used, thus, all entries on the Scoresheet are fractions. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 13 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 5: Busy Deci DAMATH A game for two players. What you need Same materials as in Activity 4, but decimal equivalent should take the place of fractions. What it is about It is a game of adding, subtracting, multiplying and dividing decimals; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 4, but instead of fractions, the decimal equivalents are added, subtracted, multiplied, and divided. In taking a chip or chips, results of mathematical operations are rounded off to the nearest hundredths. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 14 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 6: DAMATH the Odd Prime Madonna A game for two players. What you need Same materials as in Activity 1 What it is about It is a game of prime numbers; integers; squaring numbers; rounding off numbers; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 1, but in taking a chip or chips the results of algebraic operations are squared if it is an odd prime number. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 15 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 7: DAMATH the Fibo Nutty Lady A game for two players. What you need Same materials as in Activity 2 What it is about It is a game using the Fibonacci sequence; counting numbers; Cubing numbers; rounding off numbers; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 2, but in taking a chip or chips the results of mathematical operations are cubed if it is a Fibonacci number. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 16 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity A game for two players. 8: Byte – a DAMATH What you need Same materials as in Activity 3, but even numbers are to be considered as â€Å"0†, while odd numbers as â€Å"1†. What it is about It is a game of adding, subtracting, multiplying and dividing binary numbers; and point plotting Aim of the Game The player with the most points wins. Rules Same rule as in Activity 3, but in taking a piece or pieces binary arithmetic is used. Thus, initial positions of blue and red chips are as follow: Chips 0 1 0 1 0 1 0 1 0 1 0 1 Position of Blue Chip Position of Red Chip (1,2) (6,5) (3,2) (4,5) (5,2) (2,5) (7,2) (0,5) (0,1) (7,6) (2,1) (5,6) (4,1) ( 3 , 6) (6,1) (1,6) (1,0) (6,7) (3,0) (4,7) (5,0) (2,7) (7,0) (0,7) ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 17 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity A game for two players. 9: DAMATH a la Mod What you need Same materials as in Activity 3 What it is about It is a game of addition, subtraction, multiplication and Division in module 12; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 3, but in taking a piece or pieces binary arithmetic is used. Thus, initial positions of blue and red chips are as follow: Chips 1 2 3 4 5 6 7 8 9 10 11 12 Position of Blue Chip Position of Red Chip (1,2) (6,5) (3,2) (4,5) (5,2) (2,5) (7,2) (0,5) (0,1) (7,6) (2,1) (5,6) (4,1) ( 3 , 6) (6,1) (1,6) (1,0) (6,7) (3,0) (4,7) (5,0) (2,7) (7,0) (0,7) ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 18 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity A game for two players. 10 : Trig – a DAMATH What you need Same materials as in Activity 1, but the following integers should have the Corresponding trigonometric functions by changing them to degrees: Chips in degrees -1 and 10 -3 and 8 -5 and 6 -7 and 4 -9 and 2 11 and 0 Trigonometric Functions Sin Cos Tan Cot Sec Csc What it is about It is a game using trigonometric functions; trigonometric identities; changing degrees to radians and vice – versa; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 1, but in taking a piece or pieces (this time, integers are expressed in degrees) trigonometric functions and identities are used. Thus, initial positions of blue and red chips are as follow: Chips in degrees Position of Blue Chip Position of Red Chip Csc 0 (5,2) (2,5) Sin –1 (3,2) (4,5) Sec 2 (7,2) (0,5) Cos -3 (1,2) (6,5) Cot 4 (4,1) (3,6) Tan –5 (2,1) (5,6) Tan 6 (6,1) ( 1 , 6) Cot –7 (0,1) (7,6) Cos 8 (5,0) (2,7) Sec –9 (3,0) (4,7) Sin 10 (7,0) (0,7) Csc -11 (1,0) (6,7) ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 19 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity A game for two players. 11 : Sci – no DAMATH What you need Same materials as in Activity 2, but the integers are raised to their corresponding Powers as follows. Chips 1 2 3 4 5 6 7 8 9 10 11 12 Expressed in Scientific Notation 1.1 x 10-1 2.2 x 10 2 3.3 x 10-3 4.4 x 10 4 5.5 x 10-5 6.6 x 10 6 7.7 x 10-7 8.8 x 10 8 9.9 x 10-9 1.01 x 10 10 1.11 x 10-11 1.212 x 10 12 What it is a bout It is a game of adding, subtracting, multiplying and dividing numbers in scientific notation; and point plotting. Aim of the Game The player with the most points wins. Rules Same rule as in Activity 2, but addition, subtraction, multiplication, and division of numbers in scientific notation are used; thus, entries on the Scoresheet should be numbers expressed in scientific notation. ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 20 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ Activity 12 : Log – a DAMATH A game for two players. What you need Same materials as in Activity 11 (common logarithm) or as in Activity 10 ( for logarithms and trigonometric function), as the case maybe, depending player’s agreement. What it is about It is a game of common logarithms; logarithms of trigonometric functions; and point plotting. Aim of the Game Same as in Activity 11 or Activity 10, as the case maybe. Rules Same rules as in Activity 11 or Activity 10, as the case maybe, depending on the player’s agreement, but common logarithms and logarithms of trigonometric functions are used, respectively. Thus, entries on the Scoresheet should have common logarithms or logarithms of trigonometric functions, as the case maybe/ ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 21 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ A. GAMES FOR DAMATHS COMPETITIONS: Levels Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Grades Grades I – II Grades III – IV Grades V – VI First Year Second Year Third Year Fourth Year Contents Counting Numbers Whole Numbers Positive Fractions Integers Signed Fractions Radical Damath Polynomial Damath B. POSITIONS OF CHIPS: ( Elementary Level ) Level 1 2 3 4 5 6 7 8 9 10 11 12 CHIP NUMBERS I Level II Level III 0 1/10 1 2/10 2 3/10 3 4/10 4 5/10 5 6/10 6 7/10 7 8/10 8 9/10 9 10/10 10 11/10 11 12/10 BLUE CHIPS (1,2) (3,2) (5,2) (7,2) (0,1) (2,1) (4,1) (6,1) (1,0) (3,0) (5,0) (7,0) RED CHIPS (6,5) (4,5) (2,5) (0,5) (7,6) (5,6) (3,6) (1,6) (6,7) (4,7) (2,7) (0,7) POSITIONS OF CHIPS: ( Secondary Level ) CHIP 1st Year 0 -1 2 -3 4 -5 6 -7 8 -9 10 -11 2nd Year 0/10 -1/10 2/10 -3/10 4/10 -5/10 6/10 -7/10 8/10 -9/10 10/10 -11/10 NUMBERS 3rd Year 4√18 -√8 16√32 -9√2 36√32 -25√18 64√2 -49√8 100√2 -81√32 144√8 -121√18 4th Year 6x -xy2 10y -3x2y 28y -15x 36x2y -21xy2 66x2y -45y 78xy2 -55x For 4th Year Only, Blue Red Chips BLUE CHIPS (5,2) (3,2) (7,2) (1,2) (4,1) (2,1) (6,1) (0,1) (5,0) (3,0) (7,0) (1,0) RED CHIPS (2,5) (4,5) (0,5) (6,5) (3,6) (5,6) (1,6) (7,6) (2,7) (4,7) (0,7) (6,7) ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 22 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ POSITIONS OF CHIPS: ( Secondary Level ) Level 4 CHIP Level 5 NUMBERS Level VI Level VII -1 1.1 X 10 0 2 2.2 X 10 1 3.3 X 10-3 2 4 4.4 X 10 3 5.5 X 10-5 4 6 6.6 X 10 5 7.7 X 10-7 6 8 8.8 X 10 7 -9 9.9 X 10 8 1.01 X 10 10 9 -11 1.111 X 10 10 1.212 X 10 12 11 BLUE CHIPS (1,2) (3,2) (5,2) (7,2) (0,1) (2,1) (4,1) (6,1) (1,0) (3,0) (5,0) (7,0) RED CHIPS (6,5) (4,5) (2,5) (0,5) (7,6) (5,6) (3,6) (1,6) (6,7) (4,7) (2,7) (0,7) General Guidelines on DAMATHS Century Match 1. First player is determined by drawing lots. 2. Basically the rule in playing dama shall be used as follows: a. A â€Å"chip with numeral† moves diagonally forward to an adjoining vacant square. b. A chip takes an opponent’s chip or chips diagonally forward or backward. Mathematical operation such as addition subtraction, multiplication, or division of numerals shall be used depending on the vacant square’s operation symbol where the â€Å"taker† chip lands by jumping over the â€Å"taken† chip, â€Å"pass† is not allowed. c. On taking a chip or chips the following policy shall prevail: * â€Å"mayor dalawa† * â€Å"mayor tatlo† * â€Å"mayor dama† * â€Å"mayor dama dalawa† (x) takes 0 VS (x) takes 0 VS (x) takes 0 VS (dama) takes 0 (y) takes 1, takes 2 (y) takes 1, takes 2, and takes 3 (dama) takes 1 VS (x) takes 1, takes 2 over mayor dama. d. A player’s chip is declared as â€Å"dama† if it reaches the other player’s designated â€Å"dama† locations or squares. A dama chip can move or take a piece to any unoccupied square along the diagonal path. Moreover, when a â€Å"dama† takes a chip the score is doubled; when the â€Å"dama† is taken the score is also doubled; when a â€Å"dama† takes another â€Å"dama† the score is quadrupled. e. In taking more than one chip, the â€Å"taker† chip shall remain as the initial addend, minuend, multiplicand, or dividend as the case maybe. (This means that MDAS for multiple operations shall not apply in this case). f. A â€Å"move† is good only for one (1) minute, while the game’s duration shall not exceed 20 minutes. g. The remaining chips shall be added to the respective players. h. The game ends when any one of the following situations occur: ES I–Math Biongcog; MT 1 =Lauron; MT 1 =Tubin; HT 3 =Torbeso; MT 1 = Berna MT 2=Gonzaga; T2=Perez 23 Cebu Province Division = Damath Seminar Workshop 1998 10-13-2008 ______________________________________________________________________________ 1.) a player has no more chip to move 2.) 20-minute game duration had elapsed 3.) repetitive â€Å"moves† of any or both players. i. The player having the greater â€Å"total score† wins the game. In case of a â€Å"tie†, a 10-minute rematch follows thereafter untill a winner is declared. j. No player is allowed to compete in a level lower than the one specified for his grade level. k. In playing, the â€Å"TOUCH-MOVE SYSTEM† is used. Once a player â€Å"touches† a chip, it is imperative that he uses that chip for that particular move. l. A move is considered final once a player releases the chip, and he cannot change his move after he has released the chip. m. The use of calculator is recommended. n. All players in each level are ranked according to their respective number of games won to determine the winners. In case of a â€Å"triple tie†, the â€Å"the point-system† is used. Guidelines for Electrodamaths 1. ElectroDamaths is similar to Damath the whole numbers with certain variations as follows: a.) Odd numbers expressed in KWH b.) Even numbers expressed in Pesos, except ( 0 ) zero. 2. Sample in scoring: Chips + like Units + like Units + unlike Units like Units like Units unlike Units à · like Units à · like Units à · unlike Units Ãâ€" like Units Ãâ€" like Units Ãâ€" unlike Units Plus the remaining chips Move KWH 8 NS NS NS NS NS NS NS NS NS NS NS 18 NS 3 kwh + 5kwh P 2 + P 10 7 kwh + P 4 5 kwh – 9 kwh P6-P0 7 kwh P 4 3 kwh à · 5kwh P6à ·P2 7 kwh à · P 4 3 kwh Ãâ€" 5kwh P 2 Ãâ€" P 10 7 kwh Ãâ€" P 4 7 kwh + 11kwh P4+P8 Score fca in Pesos NS 12 NS NS 6 NS NS NS NS NS NS NS NS 12 26 kwh Ãâ€" P4/kwh = Total Score KWH fca in Pesos 8 12 8 12 8 12 8 18 8 18 8 18 8 18 8 18 8 18 8 18 8 18 26 26 18 30 Total kwh Ãâ€" prevailing rate at the venue TOTAL ELECTRIC CONSUMPTION