Dissolution Profile of Paracetamol Generics

Dissolution Profile of Paracetamol Generics 1 Introduction The pharmaceutical industry had an estimated turnover of $773 billion in 2008,1 however not all of this revenue was taken as profit; a significant cost goes into research and industry guideline compliance. With regards to new generic medications, proving bioequivalence is crucial to success, however necessary in vivo testing can be costly.2 Drugs which meet certain Biopharmaceutics Classification System (BCS) criteria may be exempt from these expensive tests and can be permitted a biowaiver.3 This allows in vitro dissolution testing in place of in vivo plasma analysis. Paracetamol is one such drug that has qualities which place it at the borderline of biowaiver suitability.3 It is the worlds most commonly used analgesic4 and the question arises as to whether all preparations are as effective as each other? More specifically we ask, is there is any significant difference between the dissolution profile of paracetamol generics? This literature review is in preparation of experimental t ests designed to ascertain if there is any difference in dissolution profile of eight bioequivalent preparations listed on the Australian Pharmaceutical Benefits Scheme (PBS), and whether this difference may correlate to a clinical significance in such a common place drug. 2 Search Strategy All data was sourced through internet databases, i.e. Medline, Pubmed, and the Cochrane Library. The search engines Google Scholar and UWA library were also utilized. Keywords included. KEY WORDS Paracetamol, acetaminophen, bioequivalent (therapeutic equivalency), Delayed-action Preparations, Pharmaceutical Preparations, Tablets, Drug Compounding, Chemistry, Pharmaceutical, Observer Variation, Dissolution, Metabolism, in vitro, in vivo, IVIVC, Drug Content, Bioavailability and Correlation. Boolean searching was utilised to broaden or narrow search results and once appropriate articles were sourced, citing and cited articles were also evaluated. 3 Paracetamol 3.1 History Paracetamol (acetaminophen) is one of the worlds most popular drugs for the treatment of pain and fever.4 It was first synthesized in 1878 by Morse, and was used clinically for the first time in 1887 by von Merring.4, 5 Paracetamol fell into obscurity shortly thereafter in favour of other chemically related drugs such as phenacetin.5 However, phenacetin was later found to be nephrotoxic, and the search for a substitute arose.5 In 1950, a study from Brodie and Axelrod rediscovered paracetamols suitable analgesic properties.4 Although, this drug did not experience widespread acceptance until the 1970s due to unfounded concerns about safety; but from then on, it became the most commonly used medication for pain.4 In many countries, such as the United Kingdom, paracetamol sales have exceeded those of aspirin since 1980.4 3.2 Physicochemical properties Paracetamol or N-(4-hydroxyphenyl) acetamide, is a white crystalline powder with a melting point of 168-172C (Martindale). It is sparingly soluble in water, ie. one part of paracetamol is soluble in 70 parts of water at room temperature.3 It is also freely soluble in alcohol. (Martindale) Paracetamol shows maximal UV absorption at a wavelength of 249nm and is reported to have a pKa of 9.5 at 25C.3 3.3 Pharmacology Pharmacokinetics 3.3.1 Pharmacodynamics Mechanism of Action The exact mechanism of action of paracetamol has remained largely unknown for some time.6-9 For years it has been thought to inhibit the enzyme cyclooxygenase (COX) in a similar manner to non-steroidal anti-inflammatory drugs, however definitive proof of analgesia and antipyresis being dependent on COX inhibition is still lacking.4 Recently, two independent groups have produced experimental data that has demonstrated that analgesia involves the potentiation of the cannabinoid vanilloid tone in the brain and in the dorsal root ganglia.4 Blockade of cannabinoid (CB1) receptors in rats has eliminated any analgesic properties of paracetamol and suggests that paracetamol is in fact a cannabinomimetic.4 3.3.2 Pharmacokinetics 3.3.2.1 Absorption Bioavailability: Paracetamol has been reported to have a bioavailability of 62%-89% in those of a fasted state,3, 8 this divergence from absolute bioavailability is attributed to first pass hepatic metabolism. Peak plasma concentrations are reached between 0.17-2.0 hours post-dosing.10 As expected, food has been shown to reduce absorption by increasing tmax and decreasing Cmax values. Food has not been shown to affect the amount of acetaminophen reaching the blood.3 3.3.2.2 Distribution: Paracetamol has a reported volume of distribution of 0.69-1.36L/Kg.11 Around 20%-25% of the drug is bound to plasma proteins at therapeutic dosages; however this value has been shown to increase to 20%-50% in over dosage. Paracetamol has also been shown to cross the placenta, and has a 1.24 milk/plasma ratio in breast milk.3 Paracetamol is an ADEC category A drug, i.e. it is safe to use in pregnancy, as well as breastfeeding.9 3.3.2.3 Metabolism Excretion: Around 85%-90% of paracetamol is metabolized within the liver via the process of glucuronidation and sulfation.3 These inactive metabolites are then eliminated by the kidney in the urine. Approximately 5% of paracetamol is passed out unchanged in the urine, the remaining drug is conjugated with cysteine and mercapturic acid.3, 8 The half-life of paracetamol has been reported as 1.9 4.3 hours3, 8, 10 but longer in those with renal impairment. 3.4 Indication Paracetamol is indicated in the symptomatic treatment of mild-to-moderate pain as well as fever3, 9 and has also been described to have mild anti-inflammatory properties.3 3.5 Dose Dosage Forms For adults, the optimal single dose of paracetamol is 1g,3, 9 with a maximum dose of 4g daily.9 Hepatocellular necrosis can occur from doses of 10-15g, and death may result in doses in excess of 20-25g.3 Paracetamol is available in many dosage forms, as a single active pharmaceutical ingredient (API), or in combination with other analgesics such as codeine (Panadeine), dextropropoxyphene (Di-Gesic), metoclopramide (Metomax), as well as in combination with decongestants such as pseudoephedrine in cold-and-flu preparations.9 This drug is available as immediate release (IR) tablets, sustained release (SR) tablets, chewable, elixirs, IV injections and suppositories.9 4 Biopharmaceutics Classification System The Biopharmaceutics Classification System (BCS) is a method of grouping active pharmaceutical ingredients (API) based on their solubility and intestinal permeability.12-16 The system allows for easy identification of those drugs whose in vivo absorption can be easily anticipated based on their in vitro dissolution.12, 15, 16 This implies that two different products containing the same drug will have the same rate and extent of absorption if, over time, they both have the same concentration profile at the intestinal membrane.12 Since it is the dissolution profile of a drug which determines its concentration profile in the intestinal lumen, comparability of this parameter in vitro should produce comparable absorption results in vivo.12 In reality however, only those drugs with high permeability which are formulated into IR preparations can be easily and reliably applied to this logic.12, 15, 16 4.1 BCS Drug Classes There are four classes within the BCS to which a drug can be assigned (as outlined in figure 1). Class I is comprised of those drugs with high permeability and solubility, these drugs are expected to be well absorbed and, providing dissolution is slower than gastric emptying, show a good correlation between in vitro dissolution rate and the rate and extent of in vivo absorption (IVIVC).12, 15, 16 Class II drugs also have high permeability but their solubility is low which ensures in vivo dissolution is the rate limiting step in drug absorption and thus IVIVC is expected.12 Class III drugs have a low permeability with high solubility, traditionally these drugs were believed to have little or no IVIVC,12 however recent studies have shown that if a class III drug is very rapidly dissolving then a correlation may exist.18, 19 Finally Class IV drugs have both low permeability and solubility these drugs are not expected to show any IVIVC.12 For each of the four BCS classes a drug substance is considered highly soluble when the highest [IR] dose strength is soluble in 250mL or less of aqueous media over the pH range of 1-7.5.16 The permeability of a drug is considered high if greater than 90% of a dose is absorbed across the intestinal membrane.16, 20 Using these definitions, paracetamol is classified as a BCS class III drug but it is also described as borderline class I because it is only just on the cusp of low permeability.3 4.2 Utility of the BCS The genius of the BCS is that it allows easy identification of drug candidates for which relatively cheap and fast in vitro dissolution testing can replace the more expensive, time consuming and invasive in vivo absorption testing.2 The system does away with complex bioavailability modeling that must account for fasted and fed states as well as cyclical changes in motility and gastric emptying.12, 14 The impact of the BCS on the pharmaceutical industry was so great that in 2006, creator Dr. Gordon Amidon was awarded the International Pharmaceutical Federation (FIP) Distinguished Scientist Award.21 5 Correlation between in vitro dissolution and bioavailability Following the introduction of the BCS a great deal of research was conducted exploring the power of IVIVC. It became a main focus not just of the pharmaceutical industry but also of academia and regulatory authorities.2 IVIVC became popular because it can be used as a substitute for resource intensive bioavailability testing; the concept has essentially improved the speed and cost of drug development as well as quality control in pharmaceutical manufacturing.2 5.1 Bioavailability and Bioequivalence Bioavailability is an important concept because it determines the efficacy, safety and reproducibility of the therapeutic effect of drugs and the many formulations in which they come.22 For the purpose of drugs that produce a systemic therapeutic effect, the Australian Therapeutic Goods Administration (TGA)22 defines bioavailability as the extent and the rate at which a substance or its active moiety is delivered from a pharmaceutical form and becomes available in the general circulation. Bioavailability is therefore inherently linked to drug absorption and may also be predicted using IVIVC as defined by the BCS. If two pharmaceutically equivalent (same active ingredient and content in the same formulation) products have the same bioavailability they are considered bioequivalent and will essentially have the same efficacy and safety. Bioequivalence is important because it is the basis for which innovator medicines can be substituted with generics. 5.2 Strength of in vitro in vivo correlations The BCS is a predictive tool for determining which drugs will have an IVIVC. Table 1 demonstrates that under the BCS only class II along with some class I drugs are expected to have IVIVCs.12 Research subsequent to Dr. Amidons first BCS publication has generally upheld his initial findings however exceptions to the rule have been found. 5.2.1 Drugs with IVIVC The BCS suggests that if the bioavailability of a drug is dissolution rate limited then a good IVIVC should be possible. This notion has been demonstrated for flutamide a very poorly soluble high dose compound which is not expected to have IVIVC but has dissolution rate limited absorption.23 A paper published by Posti, Katila Kostiainen23 concluded that there is a strong IVIVC for flutamide and this was identified on four separate occasions where bioavailability was studied. All four studies were of single dose, cross over design and each subsequent study increased the number of subjects tested (study I: n = 6, Study IV: n = 24). The strength of the papers methodology provides good support for its conclusions however this was undermined by a lack of documented statistical analysis. Much more compelling evidence comes from a study by Sakuma et. al.24 which was able to show an IVIVC for two BCS class I drugs after they received an enteric coating, thus eliminating the possibility that gastric emptying was the rate limiting step. The results were statistically significant, however the tablets were tested in rat models rather than human subjects and the dissolution test may not have adequately reflected the in vivo environment that enteric coated tablets are subject to.24 Further studies in human subjects demonstrating the difference in IVIVC between enteric and non-enteric coated tablets could not be identified in the literature. There are hundreds of other drugs which have an IVIVC and these are neither limited to BCS class II drugs or drugs with dissolution rate limited absorption. Theophylline is a BCS class IV drug and yet in a complete cross over study of four different theophylline tablets the in vitro dissolution was able to significantly predict several in vivo pharmacokinetic parameters (AUC Cmax) which dictate bioavailability.25 The study was small (n = 6) and not all pharmacokinetic parameters could be correlated. Other common drug examples with IVIVC include digoxin,26 rifampicin,27 diclofenac28 and lamotrigine29 and these are by no means exhaustive. 5.2.2 Drugs without IVIVC Not all drugs have an IVIVC and this can also include some BCS class II drugs. A research paper by Frick, Moller Wirbitzki 199830 demonstrated that the in vitro dissolution of glimepiride (BCS class II) is not comparable to dissolution in vivo. The study employed a single dose cross-over design with 12 subjects, Latin-Square statistical analysis was employed and the results were assumed to be significant however not all the data was accompanied by supporting confidence values. No correlation was possible because the solubility of glimepiride is low and strongly pH dependent.30 Unlike glimepiride, ciprofloxacin a quinolone antibiotic, is classified as a BCS class III drug and as a consequence would not be predicted to have an IVIVC. Correspondingly, when tested for this possibility none could be found between dissolution and any of the parameters for bioavailability (Tmax, Cmax, AUC Ka).31 5.2.3 Strength of BCS in predicting IVIVC There is a wide variance between IVIVCs that are anticipated according to the BCS and those that are actually demonstrated after experimental testing. Examples have been provided where both expected and unexpected correlations occur and this suggests that the BCS system while helpful should only be taken as a guide. Laboratory testing is still the only reliable method for determining if a correlation is occurs. Paracetamol is a BCS class III medication and as such is not expected to demonstrate strong IVIVC. Given the fact that paracetamol has a wide therapeutic index and the BCS can only be used as a guide, a safe and useable IVIVC may still exist. 5.2.4 IVIVC of paracetamol The prodigious use, vast quantities manufactured and the presence of many generic products in the marketplace makes paracetamol a prime candidate for IVIVC testing. In 1996 Retaco et. al.32 conducted a small crossover study using five subjects to assess whether an IVIVC for paracetamol may exist. The study stated that the absorption data from saliva partially correlated with those found in vitro,32 this however is not a valid conclusion. One of the subjects studied produced in vivo data that opposed a correlation and this anomaly was further confounded by the fact that statistical analysis was not performed on the IVIVC but rather covered the in vitro and in vivo data separately. This pilot study was later contradicted by Babalola et. al.33 who found limited IVIVCs and suggested that paracetamol absorption may not be limited by its dissolution rate. Similarly, a thorough, well designed, complete crossover (44) study that balanced for first order residual effects, suggested that it wa s dangerous to use dissolution as the sole test for paracetamol bioequivalence.34 Interestingly, all of these studies demonstrated bioequivalence between the various products of paracetamol even if they showed no IVIVC. 6 Biowaiver for bioequivalence testing In vivo bioequivalence studies are required to ascertain the potential differences in bioavailability between innovator and generic products which, may lead to therapeutic inequivalence. A biowaiver provides the authority and grounds for fiscally intensive bioequivalence testing to be replaced by more tolerable in vitro testing. For the most part, IVIVC must first be established in order for a drug to be considered for a biowaiver. The BCS has outlined properties of solid preparations which require evaluation in biowaivers, i.e. solubility, permeability, and dissolution rate.35 In addition to this, the non-critical therapeutic range of a drug should also be considered35 and this is the basis for which paracetamol has gained biowaiver status.3 It should be noted that products produced by the same manufacturer at the same site are exempt from bioequivalence studies.36 6.1 Paracetamol Biowaiver Several characteristics must be considered when a drug presents as a candidate for a biowaiver through dissolution testing. Paracetamol is not a classic biowaiver candidate because it is classified as a BCS Class III drug, it does however possess properties borderline to Class I3 and these enable it to fulfill the requirements of a biowaiver. 6.2 Biowaiver requirements 6.2.1 Characteristics relevant to the active ingredient 6.2.1.1 Risk of therapeutic failure or adverse drug reactions i.e. the need for critical plasma concentrations. When considering a biowaiver for a drug substance, its therapeutic use and therapeutic index also needs to be taken into account.16 In the case of paracetamol, the therapeutic indications are not critical, and there is a wide difference between the usual therapeutic dose and toxic doses. Given that an optimal therapeutic dose for an adult is 1g, and that hepatocellular necrosis can result from ingestion of 10-15g, it can be assumed that paracetamol is not a narrow therapeutic index drug.3 6.2.1.2 Risk of bioinequivalence: Previous evidence of bioavailability problems for an active substance can complicate the justification of in vitro dissolution bioequivalence correlation.35 For paracetamol, the absolute bioavailability has not been shown to vary between therapeutic dose ranges of 5-20mg/kg.3 Other studies have also demonstrated that bioequivalence in different IR paracetamol preparations is achievable.11, 32, 37 6.2.1.3 Solubility: If a drug is highly water soluble it generally lends to exemption of bioequivalence testing, however polymorphism and particle size are major determinants of dissolution and must be considered.35 A drug is considered highly soluble if the amount contained in a preparation of maximal strength dissolves in 250mL of three buffered solutions ranging between a pH of 1-8 at 37C.35 Paracetamol has a pKa of 9.5 and is therefore not substantially ionized at a pH less than 9. As a result, it can be said that its solubility does not vary with pH.3 The highest strength IR preparation of paracetamol is 500mg. Experimentally, this has been shown to dissolve in 21mL,3 which is significantly less than the 250mL that is required by the BCS guidance to prove solubility.16, 35 6.2.1.4 Pharmacokinetic properties: High permeability which is typically indicated by a linear absorption pattern, reduces the potential influence of an IR preparation on bioavailability.35 For paracetamol, the permeability is slightly below the cut-off value of 90%, i.e. one study by Stewart et al.38 found permeability to be 80% once absorbed. This formally excludes paracetamol from being considered for a biowaiver, although extensions to BCS Class III drugs have recently been given more attention.20, 39 6.2.2 Characteristics relevant to the medicinal product 6.2.2.1 Rapid dissolution: Dissolution profiles can be regarded as equal when more than 85% of the active ingredient is dissolved within 15 minutes.35 This comparison must occur between test and reference product in three buffers which with a pH range between 1-8, at 37C.35 Paracetamol tablets have been shown to dissolve within 30 minutes,32 however this rate does not satisfy BCS exemption standards. 6.2.2.2 Excipients: Those included are to be well established and not in atypically large quantities. Kalantzi et al.3 details a table of acceptable excipients which can be used within paracetamol IR tablet formulations which are considered for in vitro dissolution biowaiver. 6.2.2.3 Manufacture: Critical parameters such as particle size and polymorphism should be addressed and documentation should be provided in the dossier that is submitted to TGA.35 Paracetamol has three metastable forms, the only commercially available from is the monoclinic acetaminophen as it is the most thermodynamically stable polymorph.3 From review of the literature, it can be concluded that in vivo bioequivalence testing of solid, oral IR paracetamol dosage forms may not be necessary. This can be justified given that a paracetamol formulation can be shown to:3 Rapidly dissolve under USP guidelines Contain only the acceptable excipients, in usual quantities Demonstrates dissolution profile similar to reference product under conditions stated in USP guidelines 7 Statement of Purpose 7.1 Aim hypothesis The purpose of the proposed study is to compare the dissolution profiles of bioequivalent IR paracetamol preparations listed on the PBS. In particular, comparisons between every preparation will be made, rather than a single comparison against a referent. We hypothesize that there will be no significant difference between the dissolution profile of IR paracetamol tablets when dissolved according to USP specifications. 7.2 Methodology We propose to analyse the dissolution profiles of eight PBS listed bioequivalent paracetamol preparations, namely; APO-paracetamol, Chemmart Paracetamol, Dymadon P, Febridol, Panamax, Paracetamol Sandoz, Paralgin, and Terry White Chemists Paracetamol. Sixteen tablets of each preparation will be dissolved in compliance with USP dissolution test for tablets and capsules, using apparatus II. As mandated, tablets are to be dissolved in 900mL phosphate buffer at a pH of 5.8 with a paddle set to 50rpm. Samples will be taken at intervals of 2,5,10,15,30,45,60 minutes in concordance with practice by Dominguez et al.34 these aliquots will be examined for paracetamol by UV spectrophotometry at 289nm. These data will be statistically analysed by ANOVA. 7.3 Timeline Date Tasks to be performed Work Deadlines Week 11 (15.03 21.03) Create paracetamol standard curves, Test expected dissolution time, Order materials, Source test tablets, Visit school of statistics for advice. Literature Review Due Monday 15th March 12pm Week 12 (22.03 28.03) Testing of tablets 1 2: Dissolution UV vis Week 13 (29.03 04.04) Testing of tablets 3 4: Dissolution UV vis Week 14 (05.04 11.04) Testing of tablets 5 6: Dissolution UV vis Week 15 (12.04 18.04) Testing of tablets 7 8: Dissolution UV vis Week 16 (19.04 25.04) Week in lieu to finish experiments in case of unforeseen circumstances Week 17 (26.04 02.05) Data collation statistical analysis Briefing on the writing of the final report Wed 28.04 2pm Week 18 (03.05 09.05) Writing draft report Week 19 (10.05-16.05) Editing final draft report Week 20 (17.05 23.05) Powerpoint presentation format 1st Draft Research Project Due Friday 21st May Week 21 (24.05 30.05) Correcting draft report Week 22 (31.05 06.06) Amending powerpoint presentation Final report due Mon 31.05 12pm Week 23 (07.06 13.06) Amending final report Week 24 (14.06 20.06) Presentation rehearsal Seminars, submission of amended report to pharmacy office

Phiestria: The Unseen Killer :: essays research papers

Phiesteria: The Unseen Killer An incredibly scary new type of algae is on the loose on the eastern seaboard of the United States and worst of all not many people know about it. Phiesteria piscicida- Latin for â€Å"fish killer† has been living in the mud of rivers for millions of years, but until recently something has jolted its metabolism into overdrive and has caused it to become a fearsome predator. This newly discovered type of dinoflagellate or marine protozoa, which generally has two flagella and cellulose covering, has been living off simple nutrients in the river waters of primarily North Carolina, until now that is. Near the Neuse River in NC, there is a slaughterhouse for pigs and chickens; all of the waste from the pigs is stored in massive lagoons where it is later sprayed onto crops as fertilizer. Unfortunately, a lot of this raw sewage ends up in streams that flow into the Neuse, which in turn enters the Pamlico Sound, a 2,000-mile long estuary in NC. This ultimately brings an immense amount of nutrients to the water thus causing the Phiesteria to shape-shift and enter a state of lethal attack on everything from fish to human. The Center for Disease Control has yet to do anything about this at all, which may be the scariest fact so far. I learned about this ecological disaster while reading my newest edition (October 2001) of Maxim. As I was flipping through my new magazine I saw a horrifying picture of a fish; it looked as though something took a bite out of its neck. Interested, I continued to read, â€Å"The Coming Plague† by Jeff Wise. Basically, Maxim exposes the entire path of this deadly modern-day epidemic starting in 1987, when a veterinary graduate student at North Carolina State University, named Stephen Smith, originally found Phiesteria. Further into the article it tells about Phiesteria moving north into parts of Maryland and even going south as far as 1,000-miles to the coast of Florida and how not enough action is being done to stop this deadly organism. The entire article is broken down into segmented stories of individual peoples fight with Phiesteria. I felt this article gave a great amount of information and helped to explain all of Phiesteria’s facts. One of the most amazing things I learned while reading this article is that the organism can infect humans even if they don’t come in direct contact with them, in fact, all we have to do is breath the air that is within a close proximity to where the organism is living.

Unitizing

Unitizing is very important in learning of mathematics. It is a mental operation that helps to understand and solve complex mathematical problems by separating classifying the values involved into units. Unitizing is grouping of a known number used in representing quantities. It is useful in understanding the value as well as developing counting strategies (Wright, Leeson & Geake, 2002). In addition, unitizing is very useful in understanding and developing the meaning of division as well as multiplication of both natural numbers and fractions. Unitizing is used in quite many settings in mathematical objects. These settings include geometry, algebra, measurements, number and operations and in data analysis and probability. In geometry, unitizing is very important in visualizing changes, in addition or multiplication and in developing the ability to reason, predict and represent knowledge appropriately. Unitizing is also very useful in algebra, where it is applied in both structural and procedural algebra. Procedural algebra is how to solve a problem where numerical values to solve algebraic equations are assigned, for instance; Find x if y=7 in 3Ãâ€"2-4y=20 Here, 3Ãâ€"2-4(7) =20 3Ãâ€"2 –28 = 20 3Ãâ€"2 = 48 x2 = 48/3 = 16 x = 4 Unitizing here can be applied in for instance giving the value of x, which can be given as 2Ãâ€"2 or 2+2. In this case ‘2’ is unitizing. Structural algebra involves use of letters to manipulate algebraic expressions. In number and operations, unitizing facilitates the understanding numbers and representing them. It is also useful in understanding fractions, for instance 1/2 can be written as 1?2 or 1x ? Unitizing is very useful in understanding multiplication and division of natural numbers as well as fractions. For instance, 2 x 4=8, can better be understood through learning many ways of approaching the problem. It can also be written as 2 x (2) (2) = (2) (4) Or as 2 x (2) (2) = (2) (2) (2). Unitizing 2 simplifies the understanding of the problem. More complex values can also be used such as: 4 x 16=64 this can be better understood by unitizing 4 such that the problem is represented as: 4x (4) (4) = (4) (4) (4) Developing understanding of division is also very much facilitated by the knowledge of unitizing. For instance, in determining the number of 8’s that are in 400, division should be performed as follows; 400/8 = 50, here 8 is unitizing To get to understand this better, simpler figures than 400 should be used but still the value of the numbers should be restored. This can only be acquired through unitizing and it can be as follows, 800/2 ? 8 2 can be unitizing such that 240/2 ?(2) (2) (2) and this simplifies the problem. Section 2 Unitizing is very important since it simplifies mathematical operations and facilitates understanding of the operations. It is important since it helps in development of deep and relevant reasoning especially when the unitizing value is being determined. Unitizing is so important since it facilitates the understanding of mathematical objects such as number and operations, especially in fractions, ratios and proportions. Unitizing helps in performing mathematical operations task with a lot of flexibility and confidence. Students should always be encouraged to practice unitizing in all their mathematical activities. Failure for the students to unitize leads to operating with too complex values and hence difficulties arise in trying to solve the problems. Operating with large numbers like for example multiplying 125 and 216 is quite hectic but if unitizing is applied, the operation becomes very easy and speed in generating the answer is increased. Section 3 Students frequently use unitizing especially in addition problems using the procedure of whole number, for instance, 8 + 14 = 22 Can also be approached through unitizing such that: 8 + (7+ 7) = 22 nitizing by using 7 can be practiced by the students. Students are also using unitizing in understanding part-whole concepts. For instance, students have used unitizing to be able to arrive at answers concerning fractions like, ? + ?. This can written as ? + ? . ? whereby unitizing is done by ? However, unitizing may not be done on some operations for instance those that originate from mathematical objects like measurement (Anghileri, & Julia 2001). This is a key concept in maths especially for the appreciation of invariance of length and angle measure. Students should not unitize in measuring angles since the size of the angle does not change. Similarly, the length measure does not change unless the size of what is being measured changes students also are unable to use unitizing in probability and data analysis especially when the problems are on formulation of questions that can be addressed with data and collect, organize and display relevant data to answer them. Section 4 Students should be posed with a lot of contexts and opportunities as well as representations that will facilitate their unitizing. Many geometrical as well as algebraic problems should be provided to the students and they should be framed in such a way that unitizing is encouraged. Problems that require comparisons and representations by variables as well as these that require practice of conceptual understanding such as addition and multiplication of fractions should be given to the students. This improves the students ability for unitizing, something that facilitates their solving strategies. Representations should be encouraged among students since it is through this that they will be able to organize, record and also communicate mathematical ideas. Conclusion Unitizing is a very important mental function that is highly applicable in mathematics. It improves efficiency in solving mathematical problems. It helps students to develop a deeper meaning and understanding of mathematical operations such as multiplication, addition and division. It also enables students to develop diverse and applicable counting strategies as well as conceptual understanding. Therefore. Unitizing should highly be encouraged among the students for better performance in their solving of problems.

The Effect of Law Changes on the Growth of Divorce Rate Essay

The Effect of Law Changes on the Growth of Divorce Rate Divorce is the legal termination of a marriage. There is no doubt that divorce is much more common, becoming a norm almost. If present trends continue, it is estimated that 1 in 3 marriages will end in divorce, but is it the alteration in the legal grounds that is causing this trend? In this essay I will look at the other aspects that could be the foundation for the growth of divorce and state which I think is the most important factor. Prior to 1857, divorce could only be obtained by a private Act of Parliament. The grounds for divorce were based on matrimonial offences such as adultery, cruelty and desertion. There was a social class†¦show more content†¦It also altered the basis that financial settlements were determined by the court. The Family Law Act of 1999 ended the reliance upon showing that one of both partners were at fault, they just had to assert the marriage had broken down and undergo a period of reflection, of nine months, to â€Å"cool off† and consider whether reconciliation was possible. Counselling was encouraged and the courts accounted for children that were involved instead of automatically assuming that the children should live with the mother. This was an attempt to stem the rising number of divorces. There could be many factors that will explain the rise of divorce, one being the change of social attitudes. There is now a considerably less social stigma and blame attached to divorce; it is becoming more socially acceptable. This reduction in stigma could be a result of secularisation, the decreasing influence of religion in contemporary society. Less than 50% of marriages now involve a religious ceremony, and even those that do might not be based on a religious institution for religious reasons. The idea of a lifelong marriage blessed by God is clearly less significant now than previously. Attitudes towards the effect of divorce on children may have shifted. It had been considered in the past that couples should remain together forShow MoreRelatedDivorce Rate And Divorce Rates1224 Words   |  5 PagesDivorce rate also known as divorce demography, which is the study of demographic factors that impact divorced as a social phenomenon, the divorce demography can clearly evaluate and reflect the marriage stability and happiness index of certain countries or area and that is the reason why data statistics of divorce rate is important. According to ONS (Office of National Statistics), the divorce rate has not been that low since 1974, when it was 0.9%. 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There is many factors as to why two people divorce and its effects on the adults and children in the family. In my opinion the top three effects of divorce are former lovers losing feelings, economic troubl es, andRead MoreEssay about The Modern Canadian Family1690 Words   |  7 Pagestradition family. This essay will discuss the different types of newly developed families, and some factors contributing to this change. Same-sex couples are increasing among families. In 2001, the definition of census family was changed to incorporate same-sex couples whom live in a common-law relationship. If previous statistics before 2006 did not include same-sex common-law relationships, how accurate could the statistics have been? Herizons (2008) stated that the 2006 Canadian census was the firstRead MoreChina s One Child Policy1631 Words   |  7 Pagesreceived praise on reducing the population, but also received criticism over the late 20th century. In 1979, couples were forced to pledge not to give second birth or bear any more children (Feng, 2014). From 1979 to 2015, while the population growth rate has reduced substantially, this implementation has been tremendously restructured how Chinese families value family structure, child preferences, marriage, parenting, living arrangements, and eldercare. This one child policy has transformed intoRead MoreGambling in The Bahamas: Should it Be Legalized? 1821 Word s   |  7 Pagesregularization and taxation of web shop gaming. As noted in the results, the mass of the Bahamian people voted no against the referendum. Today, the gambling issue has reawakened and Bahamians are now in a fight against the laws of their country. Several Bahamians believe that the law discriminates against Bahamians because it prohibits Bahamians from owning and legally gambling in casinos within in their homeland. Although any form of gambling is illegal in the Bahamas, there are abundant web housesRead MoreWhy Is the Divorce Rate so Low in Japan?2056 Words   |  9 Pageshaving a low divorce rate compared to other countries. Indeed, between 1945 and 1990, the divorce rate of Japan has never been higher than 1.5 per 1000 population. Since the 1990s, the divorce rate of Japan increased, reaching 2.08 in 2005. even if we can consider this a low divorce rate in comparison with the U.S, compared with other industrialized country, it is an average rate. Then, why is J apans divorce rate considered so low? We will see first why I do not consider Japans divorce rate low, thenRead More A History Of Marriage And Divorce: Cohabitacion Can Result in a Positive Outcome1342 Words   |  6 Pagespast fourteen billion years, the world has evolved numerous times. From creatures’ extinctions to the rise of technology, the world is constantly on a path of changes. And, even though not all events have been pleasant experiences, humans have definitely had the chance to learn from those happenings: one example being, marriage and its effects on family development. Since the beginning of time, open relationships between people, one reason being for the purpose of reproduction, have existed. It isRead MoreThe Impact of China’s One Child Policy1274 Words   |  6 Pagesand to have them at a later age in life (Nadia 295). He believed that once people’s education increased so would the practice of birth control. This would help lower fertility rate and could bring some people out of poverty. After Mao Tse Dong’s death, the government took a more active stance on reducing population growth, so the One Child Policy was created and enforced. The One Child Policy became an issue in the late 1970s and early 1980s, but is still a debatable topic today. Deng Xiaoping wasRead MoreMarriage As A Social Institution2025 Words   |  9 Pagestowards the conception of marriage becoming deinstitutionalized in the west and examine the future direction of marriage as a social institution. This essay will also illustrate major empirical trends including cohabitation, same-sex marriage, and divorce as the process to the deinstitutionalization of marriage. Over the past few decades, there has been a phenomenon social shift in the practices of marriage as a social institution in the west. The term marriage notably changed from the notion of formal