Third Grade Develop understanding of fractions as numbers. CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. CCSS.Math.Content.3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. CCSS.Math.Content.3.NF.A.2.a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. CCSS.Math.Content.3.NF.A.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. CCSS.Math.Content.3.NF.A.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. CCSS.Math.Content.3.NF.A.3.b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. CCSS.Math.Content.3.NF.A.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. CCSS.Math.Content.3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 1 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8. Fourth Grade Extend understanding of fraction equivalence and ordering. CCSS.Math.Content.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n à a)/(n à b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. CCSS.Math.Content.4.NF.A.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. Build fractions from unit fractions. CCSS.Math.Content.4.NF.B.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. CCSS.Math.Content.4.NF.B.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CCSS.Math.Content.4.NF.B.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. CCSS.Math.Content.4.NF.B.3.c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. CCSS.Math.Content.4.NF.B.3.d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. CCSS.Math.Content.4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. CCSS.Math.Content.4.NF.B.4.a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 à (1/4), recording the conclusion by the equation 5/4 = 5 à (1/4). CCSS.Math.Content.4.NF.B.4.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 à (2/5) as 6 à (1/5), recognizing this product as 6/5. (In general, n à (a/b) = (n à a)/b.) CCSS.Math.Content.4.NF.B.4.c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? Understand decimal notation for fractions, and compare decimal fractions. CCSS.Math.Content.4.NF.C.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. CCSS.Math.Content.4.NF.C.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. CCSS.Math.Content.4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. 1 Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. 2 Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. Fifth Grade Use equivalent fractions as a strategy to add and subtract fractions. CCSS.Math.Content.5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) CCSS.Math.Content.5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Apply and extend previous understandings of multiplication and division. CCSS.Math.Content.5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? CCSS.Math.Content.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CCSS.Math.Content.5.NF.B.4.a Interpret the product (a/b) à q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a à q ÷ b. For example, use a visual fraction model to show (2/3) à 4 = 8/3, and create a story context for this equation. Do the same with (2/3) à (4/5) = 8/15. (In general, (a/b) à (c/d) = (ac)/(bd). CCSS.Math.Content.5.NF.B.4.b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. CCSS.Math.Content.5.NF.B.5 Interpret multiplication as scaling (resizing), by: CCSS.Math.Content.5.NF.B.5.a Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. CCSS.Math.Content.5.NF.B.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n à a)/(n à b) to the effect of multiplying a/b by 1. CCSS.Math.Content.5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CCSS.Math.Content.5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1 CCSS.Math.Content.5.NF.B.7.a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) à 4 = 1/3. CCSS.Math.Content.5.NF.B.7.b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 à (1/5) = 4. CCSS.Math.Content.5.NF.B.7.c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? 1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
Sample Solution
This page of the exposition has 2111 words. Download the full form above. The United States is home to probably the most famous and productive sequential executioners ever. Names, for example, Ted Bundy, Gary Ridgeway, and the Zodiac Killer have become easily recognized names because of the awful idea of their wrongdoings. One of the most productive sequential executioners in American history is John Wayne Gacy. Nicknamed the Killer Clown due to his calling, Gacy assaulted and killed at any rate 33 adolescent young men and youngsters somewhere in the range of 1972 and 1978, which is one of the most elevated realized casualty tallies. Gacy’s story has become so notable that his violations have been included in mainstream society and TV appears, for example, American Horror Story: Hotel and Criminal Minds. Measurable science has, and keeps on playing, a significant job in the explaining of the case and recognizable proof of the people in question. John Wayne Gacy’s history of sexual and psychological mistreatment was instrumental in arousing agent’s curiosity of him as a suspect. John Wayne Gacy was conceived on March 17, 1942, in Chicago, Illinois. Being the main child out of three youngsters, Gacy had a stressed relationship with his dad, who drank intensely and was frequently injurious towards the whole family (Sullivan and Maiken 48). In 1949, a contractual worker, who was a family companion, would caress Gacy during rides in his truck; notwithstanding, Gacy never uncovered these experiences to his folks because of a paranoid fear of retaliation from his dad (Foreman 54). His dad’s mental maltreatment proceeded into his young grown-up years, and Gacy moved to Las Vegas where he worked quickly in the rescue vehicle administration before turning into a funeral home chaperon (Sullivan and Maiken 50). As a morgue orderly, Gacy was intensely associated with the preserving procedure and conceded that one night, he moved into the final resting place of an expired high school kid and touched the body (Cahill and Ewing 46). Stunned at himself, Gacy comes back to Chicago to live with his family and graduates from Northwestern Business College in 1963, and acknowledges an administration student position with Nunn-Bush Shoe Company. In 1964, Gacy is moved to Springfield and meets his future spouse, Marlynn Myers. In Springfield, Gacy has his subsequent gay experience when a colleague unsteadily performed oral sex on him (London 11:7). Gacy moves to Waterloo, Iowa, and starts a family with Myers. Be that as it may, after normally undermining his better half with whores, Gacy submits his previously known rape in 1967 upon Donald Vorhees. In the coming months, Gacy explicitly mishandles a few different adolescents and is captured and accused of oral homosexuality (Sullivan and Maiken 60). On December 3, 1968, Gacy is indicted and condemned to ten years at the Anamosa State Penitentiary. Gacy turns into a model detainee at Anamosa and is conceded parole in June of 1970, a negligible year and a half after his condemning. He had to move to Chicago and live with his mom and watch a 10:00PM check in time. Not exactly a year later, Gacy is accused again of explicitly attacking an adolescent kid however the young didn’t show up in court, so the charges were dropped. Gacy was known by numerous individuals in his locale to be a devoted volunteer and being dynamic in network legislative issues. His job as “Pogo the Clown” the jokester started in 1975 when Gacy joined a nearby “Chipper Joker” comedian club that consistently performed at gathering pledges occasions. On January 3, 1972, Gacy submits his first homicide of Timothy McCoy, a 16-year old kid venturing out from Michigan to Omaha. Guaranteeing that McCoy went into his room employing a kitchen blade, Gacy gets into a physical squabble with McCoy before wounding him more than once in the chest. In the wake of understanding that McCoy had absentmindedly strolled into the stay with the blade while attempting to get ready breakfast, Gacy covers the body in his creep space. Gacy conceded in the meetings following his capture that executing McCoy gave him a “mind-desensitizing climax”, expressing that this homicide was the point at which he “understood demise was a definitive rush” (Cahill and Ewing 349). Just about 2 years after the fact, Gacy submits his second homicide of a unidentified young person. Gacy choked the kid before stuffing the body in his storage room before covering him (Cahill 349). In 1975, Gacy’s business was developing rapidly and his craving for youngsters developed with it. Gacy frequently tricked youngsters under his work to his home, persuading them to place themselves in cuffs, and assaulting and tormenting them before choking them (Cahill 169-170). The majority of Gacy’s homicides occurred somewhere in the range of 1976 and 1978, the first of this time occurring in April 1976. Huge numbers of the adolescents that were killed during this time were covered in a creep space under Gacy’s home. For the rest of the homicides, Gacy confessed to losing five bodies the I-55 scaffold into the Des Plaines River; in any case, just four of the bodies were ever recuperated (Linedecker 152). In December 1978, Gacy meets Robert Jerome Piest, a 15-year old kid working at a drug store and extends to him an employment opportunity at Gacy’s firm. Piest educates his mom regarding this and neglects to restore that night. The Piest family documents a missing individual’s report and the drug specialist illuminates police that Gacy would in all likelihood be the man that Jerome addressed about an occupation. When addressed by the police, Gacy denied any inclusion in Piest’s vanishing. In any case, the police were not persuaded, and Gacy’s history of sexual maltreatment and battery incited the police to look through his home. Among the things found at Gacy’s home were a 1975 secondary school class ring with the initials J.A.S., numerous driver’s licenses, binds, dress that was unreasonably little for Gacy, and a receipt for the drug store that Piest had worked at. Throughout the following not many days, agents got different calls and tips about Gacy’s rapes and the strange vanishings of Gacy’s representatives. The class ring was in the end followed back to John A. Szyc, one of Gacy’s casualties in 1977. Futhermore, after inspecting Gacy’s vehicle, specialists found a little group of strands looking like human hair, which were sent to the labs for additional examination. That equivalent night, search hounds were utilized to distinguish any hint of Piest in Gacy’s vehicle, and one of the canines demonstrated that Piest had, truth be told, been available in the vehicle. On December 20, 1977, under the pressure of consistent police observation and examination, Gacy admits to more than 30 homicides and advises his legal counselor and companion where the bodies were covered, both in the slither space and the stream. 26 casualties were found in the creep space and 4 in the stream. Gacy is captured, indicted for 33 killings, and condemned to death by deadly infusion. He endeavored a madness supplication yet was denied, and was executed on May 10, 1994. There were a few criminological markers that specialists used to attach Gacy to the killings. A portion of these include fiber examination, dental and radiology records, utilizing the deterioration procedure of the human body, and facial remaking in distinguishing the people in question. Examiners discovered filaments that took after human hair in both Gacy’s vehicle and close to the slither space where the bodies were covered. Notwithstanding these hair tests, examiners additionally discovered strands that contained hints of Gacy’s blood and semen in a similar territory. Blood having a place with the casualties was found on a portion of the filaments, which would later straightforwardly attach Gacy to the wrongdoings. The filaments in Gacy’s vehicle were broke down by scientific researchers and coordinated Piest’s hair tests. Moreover, the hunt hounds that established that Piest had been in Gacy’s vehicle demonstrated this by a “demise response”, which told specialists that Piest’s dead body had been within Gacy’s vehicle. Out of Gacy’s 33 known casualties, just 25 were ever convincingly distinguished.>
This page of the exposition has 2111 words. Download the full form above. The United States is home to probably the most famous and productive sequential executioners ever. Names, for example, Ted Bundy, Gary Ridgeway, and the Zodiac Killer have become easily recognized names because of the awful idea of their wrongdoings. One of the most productive sequential executioners in American history is John Wayne Gacy. Nicknamed the Killer Clown due to his calling, Gacy assaulted and killed at any rate 33 adolescent young men and youngsters somewhere in the range of 1972 and 1978, which is one of the most elevated realized casualty tallies. Gacy’s story has become so notable that his violations have been included in mainstream society and TV appears, for example, American Horror Story: Hotel and Criminal Minds. Measurable science has, and keeps on playing, a significant job in the explaining of the case and recognizable proof of the people in question. John Wayne Gacy’s history of sexual and psychological mistreatment was instrumental in arousing agent’s curiosity of him as a suspect. John Wayne Gacy was conceived on March 17, 1942, in Chicago, Illinois. Being the main child out of three youngsters, Gacy had a stressed relationship with his dad, who drank intensely and was frequently injurious towards the whole family (Sullivan and Maiken 48). In 1949, a contractual worker, who was a family companion, would caress Gacy during rides in his truck; notwithstanding, Gacy never uncovered these experiences to his folks because of a paranoid fear of retaliation from his dad (Foreman 54). His dad’s mental maltreatment proceeded into his young grown-up years, and Gacy moved to Las Vegas where he worked quickly in the rescue vehicle administration before turning into a funeral home chaperon (Sullivan and Maiken 50). As a morgue orderly, Gacy was intensely associated with the preserving procedure and conceded that one night, he moved into the final resting place of an expired high school kid and touched the body (Cahill and Ewing 46). Stunned at himself, Gacy comes back to Chicago to live with his family and graduates from Northwestern Business College in 1963, and acknowledges an administration student position with Nunn-Bush Shoe Company. In 1964, Gacy is moved to Springfield and meets his future spouse, Marlynn Myers. In Springfield, Gacy has his subsequent gay experience when a colleague unsteadily performed oral sex on him (London 11:7). Gacy moves to Waterloo, Iowa, and starts a family with Myers. Be that as it may, after normally undermining his better half with whores, Gacy submits his previously known rape in 1967 upon Donald Vorhees. In the coming months, Gacy explicitly mishandles a few different adolescents and is captured and accused of oral homosexuality (Sullivan and Maiken 60). On December 3, 1968, Gacy is indicted and condemned to ten years at the Anamosa State Penitentiary. Gacy turns into a model detainee at Anamosa and is conceded parole in June of 1970, a negligible year and a half after his condemning. He had to move to Chicago and live with his mom and watch a 10:00PM check in time. Not exactly a year later, Gacy is accused again of explicitly attacking an adolescent kid however the young didn’t show up in court, so the charges were dropped. Gacy was known by numerous individuals in his locale to be a devoted volunteer and being dynamic in network legislative issues. His job as “Pogo the Clown” the jokester started in 1975 when Gacy joined a nearby “Chipper Joker” comedian club that consistently performed at gathering pledges occasions. On January 3, 1972, Gacy submits his first homicide of Timothy McCoy, a 16-year old kid venturing out from Michigan to Omaha. Guaranteeing that McCoy went into his room employing a kitchen blade, Gacy gets into a physical squabble with McCoy before wounding him more than once in the chest. In the wake of understanding that McCoy had absentmindedly strolled into the stay with the blade while attempting to get ready breakfast, Gacy covers the body in his creep space. Gacy conceded in the meetings following his capture that executing McCoy gave him a “mind-desensitizing climax”, expressing that this homicide was the point at which he “understood demise was a definitive rush” (Cahill and Ewing 349). Just about 2 years after the fact, Gacy submits his second homicide of a unidentified young person. Gacy choked the kid before stuffing the body in his storage room before covering him (Cahill 349). In 1975, Gacy’s business was developing rapidly and his craving for youngsters developed with it. Gacy frequently tricked youngsters under his work to his home, persuading them to place themselves in cuffs, and assaulting and tormenting them before choking them (Cahill 169-170). The majority of Gacy’s homicides occurred somewhere in the range of 1976 and 1978, the first of this time occurring in April 1976. Huge numbers of the adolescents that were killed during this time were covered in a creep space under Gacy’s home. For the rest of the homicides, Gacy confessed to losing five bodies the I-55 scaffold into the Des Plaines River; in any case, just four of the bodies were ever recuperated (Linedecker 152). In December 1978, Gacy meets Robert Jerome Piest, a 15-year old kid working at a drug store and extends to him an employment opportunity at Gacy’s firm. Piest educates his mom regarding this and neglects to restore that night. The Piest family documents a missing individual’s report and the drug specialist illuminates police that Gacy would in all likelihood be the man that Jerome addressed about an occupation. When addressed by the police, Gacy denied any inclusion in Piest’s vanishing. In any case, the police were not persuaded, and Gacy’s history of sexual maltreatment and battery incited the police to look through his home. Among the things found at Gacy’s home were a 1975 secondary school class ring with the initials J.A.S., numerous driver’s licenses, binds, dress that was unreasonably little for Gacy, and a receipt for the drug store that Piest had worked at. Throughout the following not many days, agents got different calls and tips about Gacy’s rapes and the strange vanishings of Gacy’s representatives. The class ring was in the end followed back to John A. Szyc, one of Gacy’s casualties in 1977. Futhermore, after inspecting Gacy’s vehicle, specialists found a little group of strands looking like human hair, which were sent to the labs for additional examination. That equivalent night, search hounds were utilized to distinguish any hint of Piest in Gacy’s vehicle, and one of the canines demonstrated that Piest had, truth be told, been available in the vehicle. On December 20, 1977, under the pressure of consistent police observation and examination, Gacy admits to more than 30 homicides and advises his legal counselor and companion where the bodies were covered, both in the slither space and the stream. 26 casualties were found in the creep space and 4 in the stream. Gacy is captured, indicted for 33 killings, and condemned to death by deadly infusion. He endeavored a madness supplication yet was denied, and was executed on May 10, 1994. There were a few criminological markers that specialists used to attach Gacy to the killings. A portion of these include fiber examination, dental and radiology records, utilizing the deterioration procedure of the human body, and facial remaking in distinguishing the people in question. Examiners discovered filaments that took after human hair in both Gacy’s vehicle and close to the slither space where the bodies were covered. Notwithstanding these hair tests, examiners additionally discovered strands that contained hints of Gacy’s blood and semen in a similar territory. Blood having a place with the casualties was found on a portion of the filaments, which would later straightforwardly attach Gacy to the wrongdoings. The filaments in Gacy’s vehicle were broke down by scientific researchers and coordinated Piest’s hair tests. Moreover, the hunt hounds that established that Piest had been in Gacy’s vehicle demonstrated this by a “demise response”, which told specialists that Piest’s dead body had been within Gacy’s vehicle. Out of Gacy’s 33 known casualties, just 25 were ever convincingly distinguished.>
