{"title":"William Jacob","description":null,"products":[{"product_id":"making-of-the-anglican-church-worldwide-book-william-jacob-9780281050437","title":"The Making of the Anglican Church Worldwide","description":"This study describes the development of the Anglican communion from its origins in the Reformation up to the year 1960. It is concerned primarily with the Church of England as an institution, and with how events and ideas shaped the development of that institution.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49568509264145,"sku":"GOR005472444","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0281050430.jpg?v=1751133211"},{"product_id":"california-frog-jumping-contest-book-catherine-twomey-fosnot-9780325010243","title":"The California Frog-Jumping Contest","description":"\u003cb\u003e\u003ci\u003eThe California Frog-Jumping Contest: Algebra \u003c\/i\u003e\u003c\/b\u003eis one of five units in the \u003ci\u003eContexts for Learning Mathematics' Investigating Fractions, Decimals, and Percents\u003c\/i\u003e (4 - 6) This unit uses the context of the famous short story by Mark Twain - \u003ci\u003eThe Celebrated Jumping Frog of Calaveras County\u003c\/i\u003e - to develop equivalence and its use in solving algebraic problems. The context of a frog jumping along a track is used to foster number line representations in which students solve for an unknown amount, which is usually the length of a frog jump. Equivalent sequences of jumps are represented naturally on a double number line by having them start and end at the same location, with one expression shown on top of the line and the other shown underneath the line. The representation can then be used as a tool for solving the problem. The unit begins with a problem in which students find the length of a bullfrog's jump, knowing the full length of a sequence of his jumps and steps. This context leads to using the number line as a tool for solving problems with unknowns. Next, students must find various approaches for lining up six- or eight-foot benches for two jumping tracks of lengths 28 and 42 feet. Students utilize the equivalence 6 + 6 + 6 + 6 = 8 + 8 + 8 to change one possible solution into a second possible solution and use the number line to represent this equivalence. A similar problem about fences is used to develop a combination chart, which is a useful representation for determining net gain (or loss) after an exchange. The second half of the unit includes more frog-jumping problems as the frogs plan for their Olympic Games. Now students further explore the use of variables to represent more complex situations and solve for unknown amounts. Here, students use the number line to represent jumps in the problems and can separate off equal amounts of unknown lengths to determine the lengths of unknown amounts. As the unit progresses, the questions require that students investigate equivalent lengths of different-sized jumps and work with these equivalences flexibly to solve problems. The complexity of learning to symbolize has been the subject of extensive research. One study, summarized in \u003ci\u003eAdding It Up\u003c\/i\u003e (National Research Council 2001, 264), illustrates typical difficulties students may have. Known as the reversal error, it is illustrated by work on the following problem: At a certain university, there are six times as many students as professors. Using S for the number of students and P for the number of professors, write an equation that gives the relation between the number of students and the number of professors. A majority of students, ranging from first-year algebra students to college freshmen, wrote the equation 6S=P. Apparently they used 6 as an adjective and S as a noun, following the natural language in the problem. However, they needed to multiply the number of professors by 6 to find the number of students. The correct response is 6P=S. Because learning to write algebraic expressions is so difficult, we don't push symbolizing early in this unit. The representation of the number line is used to fix students' attention on the distinction between the lengths of jumps and the number of jumps. Once this is set, students can begin symbolizing in problems like this in a meaningful way. The unit ends with the students constructing more formal algebraic notation as they develop methods to simplify their earlier representations. 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It begins with a comparison of the cost of cat food at two stores: Bob's Best Buys where it is on sale, $15 for 12 cans, and Maria's Pet Emporium where it is on sale, $23 for 20 cans. Several important ideas and representations develop as students explore this problem, among them finding ways to determine the cost of a common numbers of cans for comparison and the use of the ratio table to represent their proportional reasoning about the context. The development of the ratio table is further supported in the next investigation as students work to determine the cost of several different amounts of bird seed sold by weight. As the unit progresses, proportional reasoning is once again the focus as students develop recipes for a variety of containers, using the recipe of Maria's gourmet puppy snack mix. In the second week the double number is introduced for computation as students investigate the readings on a farm truck's gas tank over the course of trips to several neighboring farms to pick up produce. A trip across the Pennsylvania Turnpike is also explored. This unit also includes several minilessons for addition and subtraction of fractions. Strings of related problems are used initially using money and clock models. Double number lines are introduced later in the unit to enable students to develop generalizable, strategies for addition and subtraction. This model supports students to choose a common multiple (or factor) to work with as well as further opportunities to explore equivalent fractions. Note: The context for this unit assumes that your students have had prior experience with fractions and their relationship to division with whole numbers. If this is not the case, you might find it helpful to first use the units \u003ci\u003eField Trips and Fund-Raisers\u003c\/i\u003e. 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The hallmarks of their approach include:     Supporting children as they construct mathematical strategies and big ideas  Creating realistic contexts and mathematical models that develop children’s capacity to mathematize their world","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50281134031121,"sku":"CIN0325028419G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ WELL_READ \/ SBYB","offer_id":50348462276881,"sku":"CIN0325028419A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ WELL_READ \/ INTERNAL","offer_id":50628748968209,"sku":"GOR014017239","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51392443744529,"sku":"CIN0325028419VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0325028419.jpg?v=1750844423"},{"product_id":"view-of-the-agriculture-manufacture-statistics-and-state-of-society-of-germany-a-book-william-jacob-9781241158941","title":"A View of the Agriculture, Manufacture, Statistics and State of Society of Germany, and Parts of Holland and France. Taken During a Journey Through Those Countries in 1819.","description":"Title: A view of the agriculture, manufacture, statistics and state of society of Germany, and parts of Holland and France. Taken during a journey through those countries in 1819.Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom. It is one of the world's largest research libraries holding over 150 million items in all known languages and formats: books, journals, newspapers, sound recordings, patents, maps, stamps, prints and much more. Its collections include around 14 million books, along with substantial additional collections of manuscripts and historical items dating back as far as 300 BC.The HISTORY OF EUROPE collection includes books from the British Library digitised by Microsoft. This collection includes works chronicling the development of Western civilisation to the modern age. Highlights include the development of language, political and educational systems, philosophy, science, and the arts. The selection documents periods of civil war, migration, shifts in power, Muslim expansion into Central Europe, complex feudal loyalties, the aristocracy of new nations, and European expansion into the New World. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++ British Library Jacob, William; 1820. 4 . 792.k.9.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51119276687633,"sku":"NIN9781241158941","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1241158940.jpg?v=1750824188"},{"product_id":"travels-in-the-south-of-spain-in-letter-written-a-d-1809-and-1810-with-plates-book-william-jacob-9781240913800","title":"Travels in the South of Spain, in letter written A.D. 1809 and 1810. With plates.","description":"Title: Travels in the South of Spain, in letter written A.D. 1809 and 1810.  With plates.]Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom. It is one of the world's largest research libraries holding over 150 million items in all known languages and formats: books, journals, newspapers, sound recordings, patents, maps, stamps, prints and much more. Its collections include around 14 million books, along with substantial additional collections of manuscripts and historical items dating back as far as 300 BC.The HISTORY OF TRAVEL collection includes books from the British Library digitised by Microsoft. This collection contains personal narratives, travel guides and documentary accounts by Victorian travelers, male and female. Also included are pamphlets, travel guides, and personal narratives of trips to and around the Americas, the Indies, Europe, Africa and the Middle East. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++ British Library Jacob, William; 1811. xiii. 407. 36 p.; 4 . 454.f.5.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51146294001937,"sku":"NIN9781240913800","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/124091380X.jpg?v=1750753361"},{"product_id":"travels-in-the-south-of-spain-in-letters-written-a-d-1809-and-1810-book-william-jacob-9781021094230","title":"Travels in the South of Spain, in Letters Written A.D. 1809 and 1810","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51168642597137,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51168644956433,"sku":"NIN9781021094230","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1021094234.jpg?v=1740260983"},{"product_id":"historical-inquiry-into-the-production-and-consumption-of-the-precious-metals-v1-book-william-jacob-9780548888940","title":"An Historical Inquiry Into The Production And Consumption Of The Precious Metals V1 (1831)","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51249130438929,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51249132044561,"sku":"NIN9780548888940","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0548888949.jpg?v=1750880015"},{"product_id":"travels-in-the-south-of-spain-in-letters-written-a-d-1809-and-1810-book-william-jacob-9781022683600","title":"Travels in the South of Spain, in Letters Written A.D. 1809 and 1810","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51281077010705,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51281079107857,"sku":"NIN9781022683600","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1022683608.jpg?v=1751367159"},{"product_id":"historical-inquiry-into-the-production-and-consumption-of-the-precious-metals-vo-book-william-jacob-9781358604140","title":"An Historical Inquiry Into the Production and Consumption of the Precious Metals, Volume 2","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51634528551185,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51634528813329,"sku":"NIN9781358604140","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1358604142.jpg?v=1751208571"},{"product_id":"report-on-the-trade-in-foreign-corn-book-william-jacob-9781377347011","title":"Report On the Trade in Foreign Corn","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51636651983121,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51636652114193,"sku":"NIN9781377347011","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/137734701X.jpg?v=1751051062"},{"product_id":"tracts-relating-to-the-corn-trade-and-corn-laws-book-william-jacob-9781358588730","title":"Tracts Relating to the Corn Trade and Corn Laws","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51667324895505,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51667325092113,"sku":"NIN9781358588730","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1358588732.jpg?v=1751304055"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-william-jacob.oembed","provider":"World of Books ","version":"1.0","type":"link"}