English Language Arts, Expository Writing Unit



English Language Arts, Building Content Literacy in Mathematics and Science, Lesson 2, FactorStandards Met: This lesson is part of the English Language Arts, Building Content Literacy in Mathematics and Science Unit Plan and meets the standards adumbrated therein. Big Ideas: multiple meanings—and uses—of words; basic principles of mathematics; words—vocabulary—and mathematics. This lesson aims to use guided inquiry to assist students in developing advanced literacy in the math and science content areas. In particular, this lesson aims to assist students to learn some of the most used words in mathematics by contrasting their domain-specific uses in that subject with their other uses. This lesson activates prior knowledge of the use of factor as a noun, as in definition III below, to describe numbers in the operations of division and multiplication. Students will be able to use context to determine the meaning of the word factor, as below, in three uses.Classroom Aim/Essential Questions: What does the word factor mean? How many different uses are there for this word? Which one is used in math classes?Do Now: Cultural Literacy: Axiom Class Work: 1. Guided inquiry into the meaning of the word factor in a number of contexts, both as a verb and a noun, with an emphasis on discovering the meaning to number III below, factor as a noun and as it applies to mathematics. 2. Reading comprehension exercise in which students, with the assistance of the teacher, work to understand a reading on factorials and their mathematical purpose.Homework: None.Methods and Materials: This lesson endeavors to help students develop the vocabulary to understand the work they are asked to do in math class. Specifically, this lesson seeks to assist students in securing a close familiarity with the word factor and the concepts it represents. The lesson begins with a short explanation (the Do Now) of the word Axiom drawn from The New Dictionary of Cultural Literacy. Students will then work through, using a teacher-made context clues worksheet, three definitions of the word factor, two as nouns, and one as a verb. (The order of these definitions is below, in American Typewriter Font.) Each of the first two definitions will have five contextual sentences to aid students in inferring these words’ meaning. The final, nominal, definition, most directly related to mathematics, uses ten contextual sentences to make sure students understand this word in a mathematics context.Need for Lesson: ELA MTH-SCNC LTRCY*lp2; ELA MTH-SCNC LTRCY*lp2sup; ELA MTH-SCNC LTRCY*lp2ws1; ELA MTH-SCNC LTRCY*lp2ws2Key Points:Essential Questions: What are some things we know for certain every time we encounter them in our studies?Next Lesson: Lesson 3: Simplify and SimplifyingNameDateBuilding Literacy in the Sciences and Mathematics, Lesson 2, Do Now: Cultural Literacy Worksheet “Axiom.” Cultural literacy is familiarity with and ability to understand the idioms, allusions, and informal content that create and constitute a culture. Here is a short reading from The New Dictionary of Cultural Literacy (Hirsch, E.D., Joseph F. Kett, and James Trefil, New York: Houghton Mifflin, 2002). Please answer the accompanying questions.Axiom (ak-see-uhm): In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious. The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.What is an axiom? In what field, and how, is an axiom accepted? Why?To what is the term axiomatic used to refer?Please compose a sentence using the adjective axiomatic.NameDateEnglish Language Arts, Building Content Literacy in Mathematics and Science Lesson 2 Worksheet 2: Factor and Factors. A very common word in mathematics is factor. This is another versatile word with many uses. To get a sense of how to use this word in mathematics, we’ll explore three of its meanings. The first meaning is factor as a noun. Use the context of the sentences below to work towards understanding of factor as a noun.**** knew that chocolate chips are a key factor in the production of good chocolate chip cookies.**** understands that having a big vocabulary is a factor in becoming a successful rapper.Trains and buses that run on time are a key factor in arriving to school on time.A good crust is a factor in whether or not pizza tastes good.**** knows that good behavior that supports learning is a factor in being asked out to lunch with **** teacher.Using the context for clues, factor as a noun meansThe second meaning of factor is as a verb. Pay particular attention to how this use is related, however marginally, to the other two uses of factor as nouns.When ***** factored in the cost of Ghirardelli chocolate chips (which *** thinks are best) to the bill to make a batch of chocolate chip cookies was just within **** budget.As *** was preparing to start *** career as a rapper, *** factored in the cost of a good rhyming dictionary to *** clothes and tattoo budget.When **** got a text from the MTA telling *** that the 5 train was running late, *** had to factor that into *** departure time for school.Because **** wanted to make the best pizza in New York City, and *** knew *** already had a good crust recipe, *** had to factor in the high cost of the best mozzarella cheese.Mr. Feltskog, because **** had brought a hoard of zombies into room 506, had to factor that event into in his considerations of whether or not to invite **** out to lunch with the rest of the class.Using the context for clues, factor as a verb meansFor the third meaning of factor, we return to considering it as a noun. Pay particular attention to how this definition of factor is related to the definition you arrived at in the first section of this worksheet, where you first encountered factor as a noun. Nota bene, please, that this is the way you will use this word in your math classes.**** knows that five squared (which means 5 x 5) is 25, and that when *** adds another factor of 5, *** gets 5 x 5 x 5 which is 125.When you divide 5 by a factor of 5, you get, *** wasn’t particularly surprised to learn, 1.The number 10 has four factors: 1, 2, 5, and 10.**** realized that because 1,120 is an even number, at least one of its factors had to be 2.Because **** recognized that 2,503 is a prime number, *** easily solved a division problem with this number, because *** knew this number’s only factors were 1 and 2,503.*** argued that 144 is one of those numbers that has a huge number of factors, which are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.Can you think of another number that has as many factors as 144?When you multiply the factor 13 by the factor 7, the product is 91.When you use the factor 13 to divide the number 91, the quotient is 7.One way to find the lowest common denominator of a fraction is to find the prime factors of the denominator.Using the context for clues, factor as a noun meansEnglish Language Arts, Science and Math Literacy, Lesson 2 Support: FactorI. Factor (noun): (1): one that actively contributes to the production of a result: INGREDIENTII. Factor (noun): 4 a : any of the numbers or symbols in mathematics that when multiplied together form a product; also: a number or symbol that divides another number or symbolb : a quantity by which a given quantity is multiplied or divided in order to indicate a difference in measurementIII. Factor (verb): 2 a : to include or admit as a factor - used with in or into <~ inflation into our calculations>b : to exclude as a factor - used with outNameDateFactorials! Please use the information from this reading to answer the questions on the reading comprehension worksheet that accompanies it.The symbol ! in mathematics is as much fun as it looks. It is a factorial. If you write n!it is pronounced “n factorial.” The factorial of a number is the product of all the whole numbers that are less than or equal to the number itself. For example the factorial of 6 looks like this:6!=6 x 5 x 4 x 3 x 2 x 1 = 720And 12 factorial looks like this:12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600Factorials are very important in number theory, probability, and computer science. In everyday life, they can be used to find out the number of ways a distinct group of objects can be arranged in a sequence. For example, imagine you want to figure out how many ways you could arrange six books on a shelf. For the first slot, you would have six books to choose from. For the second slot you would have five books to choose from. For the third slot, you would have four books to choose from. For the fourth slot, three books. For the fifth slot, two books. And for the last slot, one book. To calculate the number of ways you could arrange the books, you would multiply:6 x 5 x 4 x 3 x 2 x 1 = 720Intriguingly, zero factorial is equal to 1.0! = 1Why? Imagine for a moment trying to arrange zero objects on a shelf. How many different ways are there to do it? The answer is one.Additional Facts: Mathematician Christian Kemp introduced the notation n! in 1808.Factorials can also be used to find extremely large prime numbers.There are other types of factorials in mathematics. There are multifactorials, hyperfactorials, superfactorials, and superduperfactorials.Adapted from: Kidder, David S., and Noah Oppenheim. The Intellectual Devotional: Revive Your Mind, Complete Your Education, and Roam Confidently with the Cultured Class. New York: Rodale Books, 2006.NameDateFactorials! Reading Comprehension Sheet: Use your reading to answer these questions.What is the factorial of a number?In your reading, you have an illustration of the factorial of 6. What would the factorial of 7 look like? Please write out your answer.In what areas of mathematics are factorials important? What about in everyday life?To what number is the factorial of 0 equal? Why?What can factorials be used to find? ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download