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Lesson 2-2A Writing Expressions: Journal: Writing Expressions Translating Words into Algebra Homework: 1.2 Record and Practice Journal, p. 7&9 Language 1.2 Record and Practice Journal, p. 10 I. Standards SPI 0606.3.5 Common Core MCC6.EE.1 MCC6.EE.2 a, b MCC6.EE.7 I can… I can translate sentences to write expressions and equations. I can translate expression and equations to write sentences. I can write, read and evaluate expressions with variable. I can identify parts of an expression using my vocabulary words: sum, term, product, factor, quotient, coefficient. I can solve real-world problems using algebraic expressions and equations. II. Preview/Preparation/ Pre-expose Synonyms are words that have the same meaning. They are said to be synonymous. For example: student and pupil, buy and purchase, sick and ill, quickly and speedily. Make a list of homonyms (both with same spellings and different spellings). When students are done, share each group’s list with the class. Math has something like synonyms also. For example sum, together and + are synonyms. Brainstorm other synonyms in math. III. Direct Instruction with Real World Examples Learning algebra is a little like learning another language. In fact, algebra is a simple language, used to create mathematical models of real-world situations and to handle problems that we can't solve using just arithmetic. Rather than using words, algebra uses symbols to make statements about things. In algebra, we often use letters to represent numbers. Since algebra uses the same symbols as arithmetic for adding, subtracting, multiplying and dividing, you're already familiar with the basic vocabulary. In this lesson, you'll learn some important new vocabulary words, and you'll see how to translate from plain English to the "language" of algebra. The first step in learning to "speak algebra" is learning the definitions of the most commonly used words. http://www.math.com/school/subject2/lessons/S2U1L1DP.html A. Vocabulary 1. Algebraic expression – a number sentence with one or more variables. The sentence does not have an equal sign. The following are examples of expressions: a. 2 b. x c. 3 + 7 d. 2 × y + 5 e. 2 + 6 × (4 - 2) f. z + 3 × (8 - z) 2. Constant – quantity that does not change. Only numbers. In the expression 7x2 + 3xy + 8 the constant terms are 7, 3, and 8. 3. Variable – a letter that represents a quantity that can change. These letters are actually numbers in disguise. In the expression 7x2 + 3xy + 8, the variables are x and y. We call these letters "variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression. 4. Coefficients Coefficients are the number part of the terms with variables. In 3x2 + 2y + 7xy + 5, the coefficient of the first term is 3. The coefficient of the second term is 2, and the coefficient of the third term is 7. If a term consists of only variables, its coefficient is 1. B. Direct Instruction 1. Before you can learn Algebra, you have to learn how to change words into algebra. We call this turning words into algebraic expressions. Look at the sentence I wrote and watch how easy it is to change it into an algebraic expression. My Sentence: Kirstin had $17 and then she found a bag of money. What is the Known? What is the Unknown? Whenever you don’t know something, you use a letter to take its place. We will be using the same letter so it isn’t too confusing. We will use the letter n. Algebraic Expression: 17 + n That’s easy! You just put in a letter for the amount of the money in the bag because you don’t know how much money there is. I think I’ll be able to learn the language of algebra pretty quickly. That was pretty easy. Remember expressions don’t have equal signs! Let’s try another one: Hey! Try this problem: Tom had found money in his pants pocket. He already had $23 in his wallet. What is the expression to show how much money does Tom has now. I can do this one! K: Tom found $ is his pocket and has $23 in wallet NTK: how much money does he have now? So… n + $23 Hey! I know this is an algebra expression! But what is the variable and what is the coefficient? Great! Let’s try another one! My sentence: Kasey found money in a box. What is the expression for this money? Algebraic Expression: n What is this called? That’s easy! You just put in a letter for the amount of the money in the box because you don’t know how much money there is. I think I’ll be able to learn the language of algebra pretty quickly. IV. Pattern Making Look at the sentences below and the translations into the language of algebra. Find the pattern to describe why they are written the way they are. Work in your groups to discuss the possibilities. Sentences Algebraic Expressions Jill is three years older than Nancy Expression for Nancy: n Expression for Jill: n + 3 Rick weighs 56 pounds more than Ed Expression for Ed: n Expression for Rick: n + 56 Now try these! Sentences Three consecutive numbers Three consecutive even numbers Algebraic Expressions Expression for the smallest: n Expression for the next larger number: n + 1 Expression for the largest: n + 2 Expression for the smallest: n Expression for the next larger number: n + 2 Expression for the largest: n + 4 V. Pattern Making Can you do this one? Sentence: The difference of a number and 3 Expression: 3 - n Help me! Answer: Answer Subtraction and division are not commutative Help! How do I know when to add, subtract, multiply or divide? Write your thinking. Use complete sentences and explain if you were writing a textbook for fifth graders. Explore Metacognitive Reflection Plan, Explore, Evaluate Why is it important to know these phrases? Give an example of correct use and incorrect use of the phrase. VI. Practice A. Work with a partner. Match each phrase with an expression. The product of a number and three n÷3 The quotient of 3 and a number 4p 4 times a number n·3 A number divided by 3 2m Twice a number 3÷n B. Complete the following table Variable Expression x+4 y - 75 3 ÷ z or Meaning with Words x plus 4 Operation Addition Meaning with Words x plus 4 y minus 75 Operation Addition Subtraction 3 divided by z Division 6 times n Multiplication 3 𝑧 6n, 6 · n, (6)(n) Answers Variable Expression Answers x+4 y - 75 3 ÷ z or 3 𝑧 6n, 6 · n, (6)(n) C. Write the phrase as an expression. VI. 1. 8 fewer than 21 2. The product of 30 and 9 Finding Patterns with Metacognition Find my error and write an explanation of why this is an error The quotient of a number x and 2 2 ÷x Explore Metacognitive Reflection Plan, Explore, Evaluate How can we organize the clue words to help our brain remember when to add, subtract, multiply, or divide? Journal entry: Writing Expressions Note page 54 and 55 VII. Practice A. Write the phrase as an expression 1. 14 more than a number x 2. A number y minus 75 3. The quotient of 3 and a number z B. Write the phrase as an expression 1. the sum of 18 and 35 2. 6 times 50 3. 25 less than a number b 4. a number x divided by 4 5. 100 decreased by a number k VIII. Close A. Translating between words and math The distances from Charlotte, NC, to Charlotte, TN, is 470 miles. Beth already drove part of the way before she stopped for lunch. How many miles more must she drive to reach Charlotte, TN? Answer To solve this problem, you need to find how many more miles Beth must drive. To find how much more, subtract. 470 - m B. Standards SPI 0606.3.5 Common Core MCC6.EE.1 MCC6.EE.2 a, b MCC6.EE.7 I can translate sentences to write expressions and equations. I can translate expression and equations to write sentences. I can write, read and evaluate expressions with variable. I can identify parts of an expression using my vocabulary words: sum, term, product, factor, quotient, coefficient. I can solve real-world problems using algebraic expressions and equations. IX. Secondary Rehearsal 1.2 Record and Practice Journal (BIM) p. 7&9, grade in class. 1.2 Record Practice Journal (BIM) p. 10, homework Text p. 56 & 57