Разработкт уроков по вариативному компоненту

Basic Algebra – Lesson 5 – Expressions from Sentences Objective(s): By the end of this lesson the student will be able to: turn word sentences into  algebraic expressions. by Elaine Ernst Schneider Pre Class Assignment:  Completion of Basic Algebra –   Lesson 4 Resources/Equipment/Time Required:  Outline: Review: In the first lesson, you learned that numbers and variables form sentences, or algebraic  “expressions.” When you take information from a sentence and turn it into a mathematical  expression, it is called “translating.” In another lesson, you learned that when you write algebraic  expressions, use +, ­, and = signs; and for division, use / , the same way you know that when you see  a fraction, it means to divide the top number by the bottom number. Then, for multiplication, we learned to write the expression with no symbol or sign between  them (such as 3a), with an X , or using parentheses. The parenthesis is especially useful in longer  problems such as (3y)(4­2x). Then you learned how to work problems where there are no parentheses or brackets, using the Order  of Operations rule. Multiply, Divide, Add, Subtract. Now let’s put all of this to use and Yes, that’s right! We’re going to take English sentences –  WORDS – and turn them into algebraic expressions. Let’s Get Started: Subtract seven from twenty­one, then add three. The algebraic expression is: 21 – 7 + 3 No parentheses are needed because the Order of Operations tells us that addition and subtraction are  done in order from left to right. Now it’s time for you to try a few. Remember your terms: subtract, sum, product, division, multiply,  quotient. You may have to use parenthesis on some of them. Assignment(s) including Answer key: 1. Subtract 2 from x; then add y. 2. Subtract the sum of 2 and y from x. 3. Divide 10 by 3; then multiply by 5. 4. Divide x by the product of 3 and z. 5. Multiply x by 3; then add y. 6. Add x and 3; then multiply by y. 7. Subtract the product of 5 and x from 7. 8. 5 more than the product of 3 and c. 9. 13 less than the quotient 5 divided by p. 10. 4 times the sum of 10 and x. For Answers, Click Here Pre­Requisite To:  Basic Algebra Lesson 6 For more articles by this Consultant Click Here For more articles on Grade 9 Algebra 1035 likes This lesson teaches students to translate verbal phrases into algebraic expressions. Students are given  practice in writing expressions that record operations with numbers and with letters representing  numbers. Special attention is given to writing operations in the correct order. A class work and homework  worksheet is provided with keys for each. Subject(s): Mathematics Grade Level(s): 6 Intended Audience: Educators Suggested Technology: Document Camera, LCD Projector Instructional Time: 50 Minute(s) Resource supports reading in content area:Yes Freely Available: Yes Keywords: variable, expression Instructional Component Type(s): Lesson Plan, Worksheet Resource Collection: CPALMS Lesson Plan Development Initiative ATTACHMENTS Translate_Classwork.docx Translate_Teacher_Handout.docx Translate_Independent_Practice.docx Translating_Expressions_Summative.docx Translating_Expressions_Summative_Answer.docx LESSON CONTENT Lesson Plan Template:  General Lesson Plan Learning Objectives: What should students know and be able to do as a result of this  lesson? Students should be able to read a verbal phrase and rewrite it as a math expression utilizing the correct order of operations. Prior Knowledge: What prior knowledge should students have for this lesson? MAFS.5.OA.1.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Students should have prior experience with writing expressions and using variables. Students should have background knowledge of math vocabulary words that indicate operations (i.e. sum, product, quotient, difference). There is a teacher handout attached with commonly used vocabulary that could be used to help review. Guiding Questions: What are the guiding questions for this lesson?     Please refer to these questions throughout the lesson and class work. o o o In what operations might the incorrect order of doing the operations provide the wrong answer?  Answer: Subtraction and division; multiplication and addition What does the variable represent? (Insist that students include units when answering this question.)   Answer: One or more numbers. The number/s are the value of the variable. Why do we use numbers and symbols in math instead of words? Answer: easier to read and write; easier and faster to work problems. The following questions can be utilized throughout the lesson. Answers may vary. o o o o o What operation uses this action? What does this number represent in the problem? How would you represent this part of the phrase in math language? Does this expression match the word phrase? Why is the ability to translate from English phrases to math language important? How will you use this in the future?  Teaching Phase: How will the teacher present the concept or skill to students? 1. As an introduction to this lesson, students should be refreshed on vocabulary terms such as sum, difference, product, and quotient as well as the meaning or action of the four operations. The following word situations address the action of the operation without allowing students to pull out numbers without thought and perform an operation. The teacher should facilitate a discussion about each situation as students reason about what is happening in the situation. Project each problem with a document camera, or if unavailable, the problems could be copied and given to students. o o o The cafeteria bought lots of frozen pizzas to serve. If you know the total amount of money they spent and how many pizzas they bought, how could you figure out the cost of 1 pizza? Why do you believe that? What is the action of this operation?  You would divide the total cost by the number of pizzas to find the cost of one pizza. Division separates the money spent into equal stacks. Each stack represents the cost of one pizza. Division separates a quantity into equal parts. Pete bought some candy and gave some of the pieces to his best friend, Hal. How could you figure out how many pieces Pete has left? Why do you believe this? What is the action of the operation?  Subtract the number of pieces he gave to a friend from the number of pieces he purchased. You are starting with the whole, taking away a part so what is left is the other part. The subtraction action is to take away, or compare by finding the difference. Bob and Tyler do not have enough money to buy a box of donuts, but they have the exact amount needed if they combine their money. How would you find the cost of a box of donuts? What is the action of this operation?  You would find the sum of Bob's and Tyler's money. Combine is the action of addition. o Macy wants to buy each of her classmates a Coke. How would you figure out the cost? What is the action of this operation?  You would multiply the cost of the Coke by the number of classmates. Repeated addition of the same value is multiplication. 2. Begin by asking students, "How many of you love to solve word problems?" Distribute to each student a plain sheet of paper and tell them to express how they feel about working with word problems by drawing a picture, no words draw a picture only. 3. Have a student volunteer share his/her picture and the rest of the class translate what the picture means to them. Students should share their translation explaining why they interpret the picture in their own way. Express that all of this is a form of communicating, and the way we communicate in math is with the same concept. 4. Define an expression for students, "A math phrase without an equal or inequality sign." Tell students that expressions are solved. This lesson is to translate written words to numbers, operational symbols, and variables. 5. Remind students that a variable is a placeholder for one or more numbers. "Some number" is a phrase that indicates a variable is needed. 6. Utilizing a document camera or using a projector, show students how to break down a verbal expression, beginning with simple expressions. Example: Given "some number increased by 5", ask students, "What action is happening in this phrase?" (Answer: We are making larger, joining to, adding to). Then ask, "What operation indicates this action?" (Answer: Addition) x + 5 7. Example: Given "51 less than some number." Ask students, "What action is happening in this phrase?" (Answer: We are decreasing, going down, subtracting). Then ask, "What operation indicates this action?" (Answer: Subtraction) x - 51; taking away from the x. 8. Discuss the role and plays in this written sentence. Example: Sum of 12 and e. (12 + e) 9. Tell students that they have to read very carefully using context clues to determine what action is required. They will need to reread some problems in order to focus on the needed information. Example: Alex has some chips, c, and 4 drinks. Lacy has 2 fewer chips and no drinks. Write an expression for Lacy's snacks. Answer: Lacy doesn't have any drinks, so c-2 Guided Practice: What activities or exercises will the students complete with teacher  guidance? The whole group will complete the practice worksheet classwork with teacher guidance. Use the Guiding Questions to clarify and probe student thinking. Independent Practice: What activities or exercises will students complete to reinforce the  concepts and skills developed in the lesson? Students will complete the independent practice worksheet in class or as a homework assignment for extra practice. Afterwards, call on students to share their responses and justify their answers. Encourage other students to contribute to the dialogue. Closure: How will the teacher assist students in organizing the knowledge gained in the  lesson?    Summarize the lesson by asking the students for the key ideas in this lesson. These should include the following: o o o o You can translate English phrases into math expressions. Sometimes you have to read a situation more than once to understand the action of the situation. It is important to understand the action of each operation. It is important to follow the correct order of operations to determine the correct answer. For example, subtraction and division are not Commutative. Administer the Summative Assessment, when students are ready. Please see the Summative Assessment section. Collect, grade, and record the results, and return the work to the students at the next session. Then, using a document camera, review the work, calling on students to share their responses. Refer to guided questions and the answer key to continue to ask probing questions to ensure student understanding. If you have your students keep a journal, have them write about the different methods they use to communicate with the people in their lives and why they choose those methods. Summative Assessment Administer the Summative Assessment when you believe students are ready for it. o o Summative Assessment Summative Assessment Answer Key Formative Assessment The following formative assessment may be given to students on a day prior to the lesson to assess prior knowledge. Students should be told they are not expected to be able to answer all questions correctly yet. Student performance on this assessment will provide the teacher a stronger knowledge about the readiness of the students for this lesson. Students who do not perform well on #1 - 3 will need some small group or individual help in addition to careful observation during the lesson. Students who are successful with #1 - 3 should be ready for this lesson. Students who successfully complete #4 - 7 may be ready for more rigorous problems. Write an expression for each of the following:   o o o o o o o add 4 and 8, then multiply by 3 subtract 9 from 14, then multiply by 2 subtract 7 from 24, then divide by 6 the quotient of a number and 4 the product of 23 and twice a number times the sum of 9 and a number y 15 less than 7 times a number Answers: o 1. (4 + 8)3 o o o o o o 2. (14 - 9)2 3. (24 - 7)/6 4. n/4 5. 23(2n) 6. 5(9 + y) 7. 7n - 15 Problems #4 - 7 could be revisited at the end of the lesson. Throughout the lesson, the teacher should interact with students by asking questions. 2. Feedback to Students This lesson is very interactive. Feedback should be ongoing as you respond to students' questions and answers. Encourage students to answer all questions that are presented. Redirect the question and require the student to provide information proving understanding of the concept. Circulate as students are doing individual work, ensuring all work is scanned for accuracy. This is a time for individual attention if needed. See the Lesson Phase for more specific help to students. ACCOMMODATIONS & RECOMMENDATIONS Accommodations: o o o o o Highlighters might be used to highlight important words in the phrases. Peer tutors can be used to assist slow readers. If needed, display a Word Wall (list of vocabulary words and their meanings) that students can refer to and then remove it for the Summative Assessment. As a prelude to this lesson, have small groups work with translations for expressions that do not require variables. Provide English Language Learners with translations, definitions, and/or examples of unfamiliar vocabulary. Extensions: Provide problems for students to evaluate written expressions in which letters stand for numbers. Suggested Technology: Document Camera, LCD Projector     Special Materials Needed: Students: o o o o o Teacher: o o o o o  highlighters can be used plain paper class set of Translating Expressions class work worksheets class set of Writing Equivalent Expressions worksheets class set of Summative Assessment worksheets Prepare problems in the Teaching Phase for display or student use. Prepare the Formative Assessment problems for display or student use. answer keys markers Prepare the Expressions Worksheet for display or student use Further Recommendations: Students need to be reminded that the multiplication sign, x, used in elementary school is confusing when working with algebraic expressions or equations, because of the use of x as a variable. The times sign, x, is now replaced with a centered dot or parenthesis. To show multiplication of a number and a variable, a dot or parenthesis is not required. The number and variable should be written side by side. The division symbol may be replaced with a fraction bar. Please note that this lesson only addresses part a of this Standard. Additional Information/Instructions By Author/Submitter Students who participate in the lesson will experience the Mathematical Practice Standard MAFS.K12.MP.4.1, model with mathematics, as they translate English phrases into math expressions.