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Subject Area: Mathematics Lesson Design Mathematics Grade Level: Algebra I & CAHSEE Benchmark Period Duration of Lesson: Standard(s): 4.0 Students simplify expressions before solving linear equations & inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12. (2 questions on CAHSEE) Learning Objective: Students will solve linear equations Big Ideas involved in the lesson: The solution of a linear equation is the value(s) of the variable in the equation that makes the equation true. As a result of this lesson students will: Know: Vocabulary: like terms, coefficient, constant terms, exponents, variables, linear equations, combining like terms, solve, simplify, expressions, solutions, round-off error, integers, reciprocal, opposite, identity. Order of Operations. Distributive Property. Commutative Property. Associative Property. Addition, Subtraction, Multiplication, & Division Properties of Equality Understand: The solution of a linear equation in one variable can be: - one point on the number line if the equation has a unique solution. (e.g., 2x + 1 = 5, reduces to x = 2), - infinitely many solutions if the equation reduces to an identity. (e.g., 2x + 3 = x + 3 + x, reduces to 3 = 3), - no solution if the equation reduces to an incorrect statement. (e.g., 2x + 3 = x + 2 + x, reduces to 3 = 2). Be Able To Do: Identify & collect the like terms to simplify linear equations in one variable. Apply order of operations to simplify linear equations in one variable. Determine the number of solutions to a linear equation in one variable o One solution: the equation reduces to x = constant a, (x = a) o Many solutions: the equation reduces to constant a = constant a, (a = a) o No solution: the equation reduces to constant a = constant b which is not true, therefore there are no solutions, (a = b). Identify which properties are being used to solve linear equations in one variable. Solve linear equations in one variable. Assessments: What will be evidence of student knowledge, understanding & ability? Formative: ABWA Algebra tiles Problems on the board:” I do one, you do one”. Summative: Quiz Chapter test Benchmark 1 CFU Questions: 1) Students view matching exercises and are asked to show how they found solutions. 2) Show “Digital Curriculum” video (a section of it) and ask relevant questions. Anticipatory Set: a. T. focuses students b. T. states objectives c. T. establishes purpose of the lesson d. T. activates prior knowledge Instruction: a. Provide information Explain concepts State definitions Provide examples. Model b. Check for Understanding Pose key questions Ask students to explain concepts, definitions, attributes in their own words Have students discriminate between examples & non-examples Encourage students generate their own examples Use participation Lesson Design Mathematics Lesson Plan What is the solution to equation A (or what does it match with?)(Have equity cards). Attachment: Opening activity. Show digital curriculum video “Working with variables” (2:50) and use equity cards to ask questions: “how many ways can you solve the expression using distributive property? Do you get the same answer? Can you give me another example illustrating distributive property? Power Point Presentation: Paco and Diane go to the taco stand. -How many tacos did Paco first buy? -How can we express with variables and numbers the total amount of tacos after Paco’s first binge? -After he repeats the process? -How many tacos did Diane buy? -How do I express that with variables and numbers? -What is the total amount of tacos bought? -Illustrate the story with an algebraic equation. Instructor solves on the board along with the students. CFU: Tell me how you set this problem up. Is there another way to set this up? Explain how you got your answer? Set up a Frayer model to show a non-example. 3(x+2) +1=3x+6+3. Demonstrate on the overhead with algebra tiles: 2x + 7 = 11 2(3 + x) = 10 -2x + -3 = 5 Draw a picture of the very same equations. Solve using properties of equality. Guided Practice: Divide class into groups of three and write three equations similar to the a. Initiate practice activities ones in instruction. One student will use algebra tiles, another will draw and under direct teacher another one will record the equations. For example: supervision – T. works 2x + 3 = 5 problem step-by-step 3( x + 1 ) = 9 along w/students at the -3 x + -1 = 4 same time b. Elicit overt responses from Check work. Solve equations on the board using properties of equality and clarify to students the steps involved. students that demonstrate -Write equations on the board with different levels of difficulty: simple behavior in objectives expression, equation with one variable on one side, equation with a variable c. T. slowly releases student on both sides, include fractions and decimals. Have volunteers and nonto do more work on their own (semi-independent) volunteers come up to the board and correct as they go along. d. Check for understanding Attachment: Worksheet on overhead. that students were correct Questions: at each step How would you start this problem? e. Provide specific Is this the only way to start? knowledge of results Would you get the same answer if you started differently? f. Provide close monitoring 2 What opportunities will students have to read, write, listen & speak about mathematics? Closure: a. Students prove that they know how to do the work b. T. verifies that students can describe the what & why of the work c. Have each student perform behavior Independent Practice: a. Have students continue to practice on their own b. Students do work by themselves with 80% accuracy c. Provide effective, timely feedback Resources: materials needed to complete the lesson 3 Lesson Design Mathematics What was the property we used to solve this/these problems? They experimented with algebra tiles, worked in groups and they discussed it, they read and listened to the power point presentation. Quick review of the concept. Draw equity cards and ask each student to give an answer orally or using a white board. Have students write a paragraph explaining how they solved equations step by step. Select problems from the Algebra textbook, page 157# 15, 16, 17, 32-35, 42-46. Algebra tiles, computer and projector, textbook, overhead, easel board