Solving Equations. Student Probe Solve for x:
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1 Solving Equations Student Probe Solve for x: Answer: Lesson Description In this lesson students will solve linear equations for a single variable The lesson uses the illustration of wrapping and unwrapping a gift package to demonstrate how equations are solved By undoing mathematical operations in the reverse of the order of operations, students will be able to solve equations for a specified variable Rationale To solve equations means to find the values of the variable that make the equation true Students are required to employ three concepts when solving equations: balancing the equation by performing the same operation on each side of the equation, undoing operations, and reversing the order of operations The experiences students have had solving open sentences, discovering properties of the real numbers and working with the order of operations in earlier grades should form the basis for insights into mathematical structure and abstraction that help them become fluent in performing the manipulations to solve equations Preparation None At a Glance What: Solve linear equations in one variable Common Core Standard: CC9-12AREI4 Solve equations and inequalities in one variable Solve quadratic equations in one variable Matched Arkansas Standard: AR9-12SEIAC33 (SEI3AC3) SLE 3 Solve linear formulas and literal equations for a specified variable Mathematical Practices: Attend to precision Look for and make use of structure Who: Students who cannot solve linear equations for a single variable Grade Level: Algebra 1 Prerequisite Vocabulary: variable, equation, zero pair Prerequisite Skills: order of operations, operations with integers, inverse relationship between addition and subtraction, inverse relationship between multiplication and division Delivery Format: Individual, pairs, small group, whole group Lesson Length: 30 minutes Materials, Resources, Technology: Materials for wrapping a package: wrapping paper, box, tape, ribbon, present (optional) Student Worksheets: None
2 Lesson The Expect students to say or do If students do not, then the 1 Let s go through the steps of wrapping a gift Write down the steps as I demonstrate (Go through the process of wrapping the gift) Students will write down the steps of wrapping the gift in order: (1) place the present in the box (2) cover the box with wrapping paper (3) put the ribbon around the 2 Now we are going to reverse the process and open the gift Write down the steps as I demonstrate 3 What do you notice about the steps involved in wrapping and unwrapping the gift? 4 Solving an equation is like unwrapping a gift We have to undo the operations in reverse order What operations undo each other? 5 We must also unwrap in the opposite order What is the order of operations? 6 What would the reverse order be? 7 Let s solve for x What operation is How can we undo it? (See Teacher Notes) package Students will write down the steps of opening the gift, in order: (1) take off the ribbon (2) remove the paper (3) open the box and remove the gift They were the same, but in reverse order Addition and subtraction Multiplication and division Grouping symbols, exponents, multiplication and division, addition and subtraction Addition and subtraction, Multiplication and division, exponents, grouping symbols Multiplication Division Explicitly show students that the steps are reversed Addition and Subtraction Multiplication and Division Refer to Order of Operations Multiplication and Division
3 The Expect students to say or do If students do not, then the 8 Let s divide both sides of the equation by 7 What do we get? 9 Does make our 10 Now let s solve for x What operation is How can we undo it? (See Teacher Notes) 11 What should we add to both sides of the equation? 12 Does make our 13 Now let s combine what we have learned and solve for x What operations are We will need to undo them in reverse order What should we undo first? What operation will we use? 14 What should we subtract from both sides of the equation? 15 What should we undo now? What operation should we use? Yes Subtraction Addition 17 Yes Addition and multiplication Addition Subtraction 3 Multiplication Division Model for students Addition and Subtraction Model for students
4 The Expect students to say or do If students do not, then the 16 What should we divide both sides by? 2 or 17 Does make our Yes 18 Now let s solve for x We see addition, multiplication as well as parentheses in this equation What does the order of operations tell us? 19 To undo the equation we need to use the reverse order What should we do first? How do we do that? 20 Now what? How do we do that? Do grouping symbols, then multiplication, and then addition Undo the addition Subtract 2 from both sides of the equation Undo the multiplication Divide by 3 21 Now we need to undo subtraction What should we add to both sides of the equation? 22 Does make our 1 Yes 23 Repeat with additional equations as needed
5 Teacher Notes: 1 Students need to understand that equations must be kept balanced Performing an operation on one side of the equation requires performing the same operation on the other side of the equation 2 The equations in Steps 7 and 10 were chosen so that students would need to perform the inverse operation, not simply recall facts 3 It is advised that students be required to check their solutions to the equations 4 Point out a key to solving equations for a single variable is to isolate the variable Variations 1 Hands- on Equations is an excellent tool for teaching solving equations 2 As equations that students are expected to solve become more complicated, additional practice will be required Formative Assessment Solve for x: Answer: References Paulsen, K, & the IRIS Center (nd) Algebra (part 2): Applying learning strategies to intermediate algebra Retrieved on March 10, 2011 from 010pdf
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