Download Represent and Solve Simple Equations

 Student Probe Represent and Solve Simple Equations Represent and solve the following problem: Sally is buying T-­‐shirts for the softball team. The cost of each shirt is $7. There is a $25 set-­‐up fee for printing the team name on the shirts. How many shirts can Sally buy with $130? Answer: Lesson Description Using real world scenarios, this lesson expands students’ understanding of building equations of proportional relationships to include linear relationships in the form Students use tables to create the equations and then solve them. Rationale This lesson continues students’ progression from arithmetic thinking to algebraic thinking. It builds on students’ understanding of solving open sentences with whole numbers using one operation to solving linear equations and pairs of simultaneous linear equations with real numbers. Preparation Prepare a display for building and discussing the tables related to the problems. At a Glance What: Representing and solving simple linear equations Common Core State Standard: CC.7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Matched Arkansas Standard: AR.8.A.5.1 (A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-­‐step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology Mathematical Practices: Model with mathematics. Look for and express regularity in repeated reasoning. Who: Students who cannot solve word problems leading to equations in the form px+q=r Grade Level: 7 Prerequisite Vocabulary: constant, variable, expression, equation, solve Prerequisite Skills: order of operations, solving open sentences, equations of proportional relationships Delivery Format: Individual, small group Lesson Length: 30 minutes Materials, Resources, Technology: graphing calculator (optional) Student Worksheets: None Lesson The teacher says or does… 1.
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Expect students to say or do… If students do not, then the teacher says or does… Let’s solve this problem: Model for students. Melissa needs to buy Why are we multiplying by 4? # of Cost ($) bottled water for a class Extend the table until Bottles students realize the pattern. picnic she is planning. Fill 1 4(1) 4 It Up charges $4 per 2 4(2) 8 bottle. 3 4(3) 12 Create a table to show 4 4(4) 16 how much the water will 5 4(5) 20 cost. 6 4(6) 24 (See Teacher Notes.) Notice the middle column Use color to underline or of the table. circle the constant value (4) What is staying the same? 4 and the changing values. What is changing? 1, 2, 3, 4, 5, 6… Write an expression for Model for students. the cost for any number of bottles. Write an equation to find The water will cost 4x. the number of bottles Melissa can buy if she spends $88. How can we solve this Divide both sides of the Refer to Solve Open equation? equation by 4. Sentences with Multiplication What is x? and Division. What does mean? 23 bottles of water will cost Prompt students. (See Teacher Notes.) $88. The teacher says or does… Expect students to say or do… If students do not, then the teacher says or does… 6. Now let’s solve another Model for students. problem. Why are we adding 10? # o
f Mark found that Bottles Cost ($) Why are we multiplying by 3? Bottles by Bob could also provide Extend the table until 1 10+3(1) 13 water for the picnic. students realize the pattern. 2 10+3(2) 16 Bottles by Bob charges a 3 10+3(3) 19 one-­‐time fee of $10 and then $3 per bottle. 4 10+3(4) 22 Create a table to show 5 10+3(5) 25 how much the water will 6 10+3(6) 28 cost. (See Teacher Notes.) 7. Notice the middle column Use color to underline or of the table. circle the constant values (10 What is staying the same? 10 and 3 and 3) and the changing What is changing? 1, 2, 3, 4, 5, 6 values. 8. Write an expression for Model for students. the cost of any number of bottles. 9. Write an equation to find The cost of the water can be the number of bottles that expressed by . can be purchased for $88. How can we solve this First subtract 10 from each equation? side, then divide each side by 3. 10. Solve for x. Refer to Solving Open Sentences with Addition and Subtraction. Refer to Solve Open Sentences with Multiplication and Division. 11. What does mean? 26 bottles will cost $88. Prompt students. 12. Repeat with additional problems as necessary. Teacher Notes 1. By explicitly writing the middle column of the table to show the substitution, students can determine with numbers are remaining the same (the constants) and which numbers are changing (the variables). This will help students write the correct equation. 2. In order for students to make sense of problems and the mathematics involved, it is important for them to understand the solutions in terms of the problem context. 3. Representing and solving equations fluently requires a significant amount of instructional time. Be prepared to revisit this topic often over time. Variations None Formative Assessment Represent and solve the following problem: Madison wants to buy a video game that costs $60. She already has saved $25 for the purchase. Madison plans to save $5 per week for the game. How many weeks will it take Madison to have enough money for the video game? Answer: References Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide -­‐ Response to Intervention in Mathematics. Retrieved December 10, 2011, from rti4sucess: http://www.rti4success.org/images/stories/webinar/rti_and_mathematics_webinar_presentati
on.pdf Glenda Lappan, James Fey, William Fitzgerald, Susan Friel, Elizabeth Difanis Phillips. (2006). Connected Mathematics Project 2. In Moving Straight Ahead. Boston: Pearson Prentice Hall. Paulsen, K., & the IRIS Center. (n.d.). Algebra (part 2): Applying learning strategies to intermediate algebra. Retrieved on December 10, 2011 from http://iris.peabody.vanderbilt.edu/case_studies/ICS-­‐010.pdf