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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?
 The student will solve equations in the form p(x + q) = r.
 The student will compare arithmetic and algebraic solutions to word problems.
 The student will write equations in the form p(x + q) = r to represent word problems.

Prior Knowledge: What prior knowledge should students have for this lesson?
 Use variables to represent numbers (MAFS.6.EE.2.6)
 Apply the distributive property to expand an expression (MAFS.6.EE.1.3)
 Understand in the expression p(x + q), (x + q) is both a factor and a sum (MAFS.6.EE.1.2)
 Write and solve equations in the form x + p = q and px = q (MAFS.6.EE.2.7)
 Add, subtract, multiply, and divide rational numbers
 Finding perimeter

Guiding Questions: What are the guiding questions for this lesson?
 How is solving a word problem arithmetically similar to solving an equation algebraically? How do you know?
 How do you write an equation to model a word problem?
 These equations were solved differently. Are they both correct? Why or why not?

Teaching Phase: How will the teacher present the concept or skill to students?
 Display the rectangles from Find the Perimeter of Each Rectangle opening problem.
 Have students find the perimeter of each rectangle showing the steps used.
 As students work on the problem, circulate observing the strategies used.
 When students finish, discuss the various strategies allowing students to share their method of solving each problem.
 Ask: Did you use the same strategy for each rectangle? Which strategy was easier? Why?
Students should realize for Rectangle B adding the length and width together first might be easier because it adds to a whole number. For Rectangle C, multiplying by 2 first might be easier, because is a whole number.
 Summarize the different strategies used.

Guided Practice: What activities or exercises will the students complete with teacher guidance?
Question: How can we write equations to model each strategy?
 Ask: How can we write equations to model the strategies?
 Explain: When writing any equation using variables, we must first define what the variables represent.
 Ask: When finding the perimeter of the rectangle what values change as the rectangle changes? (length and width)
 Ask: What variables can we use for length and width? Does it matter whether we use x and y or l and w? (Students should understand any letter, character or even word can be used to represent a quantity in an expression or equation. However, some are easier or better choices than others depending on what they represent.)
 Model defining the variables: l = length, w = width, and P = perimeter (this is a necessary step when writing any equation)
 Ask: We used three different strategies to find the perimeter, how can we represent each using the variables?
 Strategy 1: P = l + w + l + w
 Strategy 2: P = 2l + 2w
 Strategy 3: P = 2(l + w)
(Optional: This is a good opportunity to discuss equivalent expressions and equations. Students should understand and be able to show the 3 equations are equivalent.)
Question: What happens when we know the perimeter and length, but not the width?
 Ask students to solve the problem below showing the steps:
 A rectangle has a perimeter of 29 inches. If the length is 8 inches, what is the width?
 Possible solutions:
 8 + 8=16
29  16 = 13
13/2 = 6.5
 2 * 8 = 16
29  16 = 13
13/2 = 6.5
 29/2 = 14.5
14.5  8 = 6.5
 Discuss each solution. Students may not have used solution 3, discuss why this works.
 Students should understand in solutions 1 and 2, that 8 + 8 is the same as 2 * 8.
 Ask: How could we use one of the equations we wrote earlier to find the width? (by putting the numbers in for the variables)
 Ask: If we used the equations, what steps would we use to solve each equation?
 Have students put the perimeter and length into each equation and solve for the width.
 Discuss each solution. For equation 3, some students may have distributed first. Discuss why dividing by 2 first works as well. (When dividing by 2, (8 + w) is seen as a factor instead of a sum.)
Question: How is solving the equation numerically similar to solving the equation algebraically?
 Discuss the similarities of solving each equation numerically and algebraically by comparing solution 1 and equation 1; solution 2 and equation 2; and, solution 3 and equation 3. Students should realize the same steps are used. For example, in both solution 2 and equation 2, the first step is to multiply by 2, then subtract 16, and finally divide by 2.
Optional extra problem.
 Have students use one of the perimeter equations to solve:
 The perimeter of a rectangle is 46 inches. The length is 121/3 inches, what is the width?
 Ask students which equation would be easier to use? Why?
 Solution: 102/3 inches
Writing and solving other equations in the form p(x +q) = r .
 Ask students to solve the following problem:
 Tickets to Go charges a processing fee of $6.95 for every ticket purchased. John bought 5 tickets for a concert and paid a total of $294.75. How much was each ticket?
 Arithmetic solution(s):
 5 * $6.95 = $34.75
 $294.75/5 = $58.95
 $294.75  $34.75 = $260
 $58.95  6.95 = $52 per ticket
 $260/5 = $52 per ticket
 Ask: How can we write an equation to model the problem?
 First: select a variable for the unknown and state what it represents.
 Explain: In this problem, we need to write an expression to represent the total cost.
 Ask: If we knew the price of one ticket, how would we calculate the cost of 5 tickets? (add $6.95 to the price of one ticket and multiple the sum by 5)
 Scaffold: If students do not understand this concept, ask: if the price of each ticket is $35, how would I find the total cost of 5 tickets? (add $35 plus $6.95 then multiply by 5)
 How do you translate: add $6.95 to the price of one ticket and multiply the sum by 5?
 Some students may write $6.95 + c * 5, remind students using order of operation c * 5 would be done first  we want to multiply the sum of $6.95 + c. How can we write the expression to find the sum first, then multiply by 5?
 ($6.95 + c)*5
 Explain: this can also be written as 5($6.95 + c). Ask, why can we move the 5? (Because of the commutative property of multiplication).
 Explain: to complete the equation set the expressions 5($6.95 + c) and $294.75 equal to each other: 5($6.95 + c) = $294.75  this shows both sides of the equal sign represent the total of $294.75.
 Ask the students to solve the equation.
 Discuss which method was easier and why.
 Have students try the following problem by writing and solving an equation:
 Sheila bought a sandwich and bag of potato chips for 7 people. The chips were $0.79 per bag. She spent a total of $47.18. How much was each sandwich?
 As students work on the problem, circulate and observe students' work. If a student is struggling ask guiding questions: What is that you need to find? How would you find the price of one sandwich and chips? If you knew the price of the sandwich, how would you calculate the total?
 When students are finished, have students share and explain their solutions.
 solution:
 c = cost of one sandwich (be sure students have defined the variable)
 equation:
 solution:
 7(c + $0.79) / 7 = $47.18 / 7 divide both sides by 7
 c + $0.79 = $6.74
 c + $0.79  $0.79 = $6.74  $0.79
 c = $5.95
 After reviewing the problem, ask students to share strategies for writing and solving equations.

Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the lesson?

Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
 Ask students to share strategies for writing equations to model word problems.
 Elicit that that realworld problems can be solved arithmetically and using equations. There may be multiple ways they are solved and still produce the same correct solution.

Summative Assessment
The student will independently complete the "Writing and Solving Equations" worksheet.
Writing and Solving Equations Answer Key.

Formative Assessment
The teacher will gather information during and after the opening problem and guided practice.
Through observation, questioning, and discussion the teacher will assess the students' understanding of comparing, writing, and solving word problems in various ways.
The opening word problem assesses students' ability to solve the problem arithmetically.
The guided practice assesses students' understanding of writing and solving word problems.
The teacher will use this information to guide instruction.

Feedback to Students
The student will receive feedback from the teacher and peers during and after each part of the opening activity and guided practice through questions, discussions, and observations.
Through feedback students should understand:
 The same reasoning is used to solve a problem algebraically as arithmetically.
 Starting with the unknown and working forward through a word problem makes it easier to write an equation to model the word problem.
 When writing equations, the equations p(x + q) = r is another form of px + pq = r.
Assessment
 Feedback to Students:
The student will receive feedback from the teacher and peers during and after each part of the opening activity and guided practice through questions, discussions, and observations.
Through feedback students should understand:
 The same reasoning is used to solve a problem algebraically as arithmetically.
 Starting with the unknown and working forward through a word problem makes it easier to write an equation to model the word problem.
 When writing equations, the equations p(x + q) = r is another form of px + pq = r.
 Summative Assessment:
The student will independently complete the "Writing and Solving Equations" worksheet.
Writing and Solving Equations Answer Key.
Accommodations & Recommendations
Accommodations:
For students who struggle, use whole numbers in the problems. Review writing simple expressions. Show a partially worked out solution if a student needs further scaffolding.
English Language Learners may need extra support for unfamiliar vocabulary words. Provide definitions and examples, as needed.
Extensions:
For advanced students find the perimeter of other shapes: triangle, pentagon, etc.

Suggested Technology: Overhead Projector
Special Materials Needed:
Class set of worksheets
Additional Information/Instructions
By Author/Submitter
This resource is likely to support student engagement in the following the Mathematical Practice: MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.
Source and Access Information
Contributed by:
Name of Author/Source: Erin OBrien
Is this Resource freely Available? Yes
Access Privileges: Public
* Please note that examples of resources are not intended as complete curriculum.