MidSchoolMath 1

It is important that students make connections between the steps of solving a problem arithmetically and the steps of solving the same problem with an algebraic equation. During Pen Perimeter, Farmer Jean is making a new goat pen for her cute little goats. She plans to put the pen between the barn and the house and has already decided upon the width. She buys as much fencing as she can afford, along with a few other supplies. The data provided are a receipt from Farmer Jean’s fence purchase, as well as her notebook containing a diagram of the pen.

LESSON: PEN PERIMETERWhat is the length of the new goat pen?

Pen Perimeter

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?

The Math SimulatorTM

ImmersionPlay Pen Perimeter Immersion video, whole-class. Restate the question: What is the length of the new goat pen?Facilitate classroom discussion; ask students: "What do we need to know?"

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2 Data & ComputationPrint the Data Artifact, cut into halves, and distribute to students. Allow students work time. Ask students: "Does your answer make sense?"Consider using a sharing protocol leading to mathematical insights and/or highlighting misconceptions. Allow students to revise their work.

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3 ResolutionPlay Pen Perimeter Resolution video, whole-class. Prepare and give brief lecture (Teacher Instruction).

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Download the Detailed Lesson PlanAvailable on the Teacher Dashboard

+ Simulation TrainerAssign the Simulation Trainer.Use protocols that encourage students to help each other.Use Progress Monitoring to access real-time data for the classroom.Provide individual help for students who are not making progress.

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(Use student headphones.)

7.EE.B.4aExpressions & Equations

MidSchoolMath 2Pen Perimeter

Clicker QuizLaunch the Clicker Quiz, whole-class.**As often as possible, explicitly connect arithmetic process with algebraic process.

7.EE.B.4aExpressions & Equations

Gladys: To help students more easily see the connection between arithmetic solutions and algebraic solutions, provide a simple example that students could likely solve quickly. Then connect those arithmetic methods to an equation. Example: A square has a perimeter of 20 units. What is the length of one side?

Kevin: Encourage students to explicitly define what the variable stands for when they write an equation, and to ask themselves ,"Does this make sense within the context?"

Megan: Consider asking students to use a two-column method for applicable problems. Tell students to solve each problem, in the left column, using their own strate-gies (which will likely be arithmetic in nature). After those solutions are confirmed, ask students to go back and use the right column to set up and solve equations for the same problems.

KevinSimpson

GladysGraham

MeganLeBleu

Ex. Clicker Quiz #6Standard Math Procedures

Instruction at a Glance

1 Write an equation to represent the situation.

p + 3 = 9 where p = pieces in the entire cake

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Isolate the variable using inverse operations.

Isolate the variable using inverse operations.

14

p + 3 – 3 = 9 –314

p • 4 = 6 • 414

p = 614

p = 24

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PEN PERIMETERWhat is the length of the new goat pen?

Farmer Jean is making a new pen for her cute little goats and is experimenting with diff erent dimensions. She has bought as much fencing as she can aff ord, and she wants to use all of it.

Use Farmer Jean’s diagram and her receipt to determine the length of this potential goat pen.

7.EE.B.4a

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specifi c rational numbers. Solve equations of these forms fl uently. 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?

About this standard

Date PeriodName

MidSchoolMath Pen Perimeter 1 of 2

The length of this goat pen is __________________.

APPLYING THE STANDARD

Hank’s Hot Dogs charges a preparation fee of $5 plus $3 per hot dog.

1)

Padma’s credit union charges her a members fee of $1.50 and $0.75 per transaction.

2)

Dara’s Dogs charges a $5 per hot dog and a $3 preparation fee.

3)

Gordon’s credit union charges him $1.50 per transaction and a members fee of $0.75.

4)

Jaqueline and Jenae are shopping for accessories. The prices of each item already include tax.

5)

The sum of a number and 9 is multiplied by -2. The result is -8. What is the unknown number?7)

Julio rented 1 movie and 3 video games. He paid $13.60 in total. • The movie cost $4.75 to rent • The video games each cost the same amount.How much did Julio pay for each video game?

6)

MidSchoolMath Pen Perimeter 2 of 2

Date PeriodName

How might this standard appear on a test?

Match each situation with the equation that represents the total amount paid, y.

b)

c)

d)

y = 1.50x + 0.75a)

y = 5x + 3

y = 3x + 5

y = 0.75x + 1.50

Jaqueline buys 4 bracelets and 2 necklaces. Each bracelet costs $8, and Jaqueline’s total is $70.

a. Write an equation that could be used to fi nd n, the cost of each necklace.

b. What is the cost of each necklace?

Jenae buys some scarves that are $14 each and 2 wallets that each cost $12. Jenae’s total is $94.

c. Write an equation that could be used to fi nd s, the number of scarves Jenae buys.

d. How many scarves did Jenae buy?

Check out my worked example #7

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