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THANK YOU FOR YOUR PURCHASE! The resources included in this purchase were designed and created by me. I hope that you find this resource helpful in your classroom. Please feel free to contact me with any questions as you implement this in your class. Maneuvering the Middle is an education blog with valuable tips for lesson planning, teacher organization, and math concepts in the middle school classroom. /ManeuveringTheMiddle /maneuveringthem @maneuveringthemiddle maneuveringthemiddle.com PLEASE Print and copy this resource for your personal classroom use only. Save this to both home and school computers. Only post this only for students on a password protected class website. PLEASE DO NOT Reproduce or distribute this resource to other colleagues. Post this on the internet in any form, including classroom/personal websites, network drives, or other sharing websites (i.e. Amazon Inspire, etc). Maneuvering the Middle LLC, 202-Present Products by Maneuvering the Middle, LLC may be used by the purchaser for their classroom use only. This is a single classroom license only. All rights reserved. If you wish to share this product with your team or colleagues, you may purchase additional licensing at a discounted rate. PAGE ONE

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STANDARDS EQUATIONS AND INEQUALITIES TEACHER GUIDE 6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. 6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. VOCABULARY & KEYWORDS < < > > = less than is fewer than is smaller than below value is included less than or equal to maximum at most is not more than is not greater than greater than or equal to minimum at least is not less than is not smaller than greater than is more than is larger than above value is not included equal is same COMMON MISTAKES & MISCONCEPTIONS Students may forget to flip the inequality symbol when they divide by a negative number. Students may not set up an equation or an inequality correctly based on a real-world situation. Students may struggle to solve problems because of rational number operations. Students may not use the correct inequality symbol or may not use the correct point (included or not included) when graphing their solution. Maneuvering the Middle LLC, 207

WARM -UP Name Date Pd. Coach Emanuel is trying to gain muscle. He starts 207 weighing 226 pounds. If he plans to lift weights and eat enough, then how many pounds must Coach Emanuel gain in order to be at least 250 pounds? 2. What is the value of x in this equation? 6x = 72 Maneuvering the Middle LLC, 207 EQUATIONS AND INEQUALITIES WARM -UP Name Date Pd. Coach Emanuel is trying to gain muscle. He starts 207 weighing 226 pounds. If he plans to lift weights and eat enough, then how many pounds must Coach Emanuel gain in order to be at least 250 pounds? 2. What is the value of x in this equation? 6x = 72 Maneuvering the Middle LLC, 207

CHEAT SHEET - A Solving equations Use INVERSE OPERATIONS to UNDO the equation. undo addition or subtraction undo multiplication or division isolate the variable check your work 6x=36 x=6 6(6)=36 Name Date Pd SAME STEPS as SOLVING EQUATIONS! inequalities To check your work, choose a value that is within the constraints of the inequality and plug in the number. If it is correct, then you should get a true statement. GRAPH the inequality statement on a number line to represent THE POSSIBLE SOLUTIONS. VALUE IS INCLUDED VALUE IS NOT INCLUDED Graphing inequalities 2x > 20 x > 0 CHECK 2() > 20 22 > 20 INEQUALITY VOCABULARY scientific notation Remember that each term can represent a different inequality symbol when writing inequalities. < < > > = less than is fewer than is smaller than below less than or equal to maximum at most is not more than is not greater than greater than or equal to minimum at least is not less than is not smaller than greater than is more than is larger than above equal is same Determine what is being solved for and choose a variable (number of rides, number of feet, etc). Determine the result of the situation (total cost, total height, difference in weight, etc). $3 per person total = 5 miles + x miles = cost total distance 3x 75 5 x 24 If it is not equal, then use the appropriate inequality symbol. Writing equations & inequalities Maneuvering the Middle LLC, 207

CHEAT SHEET - B Name Date Pd Solving equations Use to the equation. undo addition or subtraction undo multiplication or division isolate the variable check your work 6x=36 SAME STEPS as SOLVING EQUATIONS! inequalities To check your work, choose a value that is within the of the inequality and plug in the number. If it is correct, then you should get a true statement. the inequality statement on a number line to represent. 2x > 20 CHECK Graphing inequalities INEQUALITY VOCABULARY scientific notation Remember that each term can represent a different inequality symbol when writing inequalities. < < > > = Determine what is being solved for and choose a variable (number of rides, number of feet, etc). Determine the result of the situation (total cost, total height, difference in weight, etc). = + = If it is not equal, then use the appropriate inequality symbol. Writing equations & inequalities Maneuvering the Middle LLC, 207

CHEAT SHEET - C Solving equations Name Date Pd inequalities Graphing inequalities INEQUALITY VOCABULARY scientific notation Writing equations & inequalities Maneuvering the Middle LLC, 207

INSTRUCTIONS EQUATIONS AND INEQUALITIES CUT AND PASTE TO PREP Print and copy cut and paste activity for each student. Print and copy the cards for each student. Students will need scissors and glue. TO USE Students should cut the cards apart. Students should match each word problem to the equation, model, and solution or inequality, graph, and solution. Not all of the cards will be used. OTHER TIPS Have students show work on notebook paper and match their answers before gluing to avoid mistakes. This activity is flexible and can be done individually, in partners or in small groups. Maneuvering the Middle LLC, 207

CUT AND PASTE RECORDING SHEET Cut the cards apart. Then, glue the correct model and equation.. The sum of two angle 2. Determine the equation measures is 73.80 o. One and solve using the model angle has a measure of below. 44.25 o. What is x, the measure of the second $9.20 angle in degrees? x x x x x x Name Date Pd 3. Mrs. Martinez purchases three equally priced picture frames. The total was $44.25. What was the cost, x, of a picture frame? [EQUATION] [EQUATION] [EQUATION] [SOLUTION] [SOLUTION] [SOLUTION] 4. Caiden purchased a pair 5. Determine the equation 6. The cost of a meal was of tennis shoes and then used a coupon to save $5.00. The total cost and solve using the model below. split equally among six friends. Each friend paid $9.20. What was the after the coupon was total cost of the meal? $73.80. What was the x = cost of the pair of shoes before the coupon? [EQUATION] [EQUATION] [EQUATION] [SOLUTION] [SOLUTION] [SOLUTION] Maneuvering the Middle LLC, 207

Cut the cards apart. Then, glue the correct inequality and graphed solution. 7. Jasmine has $30 to spend at the state fair. The entrance fee is $8.00 and she will spend the remainder on tickets. How much money can Jasmine spend on tickets? 8. The school is raising money by selling wrapping paper. Each roll of paper earns the school $4.00. If the PTA would like to raise a minimum $600.00, then how many rolls of wrapping paper must be sold? 9. Drake must practice the trombone for at least 30 minutes a day. So far, he has practiced for 8 minutes. How many minutes does Drake still need to practice the trombone? [INEQUALITY] [INEQUALITY] [INEQUALITY] [GRAPH] [GRAPH] [GRAPH] 0. In order to swim at the. The auditorium at a 2. Jerod takes some lake the water level must local high school seats money to the mall. He be above 0 feet. Currently, the water level is 8.5 feet. How many feet must the water level rise in order to swim? less than 600 people. The student body will be split into four assemblies with an equal number of people. How many members of the student body are there? spends $8.50 on a snack. He would like to keep a minimum of $0.00 in his pocket at all times. How much money did Jerod take to the mall? [INEQUALITY] [INEQUALITY] [INEQUALITY] [GRAPH] [GRAPH] [GRAPH] Maneuvering the Middle LLC, 207

A B C x + 44.25 = 73.80 x + 5 = 73.80 x 5 = 73.80 D E F 3x = 44.25 x 44.25 = 73.80 G H I x + 2 = 6 x 6 x 3 = 44.25 = 9.20 6x = 9.20 J K L x = 58.8 x = 4 x = 4.75 M N O x = 88.8 x = 29.55 x = 5.2 P Q R x = 32.75 x = 8.05 x = 3.2 S T U x + 8.5 > 0 4x > 600 4x < 600 V W x X x > 22 < 600 x 8.5 > 0 4 Y Z AA x + 8 > 30 x + 8.5 < 0 x + 8 < 30 BB CC DD x >.5 x < 2400 x <.5 EE FF GG x > 50 x < 22 x 8 > 30 HH II JJ x < 22 x > 2400 x > 8.5 Maneuvering the Middle LLC, 207

QUICK CHECK Name Date Pd. Ms. Sung budgets a maximum of $320 per month for groceries. She grocery shops 4 times a month. Which inequality can be used to find the possible values of x, the amount she can spend at the grocery store during each shopping trip? A. 4 + x < 320 B. 4x 320 C. 4x 320 D. 4 + x > 320 2. If x = 5, then which inequality is true? F. 2x 2 G. x 2 < 7 H. 2x > 2 J. x 7 > 2 3. The entrance fee to the children s museum was a total of $46.00 for eight tickets. The model below shows the relationship. What was the entrance fee for one ticket?. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 0. Use the grid below. $46.00 t t t t t t t t A. $5.75 B. $5.25 C. $6.25 D. $7.00 4. An equation is modeled below using algebra tiles. Which value of x makes the equation true? x = F. x = 7 G. x = 3 H. x = -7 J. x = -3 5. Margo must sell at least 38 tubs of cookie dough to support the student council fundraiser. She has already sold 9 tubs of cookie dough. Which inequality best represents the number of tubs of cookie dough Margo still needs to sell? A. x + 9 > 38 B. x + 9 38 C. x + 9 < 38 D. x + 9 38 Maneuvering the Middle LLC, 207

6. An elevator has a maximum weight of 300 pounds. Each pallet of boxes weighs 25 pounds. Which of the following number lines best represents the solution to the inequality? 25x 300 F. G. 0 4 8 2 6 20 22 H. J. 0 4 8 2 6 20 22 0 4 8 2 6 20 22 0 4 8 2 6 20 22 7. Which situation best represents the equation below? x 5 = 60 A. Sandy collects sea shells. She had 60 shells, but then she gave away 5 shells. How many shells does Sandy have in her collection? B. Mr. Yung is 5 years younger than his brother. His brother is 60 years old. How old is Mr. Yung? C. The school band is selling raffle tickets. They have already sold 5 tickets and have 60 remaining with how many raffle tickets did they begin? D. Daniella measures a 5 inch length of rope and attaches it to another length of rope. Together the two ropes are 60 inches in length. How long was the piece of rope that Daniella attached? 8. The number line below represents the solution to which inequality? 0 2 4 6 8 0 2 F. x + 8 5 G. x + 8 5 H. x 8 5 J. x 8 5 9. Two piggy banks have a sum of $36.50. The first piggy bank has $3.75. How much does the second piggy bank have in it? A. $22.75 B. $50.25 0. What is the value of x in this equation? 8x = 66 Use the bubbles in the answer section to mark your answer. C. $2.65 D. $50.88 Maneuvering the Middle LLC, 207

ANSWER KEYS Maneuvering the Middle LLC, 207

WARM -UP Name Answer Key Date Pd. Coach Emanuel is trying to gain muscle. He starts 207 weighing 226 pounds. If he plans to lift weights and eat enough, then how many pounds must Coach Emanuel gain in order to be at least 250 pounds? 2. What is the value of x in this equation? -6x = 72 x 24 x = 2 Maneuvering the Middle LLC, 207 EQUATIONS AND INEQUALITIES WARM -UP Name Date Pd. Coach Emanuel is trying to gain muscle. He starts 207 weighing 226 pounds. If he plans to lift weights and eat enough, then how many pounds must Coach Emanuel gain in order to be at least 250 pounds? 2. What is the value of x in this equation? -6x = 72 Maneuvering the Middle LLC, 207

CUT AND PASTE RECORDING SHEET Cut the cards apart. Then, glue the correct model and equation.. The sum of two angle 2. Determine the equation measures is 73.80 o. One and solve using the model angle has a measure of below. 44.25 o. What is x, the measure of the second $9.20 angle in degrees? x x x x x x KEY Name Date Pd 3. Mrs. Martinez purchases three equally priced picture frames. The total was $44.25. What was the cost, x, of a picture frame? A I D N R L 4. Caiden purchased a pair 5. Determine the equation 6. The cost of a meal was of tennis shoes and then used a coupon to save $5.00. The total cost and solve using the model below. split equally among six friends. Each friend paid $9.20. What was the after the coupon was total cost of the meal? $73.80. What was the x = cost of the pair of shoes before the coupon? C G H M K O Maneuvering the Middle LLC, 207

Cut the cards apart. Then, glue the correct inequality and graphed solution. 7. Jasmine has $30 to spend at the state fair. The entrance fee is $8.00 and she will spend the remainder on tickets. How much money can Jasmine spend on tickets? 8. The school is raising money by selling wrapping paper. Each roll of paper earns the school $4.00. If the PTA would like to raise a minimum $600.00, then how many rolls of wrapping paper must be sold? 9. Drake must practice the trombone for at least 30 minutes a day. So far, he has practiced for 8 minutes. How many minutes does Drake still need to practice the trombone? AA T Y FF EE V 0. In order to swim at the. The auditorium at a 2. Jerod takes some lake the water level must local high school seats money to the mall. He be above 0 feet. Currently, the water level is 8.5 feet. How many feet must the water level rise in order to swim? less than 600 people. The student body will be split into four assemblies with an equal number of people. How many members of the student body are there? spends $8.50 on a snack. He would like to keep a minimum of $0.00 in his pocket at all times. How much money did Jerod take to the mall? S W X BB CC JJ Maneuvering the Middle LLC, 207

QUICK CHECK Name Date Pd. Ms. Sung budgets a maximum of $320 per month for groceries. She grocery shops 4 times a month. Which inequality can be used to find the possible values of x, the amount she can spend at the grocery store during each shopping trip? A. 4 + x < 320 B. 4x C. 4x 320 D. 4 + x > 320 2. If x = 5, then which inequality is true? F. -2x 2 G. x 2 < 7 H. 2x > 2 J. x 7 > 2 3. The entrance fee to the children s museum was a total of $46.00 for eight tickets. The model below shows the relationship. What was the entrance fee for one ticket? A. $5.75 B. $5.25 C. $6.25 D. $7.00 4. An equation is modeled below using algebra tiles. Which value of x makes the equation true? x = $46.00 t t t t t t t t. A B C D 2. F G H J 3. A B C D 4. F G H J 5. A B C D 6. F G H J 7. A B C D 8. F G H J 9. A B C D 0. Use the grid below. 8 2 5 F. x = 7 H. x = 3 G. x = -7 J. x = -3 5. Margo must sell at least 38 tubs of cookie dough to support the student council fundraiser. She has already sold 9 tubs of cookie dough. Which inequality best represents the number of tubs of cookie dough Margo still needs to sell? A. B. C. D. Maneuvering the Middle LLC, 207