# What are we going to do? CFU Students, you already know how to solve equations. Now, we will solve two-step equations. Make Connection An equation states.

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What are we going to do? CFU Students, you already know how to solve equations. Now, we will solve two-step equations. Make Connection An equation states 1 two expressions are equal. Inverse operations are operations that undo each other. 1 says or tells Vocabulary Inverse Operations + and – ● and ÷ Learning Objective Activate Prior Knowledge We will solve two-step equations. Solve the one-step equations. Equation expression x  7  9 1. x + 7 = 9 − 7 x = 2 2. x + 3 = 7 − 3 x = 4 3. 4 x = 16 4 x = 4 4 4. 2 x = 4 2 x = 2 2 7.EE.4; 6.EE.7 Solve real-world and mathematical problems by writing and solving equations Name: __________________ Wednesday, February 19, 2014

Which of the following is an example of a two-step equation ? How do you know? A 5 x  6 B 5 x  4  6 C x  4  6 Which two inverse operations would be used to solve the two-step equation 5 x  4  6 ? How do you know? What is the difference between the solution ( x  2 ) and non-solution ( x  4 )? CFU 2 has within it 3 needs (synonym) Vocabulary Concept Development A two-step equation contains 2 two operations. 2 x  3  7 multiplication addition  5  1 x4x4 subtraction division Inverse Operations + and – ● and ÷ Solving Two-Step Equations A two-step equation requires 3 two inverse operations to solve for the variable. To keep an equation balanced, inverse operations must be done on both sides of the equation. 22 2 x  3  7  3  3 2 x  4 x  2 Inverse Operation Balance Solution Checking a Solution The solution is the value of the variable that makes the equation true. SolutionSolution x  2x  2 2 x  3  7 2(2)  3  7 4  3  7 7  7 True! NOT a Solution Solution x  4x  4 2 x  3  7 2(4)  3  7 8  3  7 11  7 False! Flashcards Inverse Operations

Isolate 2 the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret 3 the solution. Hint: Answer the question. Solve two-step equations. 1 2 3 2 separate 3 explain Vocabulary How did I/you isolate the term with the variable? How did I/you solve for the variable? How did I/you check the solution? CFU 1 2 3 Skill Development/Guided Practice 1.________________________________ 2. ________________________________  3  -2 x2x2 +3 1 22 x 2 x = 2 is the solution because it makes the equation true.  6  -3 x5x5 +6 3 5 5 x 15 x = 15 is the solution because it makes the equation true. A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. Inverse Operations + and – ● and ÷

3.Jessica paid a \$50 flat fee 5 to sign up for a gym and \$25 each month. If Jessica has paid \$175 to the gym, how long has she been a member? 25 m  50  175________________________________ 4. Maurice paid \$15 to sign up for a book club and a \$7 annual 6 rate. If Maurice has paid \$36 to the book club, how long has he been a member? 7 y  15  36 ________________________________ Skill Development/Guided Practice (continued) Read the problem and identify (underline) important information. Connect the problem to the given equation. Isolate the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret the solution. Hint: Answer the question. Solve two-step equations. 1 2 3 4 a A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. How did I/you connect the problem to the given equation. How did I/you isolate the term with the variable? How did I/you solve for the variable? How did I/you check the solution? CFU 2 1a 3 4 Inverse Operations + and – ● and ÷ 5 (flat fee) one-time payment 6 yearly Vocabulary − 50 25 m  125 25 m  5 25( ) + 50 = 175 25(5) + 50 = 175 125 + 50 = 175 175 = 175 ? ? If Jessica has paid \$175 to the gym, she has been a member for five months. − 15 7 y  21 77 y  3 7( ) + 15 = 36 7(3) + 15 = 36 21 + 15 = 36 36 = 36 ? ? If Maurice has paid \$36 to the book club, he has been a member for three years.

Skill Development/Guided Practice (continued) Read the problem and identify (underline) important information. Connect the problem to the given equation. Isolate the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret the solution. Hint: Answer the question. Solve two-step equations. 1 2 3 4 a A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. How did I/you connect the problem to the given equation. How did I/you isolate the term with the variable? How did I/you solve for the variable? How did I/you check the solution? CFU 2 1a 3 4 Inverse Operations + and – ● and ÷ 5. The length of a rectangular computer monitor is 20 cm. The perimeter of the monitor is 72 cm. What is the width of the computer monitor? 2 w  2 l  P________________________________ 6. The length of a rectangular cell phone screen is 2 in. The perimeter of the cell phone screen is 10 in. What is the width of the cell phone screen? 2 w  2 l  P ________________________________ l = 20 cm w 2 w + 2(20) = 72 2 w + 40 = 72 − 40 2 w = 32 22 w = 16 The width of the computer monitor is 16 cm. 2( ) + 40 = 722(16) + 40 = 72 32 + 40 = 72 72 = 72 ? ? = 16 cm w 2 w + 2(2) = 10 2 w + 4 = 10 − 4 2 w = 6 22 w = 3 The width of the cell phone screen is 3 in. 2( ) + 4 = 102(3) + 4 = 10 6 + 4 = 10 10 = 10 ? ? = 3 in l = 2 in

Flash Cards (Inverse Operations) Inverse Operations + and – ● and ÷ What two inverse operations would be used to solve the equation? Addition & Multiplication  3  2 x3x3 A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true.

Flash Cards (Inverse Operations) Inverse Operations + and – ● and ÷ What two inverse operations would be used to solve the equation? 3 x  4   13 Addition & Division A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true.

Flash Cards (Inverse Operations) Inverse Operations + and – ● and ÷ What two inverse operations would be used to solve the equation? 6  4 x  14 Subtraction & Division A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true.

Flash Cards (Inverse Operations) Inverse Operations + and – ● and ÷ What two inverse operations would be used to solve the equation? Subtraction & Multiplication 3   2 x3x3 Back to Concept Dev A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true.

Skill Development/Guided Practice (continued) 7. A middle school hosted a fall festival to raise money for both grades in the school. The 7 th grade class used their half of the money to buy a \$750 chemistry set. After buying the chemistry set, the 7 th graders had \$350 left over. How much money did the school earn at the fall festival?________________________________ 8. Maria’s grandmother gave Maria money to share with her two sisters. The three girls split the money evenly and Maria used her share to buy a computer that cost \$550. After buying the computer, she had \$25 leftover. How much money did Maria’s grandmother give Maria and her sisters? \ ________________________________ m2m2  750  350  750 m2m2  1100 2  2 m  2200 ____ 2  750  350 2200 1100  750  350 350  350 The fall festival at the middle school earned \$2,200. m3m3  550  25  550 m3m3  575 3  3 m  1725 ____ 3  550  25 1725 575  550  25 25  25 Maria’s grandmother gave Maria and her sisters \$1,725 to share. How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5

Read the problem and identify (underline) important information. Connect the problem to the given equation. Isolate the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret the solution. Hint: Answer the question. Solve two-step equations. 1 2 3 4 a What did you learn today about solving two-step equations? (Pair-Share) Use words from the word bank. Skill Closure Access Common Core Summary Closure Word Bank two-step equation inverse operation solution isolate A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. Inverse Operations + and – ● and ÷ 1.The length of the basketball backboard is 2 m. The perimeter of the backboard is 6 m. What is the width of the basketball backboard? 2 w  2 l  P _________________________ l = 2 m w = 1 m 2 w + 2(2) = 6 2 w + 4 = 6 − 4 2 w = 2 22 w = 1 The width of the basketball backboard is 1 m. 2( ) + 4 = 62(1) + 4 = 6 2 + 4 = 6 6 = 6 ? ? Which two inverse operations would be used to solve the equation? Explain your answer. 6 z  36  60 The two inverse operations used would be addition and division because they are the inverse of subtraction and multiplication.

Independent Practice A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. Inverse Operations + and – ● and ÷ 1.________________________________ 2. ________________________________ -8 -3 44 x -12 x = -12 is the solution because it makes the equation true.  3 x – 12 =  3 +12 9 x -3 3x3x x = -3 is the solution because it makes the equation true. Isolate the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret the solution. Hint: Answer the question. Solve two-step equations. 1 2 3

Read the problem and identify (underline) important information. Connect the problem to the given equation. Isolate the term with the variable. Hint: Use inverse operations. Solve for the variable. Hint: Use inverse operations. Check and interpret the solution. Hint: Answer the question. Solve two-step equations. 1 2 3 4 a A two-step equation contains two operations. A two-step equation requires two inverse operations to solve. To keep an equation balanced, inverse operations must be done on both sides of the equation. The solution is the value of the variable that makes the equation true. Inverse Operations + and – ● and ÷ 3.Petra paid \$145 for activation 1 of a cell phone and pays \$50 monthly. If Petra has paid \$395, how long has she had her cell phone service? 50 m  145  395________________________________ 4. The length of a football field is 360 ft. The perimeter of the football field is 1040 ft. What is the width of the football field? 2 w  2 l  P ________________________________ 1 start Vocabulary − 145 50 m  250 50 m  5 50(5) + 145 = 395 250 + 145 = 395 395 = 395 ? ? If Petra has paid \$395, she has had her cell phone service for 5 months. w 2 w + 2(360) = 1040 2 w + 720 = 1040 − 720 2 w = 320 22 w = 160 The width of a football field is 160 ft. 2( ) + 720 = 10402(160) + 720 = 1040 320 + 720 = 1040 1040 = 1040 ? ? 160 ft = l = 360 feet Independent Practice (continued)

5. Bill and his four friends earned money doing chores for their neighbors. Bill spent \$15 of his share on a new book and had \$20 left. How much money did Bill and his friends earn doing chores? ________________________________ m5m5  15  20  15 m5m5  35 5  5 m  175 ____ 5  15  20 175 35  15  20 20  20 Bill and his friends earned \$175 doing chores.

Periodic Review 1 Access Common Core 1.To ensure a swimming pool is safe, a fence is being built to surround it. To surround the pool, the perimeter of the fence must be 170 m and the length 55 m. How wide does the fence need to be to surround the entire pool? 2 w  2 l  P__________________________________ 2. In basketball, each basket scores two points and free throws one point. Chandra made 7 free throws. If she scored a total of 23 points, how many baskets did she make? 2 b  f  23 _______________________________________ The width of the fence must be 30 m. If Chandra made 7 free throws and scored 23 points, she made 8 baskets. Describe and correct the error each student made below. Jami: 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus? Julio: Imani bought a magazine for \$5 and four erasers. She spent a total of \$25. How much did each eraser cost? Juliann: Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin? Jami did not use the correct inverse operation. She should have subtracted 7 instead of adding. Julio did not use the correct inverse operation. He should have divided by 4 instead of multiplying. Juliann set up the equation incorrectly. The equation should be c2c2  16  36.

Periodic Review 2 Access Common Core 1.A rental car charges an initial payment of \$125, plus \$34 every day the car is rented. Charles rents a car and pays \$363. How long did Charles rent the car? 34 d  125  363__________________________________ 2. In basketball, each basket scores two points and free throws one point. Troy made 11 free throws. If he scored a total of 19 points, how many baskets did he make? _______________________________________ Charles rented the car for seven days. If Troy made 11 free throws and scored 19 points, he made four baskets. 1 beginning Vocabulary 1. Malinda has a collection of 34 mugs. When packing to move, she put the same number of mugs in each of the first 5 boxes and 4 mugs in the last box. How many mugs were in each of the first 5 boxes? Choose Yes or No to indicate whether each statement is true or false. AThe inverse operation of subtraction (  ) will be used to solve this problem. BThe equation used to solve this problem is 5 b  4  34. CThe solution to the equation represents the number of mugs Malinda has. DThe solution to the equation is b  6. O Yes O No

Access Common Core 3.It took Sharon 85 minutes to wash three cars. She spent the same amount of time on each car. She also spent 10 minutes putting everything away. How long was Sharon washing each car? Choose Yes or No to indicate whether each statement is true or false. AThe inverse operation of addition (  ) will be used to solve this problem. BThe equation used to solve this problem is 3 m  10  85. CThe solution to the equation represents the amount of time Sharon spent washing each car. DThe solution to the equation is m  10. O Yes O No 2.Susan bought 7 reams of paper at the store. The tax on her purchase was \$2. She paid a total of \$30. How much did each ream of paper cost before tax? AThe equation used to solve this problem is 2 r  7  30. BThe inverse operation of subtraction (  ) will be used to solve this problem. CThe solution to the equation represents the number of reams of paper Susan bought. DThe solution to the equation is r  2. O Yes O No

Periodic Review 3 Access Common Core 1.Janine and her three brothers are given spending money to share. Janine sets \$75 aside to save, and spends the other \$5 on lunch that afternoon. How much money were Janine and her brothers given?__________________________________ 2. An oversized America flag is created to hang above the fence of a softball field. The flag must have a width of 10 ft. and a perimeter of 58 ft. What must the length of the American flag be? ______________________________ Janine and her brothers were given \$320. The length of the flag must be 19 ft. Match each word problem to the equation that can be used to solve it. 1.Carrie had \$32 when she got to the carnival. After riding 6 rides, she had \$20 left. What is the price of each ride? 32  6 x  20 6 x  32  20 2.Chuck jogged the same distance on Tuesday and Friday, and 8 miles on Sunday, for a total of 20 miles for the week. What is the distance Rick jogged on Tuesday and Friday? 2 x  8  20 2 x  20  8 3.Jenny wants to save \$900 to go to Puerto Rico. She now has \$180. If she saves \$45 a week, how many more weeks will it take to have \$900 saved? 45 x  180  900 45 x  180  900 4. Brian had \$26 when he went to the fair. After playing 7 games, he had \$5 left. Find the price for each game. 26  7 x  5 26  5 x  7

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