CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. Lesson to be used by EDI-trained teachers only. READY TO TEACH SM EDI ® Lessons ©2012 All rights reserved. What are we going to learn? CFU Students, you already know how to solve one-step equations. Now we will solve two-step equations. Make Connection 1 says or tells Vocabulary Inverse Operations + and – and Solve the one-step equations. Learning Objective Activate Prior Knowledge We will solve two-step equations. An equation states 1 two expressions are equal. Inverse operations are operations that undo each other. Equation x + 7 = 9 expression 1. x + 7 = 9 − 7 x = 2 2. x + 3 = 7 − 3 x = x = 16 4 x = x = 4 2 x = 2 2
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. A two-step equation contains 2 two operations. Solving Two-Step Equations Concept Development 2 has within it 3 needs (synonym) Vocabulary 2 x 3 7 addition multiplication subtraction division 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. 2 x 3 7 − 3 2 x 0 4 22 x 2 1Inverse OperationBalance1 The solution is the value of the variable that makes the equation true. Checking a Solution 2 x 3 7 2(2) 3 7 Solution ? True 7 7 x 2 2 x 3 7 2(4) 3 7 NOT a Solution ? False 11 7 x 4 2 x 3 7 Flashcards: Inverse Operations + and – and CFU 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 )? Addition & Division 1Inverse Operation Balance1 2Inverse Operation Balance2 Inverse Operation 2 Balance 2 Animated
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate 4 the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations a 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 Skill Development/Guided Practice 4 separate Vocabulary 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 Flashcards: Steps to Check a Solution 1. What is the unknown value of x in the two-step equation? 2. What is the unknown value of x in the two-step equation? x x 15 “x = 15 is the solution because it makes the equation true.”“x = 2 is the solution because it makes the equation true.” ? ? ? ? Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Skill Development/Guided Practice (continued) Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations a How did I/you connect the problem to the given two- step 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 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. A gym membership charges a flat fee 5 to sign up, as well as a monthly rate. Jessica paid $50 to sign up and $25 each month. If Jessica has paid $175 to the gym, how long has she been a member? 25 m + 50 = 175 −50 25 m = m = 5 If Jessica has paid $175 to the gym, she has been a member for five months. 25( ) + 50 = (5) + 50 = = = 175 ? ? If Maurice has paid $36 to the book club, he has been a member for three years. 4. A book club membership charges a flat fee to sign up, as well as an annual 6 rate. Maurice paid $15 to sign up and $7 each year. If Maurice has paid $36 to the book club, how long has he been a member? 7 y + 15 = 36 −15 7 y = y = 3 7( ) + 15 = 36 7(3) + 15 = = = 36 ? ? 5 one-time payment 6 yearly Vocabulary Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Skill Development/Guided Practice (continued) 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? w l = 20 cm 2 w + 2(20) = 72 2 w + 40 = 72 −40 2 w = w = 16 The width of the computer monitor is 16 cm. 2( ) + 40 = 722(16) + 40 = = = 72 ? ? 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? l = 2 in w 2 w + 2 l = P 2 w + 4 = 10 −4 2 w = 6 22 w = 3 2 ( ) + 4 = 102(3) + 4 = = = 10 ? ? The width of the cell phone screen is 3 in. w = 16 cm w = 3 in 2 w + 2(2) = 10 2 w + 2 l = P Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations a How did I/you connect the problem to the given two- step 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 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 Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Skill Development/Guided Practice (continued) 7. A middle school hosted a fall festival to raise money for both grades in the school. The seventh 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 altogether? m = 2200 The fall festival at the middle school earned $2,200. ? 1100 − 750 = 350 ? 350 = m = 1725 Maria’s grandmother gave Maria and her sisters $1,725 to share. ? 575 − 550 = 25 ? 25 = 25 Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations a How did I/you connect the problem to the given two- step 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 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 Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Solving two-step equations will help you solve problems in other classes. Solving two-step equations will help you do well on tests. 1 Does anyone else have another reason why it is relevant to solve two-step equations? (Pair-Share) Why is it relevant to solve two-step equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU 3 Relevance 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. In chemistry, we use equations to show chemical reactions. The equation below shows methane burning with oxygen. CH O 2 CO H 2 O Sample Test Question: 43. Joan needs $60 for a class trip. She has $32. She can earn $4 an hour mowing lawns. If the equation shows this relationship, how many hours must Joan work to have the money she needs? 4h + 32 = 60 A 7 hours B 17 hours C 23 hours D 28 hours Solving two-step equations will help you solve real-world problems. 2 B Street Bikes rents bicycles for $16 plus $4 per hour. Eduardo paid $36 to rent a bicycle. For how many hours did he rent the bicycle? 4 h 16 36
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. What did you learn today about solving two-step equations? (Pair-Share) Summary Closure Constructed Response Closure 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. Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations a 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? w l = 2 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 w + 4 = 62(1) + 4 = = 6 6 = 6 ? ? w = 1 m 2 w + 2 l = P Write an example of a two-step equation. How do you know it is an example of a two-step equation? Inverse Operations + and – and Now Check! Skill Closure
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Independent Practice Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations 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. A cell phone service charges a flat fee for activation 1, as well as a monthly rate. Petra paid $145 to sign up and $50 each month. If Petra has paid $395, how long has she had her cell phone service? 1. What is the unknown value of x in the two-step equation?2. What is the unknown value of x in the two-step equation? “ x = -12 is the solution because it makes the equation true.”“ x = -3 is the solution because it makes the equation true.” 3 x – 12 = x x -3 3x3x If Petra has paid $395, she has had her cell phone service for five months. 50 m = 395 − m = m = 5 50(5) = = = 395 ? ? 1 start Vocabulary Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Independent Practice (continued) 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? The width of the football field is 160 ft. w l = 360 ft 2 w + 2 l = P 2 w = 1040 − w = w = 160 2(160) = = = 1040 ? ? Home Visitor w = 160 ft 2 w + 2(360) = 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? m = 175 Bill and his friends earned $175 doing chores. ? 35 − 15 = 20 ? 20 = 20 Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations 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 Now Check!
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. 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? The width of the fence must be 30 m. l = 55ft 2 w + 2 l = P 2 w = 170 − w = w = 30 2(30) = = = 170 ? ? Home Visitor w = 30ft 2 w + 2(55) = In basketball, each basket scores two points and free throws one point. Chandra made seven free throws. If she scored a total of 23 points, how many baskets did she make? If Chandra made seven free throws and scored 23 points, she made eight baskets. Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations 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 Now Check! Periodic Review 1 − 7 2 b = b = 8 2(8) + 7 = = = 23 ? ? 2 b + f = 23 2 b + 7 = 23
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. 1. A rental car charges an initial1 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? 2. In basketball, each basket scores two points and free throws one point. Troy made eleven free throws. If he scored a total of 19 points, how many baskets did he make? Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations 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 Periodic Review 2 Charles rented the car for seven days. 34 d = 363 − d = d = 7 34(7) = = = 363 ? ? 1 beginning If Troy made eleven free throws and scored 19 points, he made four baskets. 2 b + 11 = 19 − 11 2 b = 8 22 b = 4 2(4) + 11 = = = 19 ? ? 2 b + f = 19
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. 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? Read the problem and identify (underline) important information. Connect the problem to the given two-step equation. Isolate the term with the variable. Solve for the variable. Check and interpret the solution. Hint: Answer the question. Solve two-step equations 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 Periodic Review ● 4 4 ● m = 320 Janine and her brothers were given $320. ? 80 − 75 = 5 ? 5 = 5 The length of the flag must be 19 ft. w = 10 ft 2 w + 2 l = P l = 58 − 20 2 l = l = (19) = = = 58 ? ? l = 19 ft 2(10) + 2 l = 58
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Inverse Operations + and – and 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. 1. A rental car charges an initial 1 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? 2. In basketball, each basket scores two points and free throws one point. Troy made eleven free throws. If he scored a total of 19 points, how many baskets did he make? Which of the following statements is true? How do you know? The inverse operation subtraction ( ) will be used to solve this problem. Subtraction (–) will be the first inverse operation to solve this problem. The equation used to solve this problem is The meaning of the solution to this problem is the amount of money he earned. Yes/No 34 d = 363. Yes/No Which of the following statements is true? How do you know? The inverse operation addition ( ) will be used to solve this problem. The equation used to solve this problem is The meaning of the solution to this problem is the total number of points that Troy scored. Yes/No 2 b + 11 = b + f = beginning Vocabulary Access Common Core
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. 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. 1. 4x 5 In your own words, describe why equations #1 and #2 have the same solution? ____________________________________________________________________________________________________________________________ ______________________________________________________________ 2. 4x 11 13 Inverse Operations + and – and Access Common Core
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. 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. 1. An oversized American 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? Which of the following statements is true? How do you know? The inverse operation subtraction ( ) will be used to solve this problem. The length of the American flag will be 19 ft. The equation used to solve this problem is The meaning of the solution to this problem is the length in feet of the flag. 2. To ensure a swimming pool is safe, a fence is being built to surround it. To surround the pool, the fence must be 170 m long and have a length of 55 m. How wide does the fence need to be to surround the entire pool? l = 58. Which of the following statements is true? How do you know? The meaning of the solution to the problem is the distance around the fence. The width of the fence will be 60 m. The inverse operation addition (+) will be used to solve the problem. The width of the fence will be 110 m. Yes/No Inverse Operations + and – and Access Common Core
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Inverse Operations) What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know? SubtractionDivisionAdditionMultiplication Return to Concept A two-step equation contains two operations. A two-step equation requires two inverse operations to solve.
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Inverse Operations) Return to Concept 3 x 4 13 What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know? SubtractionMultiplicationAdditionDivision A two-step equation contains two operations. A two-step equation requires two inverse operations to solve.
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Inverse Operations) Return to Concept 6 4 x 14 What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know? AdditionMultiplicationSubtractionDivision A two-step equation contains two operations. A two-step equation requires two inverse operations to solve.
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Inverse Operations) Return to Concept What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know? AdditionDivisionSubtractionMultiplication A two-step equation contains two operations. A two-step equation requires two inverse operations to solve.
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Checking Solution) Check the solution to the two-step equations. The solution is the value of the variable that makes the equation true. Is 20 the value of x that makes the equation true? “ 20 _____ the value of x that makes the equation true because _________.” Whiteboard 1 replace 2 explain Vocabulary Substitue 1 the given solution for the variable. Simplify the equation. Interpret 2 the given solution. “___ is/is not the solution because __________.” Solve two-step equations 1 2 3
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Checking Solution) Check the solution to the two-step equations. The solution is the value of the variable that makes the equation true. Is 12 the value of x that makes the equation true? “ 12 _____ the value of x that makes the equation true because _________.” Whiteboard 1 replace 2 explain Vocabulary Substitue 1 the given solution for the variable. Simplify the equation. Interpret 2 the given solution. “___ is/is not the solution because __________.” Solve two-step equations 1 2 3
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Checking Solution) 6 4 x 14 Check the solution to the two-step equations. The solution is the value of the variable that makes the equation true. Is 5 the value of x that makes the equation true? “ 5 _____ the value of x that makes the equation true because _________.” Whiteboard 1 replace 2 explain Vocabulary Substitue 1 the given solution for the variable. Simplify the equation. Interpret 2 the given solution. “___ is/is not the solution because __________.” Solve two-step equations 1 2 3
CA 7 th Grade Algebra and Functions 4.1 (3Q) Solve two-step equations. Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved. Flash Cards (Checking Solution) Check the solution to the two-step equations. The solution is the value of the variable that makes the equation true. Is 4 the value of x that makes the equation true? 7 x 6 24 “ 4 _____ the value of x that makes the equation true because _________.” Whiteboard 1 replace 2 explain Vocabulary Substitue 1 the given solution for the variable. Simplify the equation. Interpret 2 the given solution. “___ is/is not the solution because __________.” Solve two-step equations 1 2 3