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## We will solve one-step equations using the

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**Learning Objective**CALIFORNIA STANDARD: 6.AF 1.1 Write and Solve One-Step Linear Equations in One Variable. Inverse Operations We will solve one-step equations using the properties of addition, subtraction, multiplication, and division. + and – What are we going to learn? What does solve mean? Solve means __________. CFU and Activate Prior Knowledge Inverse operationsare operations that undo each other. Think about PEMDAS. What are the operations ? Which operations are grouped together? What operation would undo the change in value? 1. 6 + 2 = 8 2. 10 - 3 = 7 - + 8 2 = 6 7 3=10 Students, you already know how to use inverse operations to undo a change in value. Now, we will solve one-step equations using inverse operations. Make Connection 3. 4. 43=12 15 5 =3 123=4 3 5 =15**Concept Development**Inverse Operations A one-step equation contains2one operation. A one-step equation requires3one inverse operation to solve for the variable. • 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. addition + and – x x+ 2 = 3 = 1 4 division and CFU 2 CFU 1 Which inverse operation would be used to solve the one-step equation 4x= 8? How do you know? A Multiplication B Division Which inverse operation would be used to solve the one-step equation x-4= 6? How do you know? A Addition B Subtraction What is the difference between the solution (x= 1) and the non-solution (x= 4)? Go to Skill Dev 1 Go to Skill Dev 2 Flashcards Inverse Operations Solving One-Step Equations x+ 2 =3 Inverse Operation Balance Inverse Operation Balance x+ 0 = 1 Solution (4) x = 1 = 1 x=4 x 4 4 = 1 4 ? ? (1) + 2 =3 (4) + 2 = 3 ? 2 has within it 3 needs (synonym) Vocabulary True 1=1 NOTa Solution Solution x+ 2 = 3 x=1 x= 4 x+ 2 = 3 3=3 True 6 = 3 False**Concept Development (Clarification and CFU)**Inverse Operations A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. + and – and The solutionis the value of the variable that makes the equation true. CFU Why is 2 subtracted on both sides of the equation? Why is 1 the solution to the equation x+ 2 = 3? x+ 2 = 5 - 2 - 2 x= 3 3+ 2 = 5 x WE WANT TO ISOLATE THE VARIABLE TERM (X) . x x x**Skill Development/Guided Practice I**Inverse Operations A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. + and – The solutionis the value of the variable that makes the equation true. and How did I/you connect the problem to the equation? How did I/you solve for the variable? How did I/you interpret the solution? CFU Solve one-step equations. 1 Back to Concept Dev Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret4 the solution. Hint: Answer the question. 1 2 2 3 3 m + 7 = 10 m+ 7 =10 c+ 3 =8 c + 3 = 8 3 + 7 = 10 5 + 3 = 8 - 7 - 7 - 3 - 3 10 = 10 8 = 8 m= 3 c= 5 Samuel was given ________________ today. Isabella needs to add __________________. $3 5 cups of sugar m+ 5 =8 m+ 4 = 11 m+ 5 = 8 m+ 4 =11 3 + 5 = 8 7 + 4 = 11 - 5 - 5 - 4 - 4 8= 8 11 = 11 4 explain (synonym) Vocabulary m= 3 m= 7 Jessie started with _____________________. Shannon started with __________________. 3 marbles $7**Skill Development/Guided Practice 2**Inverse Operations A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. + and – The solutionis the value of the variable that makes the equation true. and How did I/you connect the problem to the equation? How did I/you solve for the variable? How did I/you interpret the solution? CFU Solve one-step equations. 1 Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. 1 2 2 3 3 2b=12 6b=24 2b = 12 6b = 24 2 2 2(6) = 12 6 6 6(4) = 24 12 = 12 24 = 24 b= 6 b= 4 Miguel can buy ______________________. 6 binders She has ______________________. 4 boxes of pencils m m = 7 = 6 4 3 4 ● ● 4 3 ● ● 3 m= 24 m= 21 6 = 6 7 = 7 Isabella gave out ______________________. 24 muffins Ricky and his friends earned _____________. $21**Relevance**• 5x – 6 = 4 • + 6 + 6 • 5x = 10 • 5 5 • x = 2 A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. The solutionis the value of the variable that makes the equation true. Solving one-step equations will help you solve more complex equations. 1 2 Solving one-step equations will help you do well on tests. Sample Test Question: 37. What value of k makes the following equation true? k 3 = 36 A 108 B 98 C 39 D 12 Does anyone else have another reason why it is relevant to solve one-step equations? (Pair-Share) Why is it relevant to solve one-step equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? CFU**Inverse Operations**A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. + and – The solutionis the value of the variable that makes the equation true. and Skill Closure Solve one-step equations. Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. 1 2 3 Word Bank equation one-step balanced inverse operation 3c=18 3c = 18 m+ 9 =20 m + 9 = 20 3 3 3(6) = 18 - 9 - 9 11 + 9 = 20 18 = 18 b= 6 m= 11 20 = 20 Angelina needs to save ______________________. Frank has ______________________. $11 6 cans of tennis balls Access Common Core Sam is trying to solve the equation on the left. After applying one inverse operation, his solution was m = 8. Explain why his solution is incorrect and what possible error he may have made. Sam’s solution 8 Summary Closure What did you learn today about solving one-step equations? (Pair-Share) Use words from the word bank.**Independent Practice**Inverse Operations A one-step equation requires one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. + and – The solutionis the value of the variable that makes the equation true. and Solve one-step equations. Read the problem and connect it to the equation. Solve for the variable. Hint: Use the inverse operation. Check and interpret the solution. Hint: Answer the question. 1 2 3 n+ 8 = 14 n+ 8 = 14 c+ 2 =6 12 + 8 = 14 c + 2 = 6 - 8 - 8 - 2 - 2 14 = 14 4 + 2 = 6 n= 6 c= 4 6 = 6 Gabriel needs to add ______________________. Louisa started with ______________________. 4 cups of flour 6 nickels m = 9 5 5b=35 5b = 35 5 5 5(7) = 35 5 ● ● 5 35 = 35 b= 7 m= 45 9 = 9 Mathew can buy ______________________. 7 books Jenny and her friends earned ___________________. $45**Periodic Review 1**n– 26 = 12 38 - 26 = 12 c + 6 = 11 + 26 + 26 - 6 - 6 12 = 12 5 + 6 = 11 n= 38 c= 5 11 = 11 Carmella needs to add ______________________. The bookshelf has ______________________. 5 cups of flour 38 pieces 6m = 48 6 6 6(8) = 48 4 ● ● 4 48 = 48 b= 8 m= 56 14 = 14 Claire made ______________________. 8 meatballs There were ______________________. 56 crackers in the box**Access Common Core**1. Geoffrey earns $7 for mowing lawns. Last month, he earned $42. How many lawns did he mow? Which of the following statements is true? How do you know? a. The inverse operation used to solve this problem is division (÷). b. The meaning of the solution to this problem is the amount of money earned. c. The meaning of the solution to this problem is the number of lawns mowed. d. The first step in isolating the variable is to divide both sides of the equation by m. 7m=42 Yes/No Yes/No Yes/No Yes/No 2. A set of colored pencils had 29 pencils added to it. There are currently 45 pencils altogether. How many pencils were there to start with? Which of the following statements is true? How do you know? a. The inverse operation used to solve this problem is subtraction (-). b. The meaning of the solution to this problem is the original number of pencils. c. The meaning of the solution to this problem is the number of pencils left. d. The first step in isolating the variable is to add 29 to each side of the equation. p+ 29 =45 Yes/No Yes/No Yes/No Yes/No**Periodic Review 2**p- 45 = 29 74 - 45 = 29 17 + a = 28 + 45 + 45 - 17 - 17 29 = 29 17 + 11 = 28 n= 74 a= 11 28 = 28 Larissa’s allowance is ______________________. There were __________________ originally. $11 74 pencils in the set 7m = 42 7 7 7(6) = 42 6 ● ● 6 42 = 42 b= 6 c= 78 13 = 13 Geoffrey mowed ______________________. 6 lawns Thomas and his friends made __________________. 78 cookies**Access Common Core**1. Estevan worked on his English homework for 25 minutes. He finished all his homework in 57 minutes. He worked out how long it took him to finish the rest of his homework below, but his older sister told him his answer was incorrect. Where did Estevan make a mistake? How can he fix it? 25 +h=57 +25 +25 h=82 2. Javier can make 7 paper airplanes each hour. He made 28 airplanes and has calculated how long he spent making them. Explain how he can check that his answer is correct. Is his answer correct? 7a=28 7 7 a=4**Periodic Review 3**c- 14 = 13 27 - 14 = 13 25 + h = 57 + 14 + 14 - 25 - 25 13 = 13 25 + 32 = 57 c= 27 h= 32 57 = 57 It took Estevan ______________________. Elizabeth had ______________________. 32 minutes 27 pencils 7a = 28 7 7 7(4) = 28 7 ● ● 7 28 = 28 a= 4 y= 105 15 = 15 Javier spent ______________________. 4 hours making airplanes Adolfo and his friends earned ___________________. $105**Access Common Core**1. Thomas and his 5 friends made cookies. They shared them equally and each got 13. How many cookies did they make? Which of the following statements is true? How do you know? c ÷ 13 = 6. a. The inverse operation used to solve this problem is multiplication (). b. The meaning of the solution to this problem is the amount of cookies made. c. The meaning of the solution to this problem is the number of cookies shared equally. d. The first step in isolating the variable is to multiply each side of the equation by c. Yes/No Yes/No Yes/No Yes/No 2. Claire made 6 batches of meatballs. She made a total of 48 meatballs. How many meatballs does each batch make? Which of the following statements is true? How do you know? m 6 =48. Yes/No a. The inverse operation used to solve this problem is multiplication (). b. The meaning of the solution to this problem is the number of meatballs made in each batch. c. The meaning of the solution to this problem is the number of meatballs made in total. d. The first step in isolating the variable is to divide both sides of the equation by m. Yes/No Yes/No Yes/No**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. x+ 4 =7 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Addition Subtraction**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. x+ 6 = 13 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Addition Subtraction**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. 5x=25 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Multiplication Division**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Division Multiplication**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. x+ 7 =8 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Addition Subtraction**Flash Cards (Inverse Operations)**A one-step equation requires one inverse operation to solve for the variable. 7x=49 Back to Concept Dev What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Multiplication Division