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Solving One-Step Equations using Inverse Operations

In this lesson, students will learn how to solve one-step equations using inverse operations. They will understand the concept of inverse operations and how to apply them to solve equations. The lesson will include concept development, skill development, guided practice, and relevance to real-life situations.

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Solving One-Step Equations using Inverse Operations

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  1. Learning Objective Name _____________________ Today, we will solve1 one-step equations. 1 find the answer CFU What are we going to do today? What does solve mean? Solve means to ______. Activate (or provide) Prior Knowledge Inverse operationsare operations that undo each other. What operation would undo the change in value? 1.) 2.) 3.) 4.) Inverse Operations +and- ●and÷ - + 8 2 = 6 7 3 = 10 ÷ × 12 3 = 4 3 5 = 15 CFU Students, you already know how to use inverse operations to undo a change in value. Today, we will solve one-step equations using inverse operations.

  2. Concept Development A one-step equation contains2one operation. Inverse Operations 2 has within it +and- addition x+ 2 = 3 division ●and÷ A one-step equationrequires3one inverse operation to solve for the variable. • To keep an equation balanced, inverse operations must be done on both sides of the equation. 3 needs Solving One-Step Equations x+ 2 = 3 4● ●4 Inverse Operation Balance − 2 − 2 Clarification and CFU: Solving One-Step Equations Inverse Operation Balance x= 1 x= 1 Go to Skill Dev. #1 Go to Skill Dev. #2 The solutionis the value of the variable that makes the equation true. Checking a Solution NOTa Solution Solution x+ 2 = 3 x+ 2 = 3 x+ 2 = 3 x= 1 x= 4 ? ? (1) + 2 = 3 (4) + 2 = 3 3 = 3 True 6 = 3 False CFU #2 Which inverse operations would be used to solve the one-step equation 4x= 8? How do you know? A Multiplication B Division CFU #1 Which inverse operations 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 non-solution (x= 4)? Flashcards: Inverse Operations

  3. Concept Development (Clarification and CFU) A one-step equation requires one inverse operation to solve for the variable. Inverse Operations +and- • 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. ●and÷ - 2 - 2 x=3 x Return to Concept CFU Why is 2 subtracted on both sides of the equation? Why is 1 the solution to the equation x + 2 = 3? x x x

  4. Skill Development/Guided Practice #1 A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. m + 7 = 10 c + 3 = 8 3 + 7 = 10 - 3 - 3 5 + 3 = 8 - 7 - 7 10 = 10 c= 5 8 = 8 m= 3 Isabella needs to add ______________________. Samuel was given ___________________ today. 5 cups of sugar $3 m- 4 = 11 m- 5 = 8 13 - 5 = 8 15 - 4 = 11 + 5 + 5 + 4 + 4 8= 8 11 = 11 m= 13 m= 15 Jessie started with ______________________. Shannon started with ______________________. 13 marbles $15 CFU (#1) How did I/you connect the problem to the equation? (#2) How did I/you solve for the variable? (#3) How did I/you interpret the solution? Return to Concept

  5. Skill Development/Guided Practice #2 A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. 2b = 12 6b = 24 2 2 6 6 2(6) = 12 6(4) = 24 12 = 12 24 = 24 b= 6 b= 4 Miguel can buy ______________________. There are ______________________. 6 binders 4 pencils in each box 4 ● ● 4 3 ● ● 3 m= 24 m= 21 6 = 6 7 = 7 Isabella gave out ______________________. 24 muffins Ricky and his friends earned ___________________. $21 CFU (#1) How did I/you connect the problem to the equation? (#2) How did I/you solve for the variable? (#3) How did I/you interpret the solution?

  6. 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. • 2. Solving one-step equations will help you do well on tests. CFU 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 me one of my reasons or one of your own. Which reason is more relevant to you? Why?

  7. A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. 3c = 18 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 Constructed Response Closure 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? Day 1 ______________________________________________________________________ Day 2 ______________________________________________________________________

  8. Independent Practice Name _________________________ A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. n- 8 = 4 12 - 8 = 4 c + 2 = 6 + 8 + 8 - 2 - 2 4 = 4 4 + 2 = 6 n= 12 c= 4 6 = 6 Gabriel needs to add ______________________. Louisa started with ______________________. 4 cups of flour 12 nickels 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

  9. Periodic Review 1 Name _________________________ A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. 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

  10. Periodic Review 2 Name _________________________ A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. 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

  11. Periodic Review 3 Name _________________________ A one-step equation requires one inverse operation to solve for the variable. Inverse Operations • 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. 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

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  13. Concept Development (Flashcard 1 of 6) 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? Subtraction Addition

  14. Concept Development (Flashcard 2 of 6) A one-step equation requires one inverse operation to solve for the variable. x+ 6 =3 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Addition Subtraction Return to Concept

  15. Concept Development (Flashcard 3 of 6) 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

  16. Concept Development (Flashcard 4 of 6) 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

  17. Concept Development (Flashcard 5 of 6) 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

  18. Concept Development (Flashcard 6 of 6) A one-step equation requires one inverse operation to solve for the variable. 7x=49 What is the operation of the equation? What inverse operation would be used to solve the equation? How do you know? Multiplication Division Return to Concept

  19. EDI – Cognitive, Teaching and English Learners Strategies

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