Solve It! Warm-Up

Objective: To activate prior knowledge about simple equations and introduce the concept of an unknown.

Instructions:

Look at the following problems. Try to figure out the missing number in your head or by quickly writing it down.

1. 3 + ? = 7
   
   
   
2. 10 - ? = 4
   
   
   
3. 2 * ? = 12
   
   
   
4. ? / 5 = 2
   
   
   

Think about it: How did you figure out the missing number in each problem? What strategies did you use?

Solving for 'X' Script

Warm-Up: Solve It! (5 Minutes)

Teacher: "Good morning/afternoon, everyone! Let's start with a quick warm-up called 'Solve It!'. I've handed out a short paper with a few problems. Your task is to figure out the missing number in each one. You can do it in your head or jot it down quickly. We'll take about 2-3 minutes for this. Go ahead!"

(Allow students to work. Circulate and observe.)

Teacher: "Alright, pencils down. Let's discuss! Who can tell me what number was missing in the first problem: 3 + ? = 7?"

Student: "4!"

Teacher: "Excellent! How did you figure that out?"

Student: "I knew 3 plus 4 is 7." or "I did 7 minus 3."

Teacher: "Great strategies! What about 10 - ? = 4?"

Student: "6!"

Teacher: "Perfect! And for 2 * ? = 12?"

Student: "6!"

Teacher: "You're on fire! Last one: ? / 5 = 2?"

Student: "10!"

Teacher: "Fantastic! Today, we're going to dive deeper into how we solve for these 'missing numbers' but using a special symbol, 'X'. We call these algebraic equations, and learning to solve them is a superpower for understanding math!"

Introduction: What is 'X'? (5 Minutes)

Teacher: (Display Solving for 'X' Slide Deck - Slide 1: "Solving for 'X': Unlocking the Unknown!")

"So, you just solved for a lot of 'missing numbers.' In algebra, instead of a question mark or a blank, we often use letters like 'x' or 'y' to represent an unknown number. We call these variables. Don't let the letter scare you! 'X' is just a placeholder, a secret agent number waiting to be revealed!"

(Display Solving for 'X' Slide Deck - Slide 2: "Remember Your Warm-Up?")

"Remember the warm-up? When you solved 3 + ? = 7, you were essentially solving 3 + x = 7. Your brain already knows how to do this! We're just going to formalize the steps."

Direct Instruction: Inverse Operations (5 Minutes)

Teacher: (Display Solving for 'X' Slide Deck - Slide 3: "Equations are Like a Balance!")

"The key to solving equations is to remember that an equation is like a balanced scale. Whatever you do to one side of the equation, you must do to the other side to keep it balanced. Our goal is always to get 'X' all by itself on one side of the equal sign."

(Display Solving for 'X' Slide Deck - Slide 4: "Inverse Operations: Your Key to 'X'")

"To get 'X' alone, we use something called inverse operations. Inverse operations are opposites that 'undo' each other. Think about putting on your shoes and then taking them off – taking them off 'undoes' putting them on.

"The first pair of inverse operations we'll look at are addition and subtraction."

(Display Solving for 'X' Slide Deck - Slide 5: "Example 1: Using Subtraction")

Teacher: "Let's look at an example: x + 5 = 10. We want to get 'X' by itself. What operation is happening to 'X' right now? It's being added by 5. So, what's the inverse, or opposite, of adding 5?"

Student: "Subtracting 5!"

Teacher: "Exactly! So, we subtract 5 from both sides of the equation. x + 5 - 5 = 10 - 5. On the left, the +5 and -5 cancel out, leaving just 'X'. On the right, 10 - 5 equals 5. So, x = 5! We found our missing number."

(Display Solving for 'X' Slide Deck - Slide 6: "Example 2: Using Addition")

Teacher: "Here's another one: x - 3 = 7. How do we get 'X' alone this time? What's the opposite of subtracting 3?"

Student: "Add 3!"

Teacher: "Right! We add 3 to both sides. x - 3 + 3 = 7 + 3. The -3 and +3 cancel, leaving 'X'. And 7 + 3 is 10. So, x = 10."

(Display Solving for 'X' Slide Deck - Slide 7: "Inverse Operations: Part 2")

Teacher: "Now, the other pair of inverse operations are multiplication and division."

(Display Solving for 'X' Slide Deck - Slide 8: "Example 3: Using Division")

Teacher: "Consider 2x = 12. Remember, when a number is right next to a variable, it means multiplication, so this is 2 times x equals 12. What's the inverse of multiplying by 2?"

Student: "Dividing by 2!"

Teacher: "Perfect! We divide both sides by 2. 2x / 2 = 12 / 2. The 2s on the left cancel, leaving 'X'. And 12 divided by 2 is 6. So, x = 6."

(Display Solving for 'X' Slide Deck - Slide 9: "Example 4: Using Multiplication")

Teacher: "Finally, x / 4 = 3. What's happening to 'X' here? It's being divided by 4. What's the opposite of dividing by 4?"

Student: "Multiplying by 4!"

Teacher: "You got it! We multiply both sides by 4. (x / 4) * 4 = 3 * 4. The 4s cancel on the left, leaving 'X'. And 3 times 4 is 12. So, x = 12."

Guided Practice: Equation Challenge (7 Minutes)

Teacher: (Display Solving for 'X' Slide Deck - Slide 10: "Your Turn! Practice Time!")

"Now it's your turn to practice! I'm handing out the Equation Challenge Worksheet. Work through these problems using the inverse operations we just discussed. Remember to keep your equation balanced! I'll be walking around to help if you have questions. We'll come back together to discuss some of the answers."

(Circulate, provide individual support, and answer questions. After about 5 minutes, bring the group back together.)

Teacher: "Let's pause and discuss a few of these. Who solved problem #1, x + 7 = 15? What did you get for x?"

Student: "x = 8!"

Teacher: "How did you solve it?"

Student: "I subtracted 7 from both sides."

Teacher: "Great job! What about #4, 5x = 20?"

Student: "x = 4!"

Teacher: "Excellent! How did you get that?"

Student: "I divided both sides by 5."

(Address other questions and clarify misconceptions using the Equation Challenge Answer Key as a reference. Facilitate a brief Solving for 'X' Discussion based on common errors or difficulties.)

Activity: Inverse Operation Game (5 Minutes)

Teacher: "To make this even more fun, we're going to play the Inverse Operation Game! I'm going to give each of you an equation, and you'll quickly tell me what inverse operation you would use to start solving for 'X'. Then we'll try to solve it together."

(Lead the Inverse Operation Game as described in its material. Provide equations, have students identify inverse operations, and then quickly solve. Keep it fast-paced and engaging.)

Cool-Down: Variable Vision (3 Minutes)

Teacher: "Great work today, everyone! To wrap things up, I have one last quick task for you: the Exit Ticket: Variable Vision. Please complete this independently. It will help me see what stuck with you today and what we might need to review. When you're done, please turn it in."

(Collect exit tickets and review them later, possibly using the Solving for 'X' Rubric for assessment if desired.)

Solving for 'X' Discussion: Our Strategies

Objective: To reflect on the process of solving for 'X', share strategies, and address common misconceptions.

Opening Questions:

1. What was one new thing you learned today about solving for 'X'?
   
   
   

2. When you look at an equation like x + 6 = 10 or 3x = 15, how do you decide which inverse operation to use first? What's your thought process?
   
   
   

3. What was the most challenging part of solving for 'X' today? What made it tricky?
   
   
   

4. Can you think of a real-life situation where knowing how to solve for an unknown (like 'X') would be useful? (e.g., sharing candy, splitting a bill, figuring out travel time)
   
   
   

Group Share & Clarification:

• Invite students to share their answers to the questions.
• Pay close attention to misconceptions or areas where students struggled.
• For question 2, guide students to articulate the correct inverse operations for addition/subtraction and multiplication/division.
• For question 3, acknowledge challenges and provide brief re-explanations or alternative analogies if needed.
• For question 4, encourage diverse examples and connect the mathematical concept to practical applications.
• Follow-up Prompt: "How does thinking about equations as a 'balance' help you remember to do the same thing to both sides?"
  
  
  
• Summary: Briefly recap the main idea of using inverse operations to isolate the variable and keep the equation balanced.

Equation Challenge Worksheet

Objective: Practice solving one-step algebraic equations using inverse operations.

Instructions: Solve each equation for the variable 'x'. Show your work by writing down the inverse operation you perform on both sides of the equation.

Part 1: Addition and Subtraction Equations

1. x + 7 = 15
   
   
   
   
   
   
   

2. x - 4 = 11
   
   
   
   
   
   
   

3. 12 + x = 20
   
   
   
   
   
   
   

4. x - 9 = 2
   
   
   
   
   
   
   

5. 6 + x = 18
   
   
   
   
   
   
   

Part 2: Multiplication and Division Equations

6. 3x = 21
   
   
   
   
   
   
   

7. x / 5 = 6
   
   
   
   
   
   
   

8. 7x = 49
   
   
   
   
   
   
   

9. x / 2 = 13
   
   
   
   
   
   
   

10. 10x = 90
    
    
    
    
    
    
    

Inverse Operation Game: Solve for X Challenge!

Objective: To quickly identify and apply inverse operations to solve one-step algebraic equations.

Materials: Index cards or small slips of paper with simple one-step equations (e.g., "x + 3 = 8", "4x = 20", "x - 7 = 5", "x / 6 = 2"). You can also just call them out orally.

How to Play:

1. Teacher Calls Out Equation: The teacher will call out or display a simple one-step equation (e.g., x + 9 = 12).

2. Students Identify Inverse Operation: Students (individually or in small teams) quickly identify the inverse operation needed to isolate 'x'. For x + 9 = 12, the inverse is "subtract 9".

3. Students State Solution: Students then state the value of 'x'. For x + 9 = 12, they would say "x = 3".

4. Points (Optional): If playing in teams, award points for correct inverse operation and correct solution.

Game Play Options:

• Round Robin: Go around the group, giving each student an equation. If they get it right, move to the next student. If they struggle, offer a hint and move on, or let another student help.

• Team Challenge: Divide into two small teams. Alternate turns. The first team to correctly state the inverse operation and solution earns a point.

• Whiteboard Dash: If students have mini-whiteboards, call out an equation, and they write down the inverse operation and the solution. They hold up their whiteboards when ready. This allows for quick assessment of all students.

Example Equations for the Game:

• x + 5 = 15 (Subtract 5; x = 10)
• x - 2 = 8 (Add 2; x = 10)
• 4x = 16 (Divide by 4; x = 4)
• x / 3 = 7 (Multiply by 3; x = 21)
• x + 10 = 10 (Subtract 10; x = 0)
• 6x = 30 (Divide by 6; x = 5)
• x - 1 = 0 (Add 1; x = 1)
• x / 8 = 1 (Multiply by 8; x = 8)

Equation Challenge Answer Key

Objective: To provide correct solutions and step-by-step reasoning for the Equation Challenge Worksheet.

Part 1: Addition and Subtraction Equations

1. x + 7 = 15

   • Thought Process: The variable 'x' has 7 added to it. To isolate 'x', I need to perform the inverse operation of addition, which is subtraction. I will subtract 7 from both sides of the equation to maintain balance.
   • Solution:
     x + 7 - 7 = 15 - 7
     x = 8

2. x - 4 = 11

   • Thought Process: The variable 'x' has 4 subtracted from it. To isolate 'x', I need to perform the inverse operation of subtraction, which is addition. I will add 4 to both sides of the equation to maintain balance.
   • Solution:
     x - 4 + 4 = 11 + 4
     x = 15

3. 12 + x = 20

   • Thought Process: The variable 'x' is being added to 12. To isolate 'x', I need to perform the inverse operation of addition, which is subtraction. I will subtract 12 from both sides of the equation to maintain balance.
   • Solution:
     12 + x - 12 = 20 - 12
     x = 8

4. x - 9 = 2

   • Thought Process: The variable 'x' has 9 subtracted from it. To isolate 'x', I need to perform the inverse operation of subtraction, which is addition. I will add 9 to both sides of the equation to maintain balance.
   • Solution:
     x - 9 + 9 = 2 + 9
     x = 11

5. 6 + x = 18

   • Thought Process: The variable 'x' is being added to 6. To isolate 'x', I need to perform the inverse operation of addition, which is subtraction. I will subtract 6 from both sides of the equation to maintain balance.
   • Solution:
     6 + x - 6 = 18 - 6
     x = 12

Part 2: Multiplication and Division Equations

6. 3x = 21

   • Thought Process: The variable 'x' is being multiplied by 3. To isolate 'x', I need to perform the inverse operation of multiplication, which is division. I will divide both sides of the equation by 3 to maintain balance.
   • Solution:
     3x / 3 = 21 / 3
     x = 7

7. x / 5 = 6

   • Thought Process: The variable 'x' is being divided by 5. To isolate 'x', I need to perform the inverse operation of division, which is multiplication. I will multiply both sides of the equation by 5 to maintain balance.
   • Solution:
     (x / 5) * 5 = 6 * 5
     x = 30

8. 7x = 49

   • Thought Process: The variable 'x' is being multiplied by 7. To isolate 'x', I need to perform the inverse operation of multiplication, which is division. I will divide both sides of the equation by 7 to maintain balance.
   • Solution:
     7x / 7 = 49 / 7
     x = 7

9. x / 2 = 13

   • Thought Process: The variable 'x' is being divided by 2. To isolate 'x', I need to perform the inverse operation of division, which is multiplication. I will multiply both sides of the equation by 2 to maintain balance.
   • Solution:
     (x / 2) * 2 = 13 * 2
     x = 26

10. 10x = 90

    • Thought Process: The variable 'x' is being multiplied by 10. To isolate 'x', I need to perform the inverse operation of multiplication, which is division. I will divide both sides of the equation by 10 to maintain balance.
    • Solution:
      10x / 10 = 90 / 10
      x = 9

Exit Ticket: Variable Vision

Objective: To quickly assess student understanding of solving for 'X' using inverse operations.

Instructions: Answer the following questions honestly and to the best of your ability.

1. In your own words, what does the letter 'x' represent in an equation like x + 3 = 10?
   
   
   

2. What is an inverse operation? Give one example of a pair of inverse operations.
   
   
   

3. Solve the following equation for 'x':
   x - 8 = 12
   Show your work:
   
   
   
   
   
   
   

4. Solve the following equation for 'x':
   5x = 35
   Show your work:
   
   
   
   
   
   
   

5. How confident do you feel about solving for 'x' in simple equations? (Circle one)
   Not confident at all | A little confident | Pretty confident | Very confident

Solving for 'X' Rubric

Objective: To assess student understanding and application of inverse operations to solve one-step algebraic equations.