lenny

Isolating 'y'

user image

Lesson Plan

Isolating 'y' Lesson Plan

Students will be able to confidently solve linear equations for the variable 'y' using inverse operations and algebraic properties.

Mastering the skill of isolating 'y' is fundamental in Algebra. It helps students understand how to rearrange equations, which is vital for graphing lines, understanding functions, and solving more complex algebraic problems in the future.

Audience

7th Grade Students (Algebra 1)

Time

30 minutes

Approach

Small group practice with guided examples and a collaborative worksheet.

Materials

Isolating 'y' Slide Deck, Small Group Practice Worksheet, Small Group Worksheet Answer Key, Warm-Up: Ready, Set, Solve!, and Cool-Down: 'Y' Do We Care?

Prep

Prepare Materials

10 minutes

Step 1

Warm-Up: Ready, Set, Solve!

5 minutes

  • Distribute or project the Warm-Up: Ready, Set, Solve!.
    * Ask students to individually solve 2-3 simple multi-step equations for any given variable. This will activate prior knowledge of inverse operations.
    * Briefly review answers as a class.

Step 2

Introduction: Why Isolate 'y'?

5 minutes

  • Present the first few slides of the Isolating 'y' Slide Deck to introduce the concept of solving for 'y' and its importance (e.g., graphing, functions).
    * Briefly explain the goal of isolating 'y': getting 'y' by itself on one side of the equation.
    * Walk through one simple example from the slide deck as a whole class.

Step 3

Small Group Practice

15 minutes

  • Divide students into small groups (3-4 students per group).
    * Distribute one Small Group Practice Worksheet per group.
    * Instruct groups to work collaboratively to solve each equation for 'y'. Encourage them to discuss their steps and help each other.
    * Circulate among the groups, providing support, answering questions, and facilitating discussion. Use the Small Group Worksheet Answer Key to check their progress or guide them if they get stuck.

Step 4

Cool-Down: 'Y' Do We Care?

5 minutes

  • Bring the class back together.
    * Distribute or project the Cool-Down: 'Y' Do We Care?.
    * Ask students to independently answer the reflection question about why solving for 'y' is important and one key step in the process.
    * Collect responses as an exit ticket.
lenny
0 educators
use Lenny to create lessons.

No credit card needed

Slide Deck

Welcome to 'Isolating 'y'!'

Today, we're going to become experts at getting a special variable, 'y', all by itself in an equation.

Why is 'y' so important? We'll find out!

Welcome students and introduce the topic: Solving for 'y'. Explain that this is a core skill in algebra.

What Does 'Isolating Y' Mean?

It means getting 'y' all by itself on one side of the equal sign!

Think of it like this:

2x + y = 5

We want y = ...

This is super important for:

  • Graphing lines
  • Understanding functions
  • Solving real-world problems!

Explain that solving for 'y' is like unraveling a present. We do inverse operations to get 'y' alone. Connect it to previous knowledge of solving for 'x'.

Let's Practice: Example 1

Solve for 'y':

x + y = 7

  • Step 1: What's with the 'y'? (It has an 'x' added to it.)
  • Step 2: How do we get rid of 'x'? (Subtract 'x' from both sides.)

x + y - x = 7 - x

y = 7 - x (or y = -x + 7)

Walk through a basic example. Emphasize using inverse operations. Show each step clearly.

Let's Practice: Example 2

Solve for 'y':

2y = 6x + 4

  • Step 1: What's with the 'y'? (It's multiplied by 2.)
  • Step 2: How do we get rid of the 2? (Divide everything on both sides by 2.)

2y / 2 = (6x + 4) / 2

y = 3x + 2

Introduce a slightly more complex example involving multiplication. Again, go step-by-step.

Let's Practice: Example 3 (Challenge!)

Solve for 'y':

3x + 4y = 12

  • Step 1: What's farthest from 'y'? (The 3x term is being added.)
  • Step 2: Move the 3x term. (Subtract 3x from both sides.)

4y = 12 - 3x

  • Step 3: What's left with the 'y'? (It's multiplied by 4.)
  • Step 4: Move the 4. (Divide everything on both sides by 4.)

y = (12 - 3x) / 4 (or y = 3 - (3/4)x)

Present a challenge example with both addition/subtraction and multiplication/division. Remind students of the order of operations (reverse PEMDAS).

Your Turn! Small Group Practice

Now it's time to work together!

  • Get into your small groups.
  • You'll receive a Small Group Practice Worksheet.
  • Work together to solve each equation for 'y'.
  • Discuss your steps and help each other out!

I'll be circulating to assist where needed.

Explain that students will now work in small groups on a worksheet. Reiterate expectations for collaboration.

lenny

Warm Up

Warm-Up: Ready, Set, Solve!

Solve each equation for the indicated variable. Show your steps!

  1. x + 5 = 12 (Solve for x)






  2. 3m = 18 (Solve for m)






  3. 2p - 7 = 11 (Solve for p)






  4. 4 + 2k = 10 (Solve for k)






lenny
lenny

Worksheet

Small Group Practice: Isolating Y

Work with your group to solve each equation for the variable y. Show all your steps clearly!

  1. x + y = 10











  2. y - 3x = 5











  3. 2y = 8x + 6











  4. 3y - 9x = 15











  5. 4x + y = 2











  6. -5x + 2y = 10











  7. x - 3y = 9











  8. 2x + 5y = 15











lenny
lenny

Answer Key

Small Group Practice Worksheet: Answer Key

Here are the step-by-step solutions for each equation. Remember to show all your work!

  1. x + y = 10

    • Goal: Get y by itself.
    • Step 1: Subtract x from both sides.
      x + y - x = 10 - x
    • Solution: y = 10 - x (or y = -x + 10)

  2. y - 3x = 5

    • Goal: Get y by itself.
    • Step 1: Add 3x to both sides.
      y - 3x + 3x = 5 + 3x
    • Solution: y = 5 + 3x (or y = 3x + 5)

  3. 2y = 8x + 6

    • Goal: Get y by itself.
    • Step 1: Divide both sides by 2.
      2y / 2 = (8x + 6) / 2
    • Solution: y = 4x + 3

  4. 3y - 9x = 15

    • Goal: Get y by itself.
    • Step 1: Add 9x to both sides.
      3y - 9x + 9x = 15 + 9x
      3y = 15 + 9x
    • Step 2: Divide both sides by 3.
      3y / 3 = (15 + 9x) / 3
    • Solution: y = 5 + 3x (or y = 3x + 5)

  5. 4x + y = 2

    • Goal: Get y by itself.
    • Step 1: Subtract 4x from both sides.
      4x + y - 4x = 2 - 4x
    • Solution: y = 2 - 4x (or y = -4x + 2)

  6. -5x + 2y = 10

    • Goal: Get y by itself.
    • Step 1: Add 5x to both sides.
      -5x + 2y + 5x = 10 + 5x
      2y = 10 + 5x
    • Step 2: Divide both sides by 2.
      2y / 2 = (10 + 5x) / 2
    • Solution: y = 5 + (5/2)x (or y = (5/2)x + 5)

  7. x - 3y = 9

    • Goal: Get y by itself.
    • Step 1: Subtract x from both sides.
      x - 3y - x = 9 - x
      -3y = 9 - x
    • Step 2: Divide both sides by -3.
      -3y / -3 = (9 - x) / -3
    • Solution: y = -3 + (1/3)x (or y = (1/3)x - 3)

  8. 2x + 5y = 15

    • Goal: Get y by itself.
    • Step 1: Subtract 2x from both sides.
      2x + 5y - 2x = 15 - 2x
      5y = 15 - 2x
    • Step 2: Divide both sides by 5.
      5y / 5 = (15 - 2x) / 5
    • Solution: y = 3 - (2/5)x (or y = -(2/5)x + 3)
lenny
lenny

Cool Down

Cool-Down: 'Y' Do We Care?

  1. In your own words, why is it important to be able to solve an equation for 'y'? Think about what we discussed today and what you might learn next in math!











  2. What is one key step you always remember when trying to get 'y' by itself?






lenny
lenny