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Which subjectMathematics
What topicMulti step equations
What length (min)30
What age groupYear or Grade 8
Class size20
What curriculum
Include full script
Check previous homework
Ask some students to presents their homework
Add a physical break
Add group activities
Include homework
Show correct answers
Prepare slide templates
Number of slides5
Create fill-in cards for students
Create creative backup tasks for unexpected moments

Lesson plan

Lesson Plan: Multi-Step Equations

Subject

Mathematics

Topic

Multi-Step Equations

Grade/Age Group

Grade 8

Length

30 minutes

Number of Students

20

Objectives

Materials

National Curriculum Alignment

This lesson aligns with the National Council of Teachers of Mathematics (NCTM) standards for Algebra, including understanding and applying properties of operations and working with expressions and equations.

Lesson Structure

Step Number Step Title Length (minutes) Details
1 Introduction and Warm-up 5 Briefly review one-step equations as a foundation for multi-step equations. Introduce the concept of multi-step equations.
2 Direct Instruction 10 Provide a step-by-step explanation of how to solve multi-step equations, including a few examples on the whiteboard. Emphasize inverse operations.
3 Activity: Printable Cards 5 Distribute printable cards to students. Instruct them to fill in the cards by solving provided equations as practice.
4 Collaborative Practice 5 Allow students to work in pairs to discuss their answers on the cards, providing assistance and feedback to each other.
5 Collection of Cards 3 Collect the filled cards or conduct a quick random check on what students have completed to gauge understanding without formal presentation.
6 Homework Assignment 2 Assign homework that reinforces the day’s lesson (no presentation required). Briefly outline expectations for the homework.
7 Closing and Q&A 2 Summarize key takeaways from the lesson and allow time for any questions regarding multi-step equations or homework.

Homework

Additional Notes

Lesson script

Introduction and Warm-up

"Good morning, everyone! Today, we are going to dive into an exciting topic in mathematics: multi-step equations. But before we do that, let’s do a quick review of one-step equations. Who can remind me how we solve a one-step equation? Yes! We isolate the variable using inverse operations. Excellent! Now, multi-step equations build on this concept, so let’s explore what that means together."

Direct Instruction

"Now, let’s get into the nitty-gritty of multi-step equations. To solve these equations, we will be using multiple steps, combining different operations. I’ll show you a couple of examples on the whiteboard.

Here’s our first example: (2x + 3 = 11).

Step one: I will subtract 3 from both sides. What do we have? Correct! (2x = 8).

Now, what’s our next step? Yes! We’ll divide by 2 to isolate (x). So, what is (x) equal to? That's it—(x = 4).

Let’s try another one—(3(x - 2) + 4 = 13).

First, I’ll distribute the 3. What do you get? Right, (3x - 6 + 4 = 13).

Now can anyone tell me the next step? Exactly! We’ll combine like terms to get (3x - 2 = 13).

From there, you would add 2 to both sides. Great work, everyone! Now, can anyone tell me what we do next? Yes! Divide by 3 to find (x). So, what is (x) equal to here? Perfect—(x = 5).

Remember, the key is using those inverse operations at each step. Now that we've laid the groundwork, let’s move on to some practice!"

Activity: Printable Cards

"Now I have some printable cards for each of you. Inside these cards, you will find several equations that we just discussed. Your task is to solve these equations one by one and fill in your answers on the cards.

Take about 5 minutes to complete this task. If you finish early, double-check your work or help your neighbor. Ready? Go ahead and start!"

Collaborative Practice

"Okay, time’s up! Now, pair up with a partner. You will discuss your answers and the steps you took to arrive at those answers. This is a great opportunity to teach each other, ask questions, and provide feedback. Remember, collaboration can really enhance your understanding! You have 5 minutes to work together."

Collection of Cards

"All right, everyone, let’s bring it back together. I’m going to collect your cards now. I will read them quickly and check for understanding. If you didn’t finish, no worries! Just hold onto your cards, and we will go over the answers together during our next class. Remember, this is a low-pressure check to see where we’re at."

Homework Assignment

"Before we wrap up, let me assign some homework to reinforce what we learned today. You will be given a set of multi-step equations to solve at home. Please make sure to show all your work step by step. We will go over any questions or challenges in our next class. Keep practicing these skills!"

Closing and Q&A

"Great job today, everyone! To sum everything up, we learned how to solve multi-step equations using inverse operations, and we practiced extensively. Does anyone have questions on what we talked about or the homework assignment? If you’re uncertain about anything, now's the time to ask. Remember, practice is key to mastering this! Thanks for your hard work today!"

Homework

  1. Solve the following multi-step equations, showing all your work:

    • a) (4x - 7 = 21)
    • b) (5(x + 2) = 35)
    • c) (2(3x - 1) + 4 = 16)
    • d) (6x + 2 = 4x + 18)

  2. For each equation below, apply the steps learned in class to isolate the variable (x):

    • a) (7 - 2x = 13)
    • b) (3(x - 5) + 2 = 19)
    • c) (-2(x + 4) = 10)
    • d) (\frac{1}{2}(x + 6) = 8)

  3. Create your own multi-step equation that has a solution of (x = 3). Show the steps to solve your equation.

  4. Review the following equation and identify any mistakes made in the solution process:

    • Equation: (2x + 5 = 17)
    • Incorrect steps:
      1. Subtract 5 from both sides to get (2x = 12) (Correct)
      2. Divide by 2 to find (x = 6) (Incorrect)
    • Explain what the correct solution process should be.

  5. Pick one of the equations you solved in question 1, and explain in writing how you solved it step by step. What inverse operations did you use at each stage?

  6. Find a real-world scenario where you would need to solve a multi-step equation. Write a brief explanation of your scenario and the equation that represents it.

  7. Reflect on your understanding: What part of today’s lesson on multi-step equations did you find most challenging? Write a few sentences about it, and bring any questions to our next class for discussion.

Printables

| Question                                                                         | Answer |
|----------------------------------------------------------------------------------|--------|
| What is the first step to solving a multi-step equation?                        |        |
| After isolating the variable in the equation \(2x + 3 = 11\), what do you get? |        |
| What operation do you perform to solve for \(x\) in \(2x = 8\)?                |        |
| In the equation \(3(x - 2) + 4 = 13\), what do you need to do first?          |        |
| What form do we get after distributing in \(3(x - 2) + 4\)?                   |        |
| Once you have \(3x - 2 = 13\), what is the next step to isolate \(x\)?       |        |
| How do you combine like terms in the equation \(3x - 6 + 4\)?                  |        |
| What do you need to remember when using inverse operations?                     |        |
| How can collaboration enhance your understanding of solving equations?          |        |
| Why is it important to show all your work when solving equations for homework?  |        |