Full lesson	Create for a teacher a set of content for giving a lesson, beginning with the lesson plan. Each new block of materials must begin with an H1 heading (other subheaders must be H2, H3, etc). When you describe required pictures, write those descriptions in curly brackets, for example: {A picture of a triangle}
Which subject	Mathematics
What topic	7.EE.1
What length (min)	30
What age group	Year or Grade 7
Class size	20
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 slides	5
Create fill-in cards for students
Create creative backup tasks for unexpected moments

Lesson plan

Topic

7.EE.1 - Expressions and Equations

Objectives

• Understand and apply the properties of operations to generate equivalent expressions.
• Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers.
• Develop skills in simplifying expressions and solving equations.

Materials

• Whiteboard and markers
• Graphing calculators (optional)
• Worksheets for practice
• Homework assignments
• Projector for displaying examples

Grade/Age Group

Grade 7

Subject

Mathematics

Class Size

20 students

National Curriculum Alignment

This lesson aligns with the Common Core State Standards for Mathematics, specifically addressing standards related to expressions and equations.

Lesson Structure

Step Number	Step Title	Length (minutes)	Details
1	Introduction	5	Introduce the topic of expressions and equations. Discuss the importance of understanding how to manipulate expressions in real-life scenarios.
2	Direct Instruction	10	Teach the properties of operations (commutative, associative, distributive). Provide examples and demonstrate how to apply these properties to expressions.
3	Guided Practice	5	Work through a few practice problems as a class, ensuring everyone understands how to apply the properties of operations to generate equivalent expressions.
4	Independent Practice	5	Distribute worksheets for students to practice on their own. Circulate the room to provide help as needed, ensuring all students are engaged.
5	Assign Homework	2	Assign homework that reinforces the concepts learned in class. Inform students they will be checking homework completion but not presenting in front of the class.
6	Conclusion and Review	3	Summarize the key points covered in the lesson. Allow for a few minutes of questions or clarifications before the class ends.

Homework

• Assign relevant practice problems that align with the lesson objectives for students to complete at home. This will reinforce their understanding of the material covered in class.

Assessment

• Monitor student understanding during guided practice and independent practice.
• Review homework submissions the following class to assess comprehension and provide feedback.

Lesson script

Introduction

"Good morning, class! Today, we are going to dive into an important topic in mathematics: expressions and equations. Understanding how to manipulate expressions is not just a skill you need for math class; it's essential for solving real-life problems, whether you're budgeting your allowance or figuring out how long you can run on a given amount of fuel. By the end of this lesson, you’ll understand how to create and solve expressions using properties of operations. Let's get started!"

Direct Instruction

"First, let’s talk about the properties of operations. There are three key properties we’ll focus on today: the commutative property, the associative property, and the distributive property.

1. Commutative Property: This means that the order in which we add or multiply numbers doesn't change the result. For example, (4 + 5) is the same as (5 + 4), and (3 \times 7) is the same as (7 \times 3).

2. Associative Property: This property tells us that when we add or multiply three or more numbers, the way we group them doesn’t affect the sum or product. For example, ( (2 + 3) + 4) is equal to (2 + (3 + 4)).

3. Distributive Property: This property links multiplication and addition. It tells us that multiplying a number by a sum is the same as multiplying each addend separately and then adding the products. For example, (2 \times (3 + 4)) is the same as (2 \times 3 + 2 \times 4).

Now, let’s take a look at how we can apply these properties to generate equivalent expressions. For instance, if we take the expression (5(x + 2)), we can use the distributive property to rewrite it as (5x + 10).

Does everyone understand these properties? Are there any questions?"

Guided Practice

"Great! Now, let’s practice applying these properties together.

Here’s the first example: Simplify the expression (3(a + 4) - 2a).

1. First, use the distributive property to expand (3(a + 4)).
2. Next, combine like terms.

Let’s do this together. What is (3(a + 4)) when we distribute? Yes, that’s right! It becomes (3a + 12).

Now, what do we get when we subtract (2a)? Correct! We end up with (3a - 2a + 12).

Now, can anyone tell me what (3a - 2a) simplifies to? Exactly, it simplifies to (a).

So our final expression is (a + 12). Well done! Now let’s try another one."

Independent Practice

"Now it’s time for you to try some problems on your own. I’m going to pass out the worksheets. Please work on simplifying these expressions using the properties we just discussed.

Remember, I’ll be walking around to help, so don’t hesitate to raise your hand if you’re stuck. You have five minutes to complete as many as you can. Ready? Go!"

Assign Homework

"Alright, time's up! Please stop working on the worksheets. For homework, I want you to complete the assigned practice problems that will reinforce today’s lesson. I will be collecting these during our next class, but you do not need to present them in front of the class—just make sure you complete them to the best of your ability."

Conclusion and Review

"To wrap up today’s lesson, let’s quickly recap what we covered. We learned about the commutative, associative, and distributive properties, and how we can use them to generate equivalent expressions.

Does anyone have any final questions or need clarification on anything?

Great! Thank you all for your participation today. Please ensure you work on your homework, and I’ll see you all in our next class!"

Homework

1. Define the commutative property in your own words and provide an example involving both addition and multiplication.

2. Explain the associative property. How does it relate to grouping in addition and multiplication? Provide one example for each operation.

3. Describe the distributive property and give an example of how it can be used to simplify an expression.

4. Simplify the following expression using the properties of operations: (4(x + 5) - 3x).

5. Use the distributive property to expand the expression: (6(2 + y)).

6. Combine like terms in the expression: (5a + 3 - 2a + 7).

7. Create your own expression using the distributive property and simplify it. Show your steps clearly.

8. Explain how understanding the properties of operations can help in real-world situations, such as budgeting or planning.

9. Solve the following problem using the associative property: ( (8 + 2) + 5 ). Show how regrouping changes the order of operations.

10. Reflect on today’s lesson: What was the most challenging part of simplifying expressions, and how do you plan to overcome that challenge in future practice?