Writing my lessons with OpenAI

 Good unit plans require backward planning so let's create an assessment.

Write a performance task for the mathematical standard Solve linear equations in one variable.

Performance Task: Linear Equation Word Problems

You have been hired by a furniture company to help them price their products. The company has determined that the price of a table is directly proportional to its length. They have found that a 6 foot long table costs $300.

You are given the following information:

• The cost of a table is directly proportional to its length
• A 6 foot long table costs $300

Using this information, you need to answer the following questions:

1. Write an equation that represents the relationship between the length of a table (in feet) and its cost (in dollars).

• 2. A customer wants to purchase a 9 foot long table. How much will it cost?
• 3. The company wants to sell a 4 foot long table for $200. Is this possible, and if so, what will the cost be?

To complete this task, you will need to use your knowledge of linear equations to solve for the unknown variables. Be sure to show all of your work and explain your reasoning.

 Going to need some lesson objectives 

Write lesson objectives for the mathematical standard Solve linear equations in one variable.

Here are some potential lesson objectives for teaching students how to solve linear equations in one variable:

1. Students will be able to correctly set up and solve linear equations in one variable using the proper techniques and notations.
2. Students will be able to understand the concept of solving an equation as finding the value(s) that make the equation true.
3. Students will be able to use the process of isolating the variable to solve linear equations in one variable.
4. Students will be able to solve linear equations with fractions and decimals, including those that require the use of the distributive property or combining like terms.
5. Students will be able to check their solutions to ensure that they are correct.
6. Students will be able to accurately interpret and communicate the solution(s) to a linear equation in the context of the problem.

 I also need some language objectives 

Write language objectives for a unit based on the mathematical standard Solve linear equations in one variable.

Here are some language objectives for a unit based on the mathematical standard "Solve linear equations in one variable":

1. Students will be able to define and use the terms "linear equation" and "variable" in context.
2. Students will be able to write linear equations in standard form, using proper mathematical notation.
3. Students will be able to solve linear equations using various methods, such as graphing, substitution, and elimination.
4. Students will be able to interpret the solutions to linear equations in the context of the problem.
5. Students will be able to communicate their understanding of solving linear equations using proper mathematical language and notation.

 

 A few essential questions I thought these were supposed to be one big essential question for a unit, but now they want one per lesson. that seems redundant with the objective, but ok. Also now we have 3 goals for each lesson which seems to be overly complicating things, but hey Hattie and Marzano and any other  geniuses who write books can't be wrong.

Write some essential questions for a unit teaching the mathematical standard Solve linear equations in one variable.

1. What is a linear equation in one variable and how do we recognize one?
2. How do we solve a linear equation by using the properties of equality?
3. How do we use the concept of inverse operations to solve a linear equation?
4. How do we check our solution to a linear equation to make sure it is correct?
5. What is the difference between a consistent system of linear equations and an inconsistent system?
6. How do we solve a system of linear equations using graphing?
7. How do we solve a system of linear equations using the substitution method?
8. How do we solve a system of linear equations using the elimination method?
9. How do we use linear equations to model and solve real-world problems?
10. How do we use linear equations to make predictions in real-world situations?

 Each lesson should prepare for student misconceptions so let's look at those

What are some misconceptions when teaching the standard Solve linear equations in one variable.

There are a few common misconceptions that students may have when learning how to solve linear equations in one variable:

1. They may think that the only way to solve an equation is by using the "balance method," which involves setting up an equation and then manipulating the terms on both sides until they are equal. However, there are actually many different techniques that can be used to solve linear equations, such as graphing, substitution, and elimination.

2. They may think that the solution to an equation must be a whole number. However, it is possible for the solution to be a fraction or a decimal.

3. They may think that they can only use the properties of equality (such as the addition property and the multiplication property) to manipulate the equation, but they can also use the properties of operations (such as the associative property and the distributive property) to simplify expressions within the equation.

4. They may think that they have to use the same operation on both sides of the equation in order to solve it. However, it is often necessary to use different operations on different sides of the equation in order to isolate the variable.

 Lets write the unit

write a unit of lessons for the mathematical standard Solve linear equations in one variable. using the lesson objectives Students will be able to correctly set up and solve linear equations in one variable using the proper techniques and notations. Students will be able to understand the concept of solving an equation as finding the value(s) that make the equation true. Students will be able to use the process of isolating the variable to solve linear equations in one variable. Students will be able to solve linear equations with fractions and decimals, including those that require the use of the distributive property or combining like terms. Students will be able to check their solutions to ensure that they are correct. Students will be able to accurately interpret and communicate the solution(s) to a linear equation in the context of the problem.

Lesson 1: Introduction to Solving Linear Equations in One Variable

• Objectives:
  • Students will be able to understand the concept of solving an equation as finding the value(s) that make the equation true.
  • Students will be able to correctly set up and solve linear equations in one variable using the proper techniques and notations.

Materials:

• Graph paper
• Calculator (optional)

Warm-up:

• Review the definition of a linear equation.
• Ask students to provide examples of linear equations in one variable.

Direct Instruction:

• Define the term "solution" to a linear equation as the value(s) that make the equation true.
• Discuss the steps of the process of solving a linear equation in one variable:
  1. Isolate the variable on one side of the equation by performing the same operations on both sides of the equation.
  2. Simplify the equation by combining like terms, if applicable.
  3. Check the solution by substituting it back into the original equation and verifying that it makes the equation true.

Guided Practice:

• Have students solve the following linear equations in one variable:
  1. 3x = 9
  2. 5x + 3 = 2x + 9
  3. 2(x + 1) = 10

Independent Practice:

• Have students solve the following linear equations in one variable:
  1. 4x - 2 = 6x + 3
  2. (x + 3)(x - 2) = 0
  3. 2x + 4 = 6x - 8

Closure:

• Review the steps of the process of solving a linear equation in one variable.
• Ask students to share any questions or difficulties they had during the independent practice.

Assessment:

• Collect and review the independent practice problems for accuracy.

Lesson 2: Solving Linear Equations with Fractions and Decimals

• Objectives:
  • Students will be able to solve linear equations with fractions and decimals, including those that require the use of the distributive property or combining like terms.
  • Students will be able to accurately interpret and communicate the solution(s) to a linear equation in the context of the problem.

Materials:

• Graph paper
• Calculator (optional)

Warm-up:

• Review the steps of the process of solving a linear equation in one variable.
• Ask students to provide examples of linear equations in one variable that contain fractions or decimals.

Direct Instruction:

• Review the distributive property and how it can be used to simplify linear equations with fractions and decimals.
• Discuss the importance of keeping the same units when solving linear equations with fractions and decimals.

Guided Practice:

• Have students solve the following linear equations in one variable:
  1. 3/5x = 6/10
  2. 2.4x + 3.6 = 1.8x + 9
  3. 2.5(x + 1) = 5

Independent Practice:

• Have students solve the following linear equations in one variable:
  1. 4.3x - 2.1 = 6.6x + 3.3
  2. (1.5x + 3)(0.5x - 2) = 0
  3. 3.2x + 4.8 = 6.4x - 9.6

Closure:

• Review

 

Ok I don't like direct instruction lets change the prompt to include inquiry based instruction and let's ask for essential questions and language objectives for each lesson.  Just do everything at once. 

Notice I meant formative assessment, but wrote formal assessment but that didn't bother the AI 

The unit is only three lessons, but hey I guess it will work. I doubt it will win any awards or be a successful unit for most students, but it's a start. 

Write an inquiry based 8th mathematical unit of study teaching the standard "Solve linear equations in one variable" include essential questions, objectives, language objectives, formal assessments for each day and a summative assessment at the end.

Unit Title: Solving Linear Equations in One Variable

Essential Questions:

• What is a linear equation in one variable and how can we solve it?
• How do we use the properties of equality to solve linear equations?
• How do we interpret the solutions of linear equations in real-world contexts?

Objectives:

• Students will be able to solve linear equations in one variable using the properties of equality.
• Students will be able to interpret the solutions of linear equations in real-world contexts.

Language Objectives:

• Students will be able to read and understand mathematical notation and language related to linear equations in one variable.
• Students will be able to communicate their understanding of solving linear equations in one variable through written and oral explanations.

Day 1: Introduction to Linear Equations

• Begin by introducing the concept of a linear equation in one variable and provide examples.
• Have students work in pairs to solve a few simple linear equations.
• As a class, discuss the steps used to solve the equations and any difficulties that arose.

Formal Assessment: Observation of student participation in class discussion and solving equations in pairs.

Day 2: Using the Properties of Equality to Solve Linear Equations

• Review the properties of equality (reflexive, symmetric, transitive, and substitution).
• Have students work in pairs to solve linear equations using the properties of equality.
• As a class, discuss the steps used to solve the equations and any difficulties that arose.

Formal Assessment: Observation of student participation in class discussion and solving equations in pairs.

Day 3: Interpreting Solutions in Real-World Contexts

• Introduce the concept of interpreting solutions in real-world contexts.
• Have students work in groups to solve linear equations and interpret the solutions in the context of a given scenario.
• As a class, discuss the different interpretations and any challenges that arose.

Formal Assessment: Observation of student participation in class discussion and solving equations in groups.

Day 4: Practice Solving Linear Equations

• Have students work independently to solve a variety of linear equations.
• As a class, go over the solutions and discuss any challenges that arose.

Formal Assessment: Individual practice solving linear equations.

Summative Assessment:

• Administer a summative assessment that assesses the students' ability to solve linear equations in one variable and interpret the solutions in real-world contexts. This could be in the form of a written test or a group project where students must solve a series of linear equations and present their solutions in the context of a given scenario.

 

Well the lessons are pretty basic, but on par with the stuff I turn in for my weekly lesson plans. It's difficult to put that much time into a fill in the blank lesson plan, not that my daily lessons are not actually planned. I just do most of the individualization the night before or the morning of because I use what happened in class the day before to inform me of that.

Asking for each part individually does give a nice run of the mill lesson. There isn't much thought into the individual students, or differentiation, or motivation, etc... basically what I expected. I might look at the objectives and language objects for inspiration. It also creates some simple basic performance assessments I can use for students. That may be the best part. In my school students tend to jump to doing work before they try to learn and expect to get a passing grade. Having a million easily created tasks for students who like to scribble answers that have nothing to do with the actual problem will be useful. Maybe I can finally convince students who do that, that it will never improve their grade until they start actually giving me reasonable answers that I can at least give feedback on.