Instructional Decision-Making a. Decision making: i. Provide at least four examples of instructional decision-making based on pre-assessment data and on students' learning or responses during the lessons. Describe what you did and clarify why these actions would improve student progress toward the objectives. **Special educators: Adaptations may be needed while you are teaching the lessons. These decisions would not be based on the pre-test. These decisions will acceptable in this section. b. Strategies: i. Describe two instructional strategies and activities that contributed most to student learning. Describe why you think these strategies and/or activities were effective in helping your students reach the objectives of the lessons. c. Formative Assessments: i. Describe how you used formative assessment to monitor student progress. d. Barriers: i. Describe what you believe were the two greatest barriers to learning for your students in this unit. Focus only on factors you can affect as a teacher.

Pre Assessment:

Instructions for Students:

• Write your answers clearly.
• Show all your work for short answer questions.
• For the word problem, ensure you write down the equation you set up before solving.

Part 1: Multiple Choice Questions

Choose the best answer for each question.

1. What is a linear equation? a) An equation that involves exponents b) An equation that represents a straight line when graphed c) An equation that contains only one variable d) An equation with no variables
2. Which of the following is a linear equation? a) x2+3=7x^2 + 3 = 7x2+3=7 b) 2x+5=3x42x + 5 = 3x - 42x+5=3x4 c) 3x+1=3x+13x + 1 = 3x + 13x+1=3x+1 d) y=2x+1y = 2x + 1y=2x+1
3. What is the slope of the line represented by the equation y=3x+2y = 3x + 2y=3x+2? a) 2 b) 3 c) 0 d) -3
4. If 2x+4=122x + 4 = 122x+4=12, what is the value of xxx? a) 4 b) 3 c) 2 d) 5
5. Which equation represents a horizontal line? a) y=5y = 5y=5 b) x=5x = 5x=5 c) y=2x+1y = 2x + 1y=2x+1 d) (y = -3x\

Part 2: Short Answer

Solve the following equations and show your work.

1. Solve for x: 5x10=205x - 10 = 205x10=20
2. Solve for yyy: 3y+4=193y + 4 = 193y+4=19
3. Solve for x: 2(x+3)=162(x + 3) = 162(x+3)=16
4. Solve for x: 4x7=5x+14x - 7 = 5x + 14x7=5x+1

Part 3: Word Problem

Read the problem and solve using a linear equation.

1. A total of $60 is to be divided equally among 5 friends for a dinner. If you also include a tip of $10 for the waiter, how much does each friend need to contribute?

Set up an equation and solve for the amount each friend needs to pay. (Hint: Let x be the amount each friend contributes.)

The pre-assessment was administered to gauge students' prior knowledge before the unit began.

Aggregating and Analyzing Pre-Assessment Data

After administering the pre-assessment, the results were collected and analyzed. Here's a breakdown:

Skill Area	% of Students Mastery
Define Linear Equations	75%
Solve One-Step Equations	65%
Solve Two-Step Equations	45%
Solve Word Problems	35%

Analysis:

Many students have a foundational grasp of linear equations but face challenges when it comes to more complex, multi-step problems. Notably, the lowest performance was observed in solving word problems, highlighting a significant need to emphasize real-world applications in our instruction. By integrating practical examples and relatable scenarios into lessons, we can help students develop their problem-solving skills and improve their confidence in tackling these types of equations. This focus on application will not only enhance their understanding of linear equations but also demonstrate their relevance in everyday life.

Data Display:

A bar graph will be used to display pre-assessment data, with the performance in different skill areas. (Ensure the graph does not reveal individual student identities.)

Adjustments to Instructional Plans Based on Pre-Assessment Data

Based on the data, we can tailor our lessons for optimal effectiveness. In Lesson 1, we should reinforce the basics of linear equations but move through the content more quickly, as 75% of students already understand the foundational concepts. For Lesson 2, it's important to dedicate more time to multi-step equations, with a focus on strategies that help simplify and solve these problems effectively. In Lesson 3, we need to incorporate additional practice with word problems, emphasizing a step-by-step approach to breaking down and solving them. This targeted strategy will address the areas where students struggle and enhance their overall understanding of linear equations.

Delivering Instruction and Formative Assessments

During the three lessons, I used several formative assessments:

• Lesson 1: Exit ticket to check if students can solve basic equations.
• Lesson 2:Group work to observe how well students solve multi-step problems.
• Lesson 3: A worksheet with word problems to check for comprehension.

The formative assessments helped identify students who were still struggling with multi-step problems. I adjusted my teaching in real-time, providing additional examples and one-on-one support.

Administer Post-Assessment

The post-assessment was similar in format to the pre-assessment, including multiple-choice, short-answer, and word problems to measure students' mastery of the learning objectives after instruction.

Post Assessment:

Part 1: Multiple Choice Questions

Choose the best answer for each question.

1. What is the solution to the linear equation 3x4=113x - 4 = 113x4=11? a) 5 b) 3 c) 4 d) 7
2. Which equation represents a line with a slope of 2? a) y=2x+1y = 2x + 1y=2x+1 b) y=2x+3y = -2x + 3y=2x+3 c) y=3x+2y = 3x + 2y=3x+2 d) y=x+2y = x + 2y=x+2
3. What is the value of xxx in the equation 4(x1)+2=144(x - 1) + 2 = 144(x1)+2=14? a) 5 b) 3 c) 4 d) 2
4. If 5x+3=235x + 3 = 235x+3=23, what is xxx? a) 4 b) 5 c) 3 d)
5. Which of the following is NOT a linear equation? a) y=2x1y = 2x - 1y=2x1 b) y=12x+4y = \frac{1}{2}x + 4y=21x+4 c) x2+y=6x^2 + y = 6x2+y=6 d) 3y2x=63y - 2x = 63y2x=6

Part 2: Short Answer

Solve the following equations and show your work.

1. Solve for xxx: 7x+2=237x + 2 = 237x+2=23

1. Solve for y: 82y=48 - 2y = 482y=4

1. Solve for x: 3(x2)+6=153(x - 2) + 6 = 153(x2)+6=15

1. Solve for x: 2x+3=4x52x + 3 = 4x - 52x+3=4x5

Part 3: Word Problem

Read the problem and solve using a linear equation.

1. You are buying xxx notebooks at $3 each and yyy pens at $2 each. If your total spending is $30 and you buy 4 pens, how many notebooks can you buy?

Set up an equation and solve for x (the number of notebooks). (Hint: Write an equation based on the total cost of pens and notebooks.)

Aggregating and Analyzing Post-Assessment Data

The post-assessment data showed significant improvement:

Skill Area	% of Students Mastery (Post)
Define Linear Equations	90%
Solve One-Step Equations	85%
Solve Two-Step Equations	75%
Solve Word Problems	70%

Data Display:

A comparative bar graph will be created, displaying pre-assessment vs. post-assessment results, without identifying students.

Reflective Commentary on the Whole Process

The entire process of designing lessons, administering assessments, and adjusting instruction based on data proved invaluable. Here are the 7 components of the Conceptual Framework that guided the reflection:

1. Content Knowledge: The unit effectively built on students' prior knowledge and expanded their understanding of linear equations.
2. Instructional Practice: Using formative assessments helped tailor the instruction to meet students' needs.
3. Assessment: Both pre- and post-assessments provided critical data for measuring student progress and adjusting instruction.
4. Diversity of Learners: The lessons were differentiated for students at different levels, and formative assessments allowed for immediate intervention.
5. Technology Integration: Data analysis tools were used to display and interpret pre- and post-assessment results.
6. Professional Responsibility: Reflecting on the effectiveness of the lessons and adapting them in real time showed a commitment to student growth.
7. Collaboration: Working with colleagues and reviewing school data ensured that the lessons were aligned with school standards and student needs.

Through this structured process, I was able to significantly improve student outcomes by using data to drive instruction and ensure that all students made progress.