ADDIE PHASE THREE: Summary of Planned Assignments To complete the Implementation and Evaluation components of the ADDIE instructional unit, use your textbook as a resource, along with the videos avail

Critical Thinking/Problem/Project-Based Design Model Lesson Plan Design Template

Research-Based Support for Using the Problem-Based Learning Model

The Problem-Based Learning (PBL) model stems from constructivism; the focus involves a greater emphasis on meaningful learning characterized by constructive and authentic engagement (Savery & Duffy, 1995). The Incorporation of PBL in the learning-teaching process when teaching fraction operations is because it allows movement from memorization to problem-solving hence improving critical thinking. When trying to solve a real-life situation for example a change in a recipe, then the situation becomes real, making understanding deeper and the situation realistic (Hmelo-Silver, 2004). Moreover, PBL also enhances cooperation among students so that they can develop solutions, enhancing communication and cooperation (Johnson & Johnson, 1999). Operations involving fractions can be useful in daily life or situations such as cooking or creating a budget, making fractions a suitable subject to teach through PBL as it lets the students see the practical usage of the knowledge they are acquiring.

Present or identify the problem. (20%)

Present a problem for students to explore that has real-world implications. Components of this section include the real-world problem, the relevance of the problem, an outline of the tasks expected of the students, and a timeline for the students to use. The problem should be presented and the questions posed to the students should be presented in a manner that promotes student examination of the problem, provides an opportunity for students to identify the problem, and records the problem in a way that makes sense to the student and promotes critical thinking. It is also in this section that you should introduce the problem by engaging students in a project.

Present or Identify the Problem (20%)

Problem Scenario:

Students will solve a problem of how to scale a recipe for a large event. They will need to continue ingredient proportions on portions of recipes, meaning that they will be adding, subtracting, multiplying, and dividing fractions.

Real-World Relevance:

This problem is realistic in the sense that there are times that one has to scale up or down on a recipe, and would affect many depending on what one wants to produce. The concept of operations on fractions is essential and can be later implemented in cooking, constructing financial matters, and many others.

Tasks Expected of Students:

1. Identify the Problem: For this activity, students will be given a recipe for four people and asked to proportionally convert it into 12 people, then into 18 people.

2. Outline of Tasks:

• Decide what fraction operations you need to perform on each ingredient to get the desired amount.

• Perform the operations through correct computation and application of online fraction calculators and manipulatives.

• Present their findings by creating a scaled recipe for twelve people as well as a scaled recipe for eighteen people.

1. Timeline:

• Day 1: Discussion of the problem and the ideas generated by a group.

• Day 2: Solving and adjusting the recipe for 12 people.

• Day 3: The equation is for 18 people and group discussions.

• Day 4: Outcomes and implications.

Guiding Questions:

• What mathematical operations will help you scale the recipe?

• How do you ensure that the proportions remain the same when changing the number of servings?

• What tools (e.g., online calculators) can you use to check your work?

Develop a plan for solving the problem. (25%)

In this section, you are promoting critical thinking by having students consider options for solving the problem. You should present probing questions that promote students' analysis of the problem. Describe how the lesson is scaffolding from students' prior learning. Provide structure for the students to explore their problem present their thoughts and plan on how the problem will be solved. Describe your use of methods for differentiating instruction in this problem-based assignment. Evidence and discussion of the process involved in achieving the problem-based learning model goals should be present in this section of your assignment.

To put into more thought and analysis, students will form groups to solve this problem by how they will scale up the recipe. They will need to consider the following steps:

1. Analyzing the Problem:

Students thereafter recall that the ingredients have to be adjusted by increased portions. They will analyze which type of mathematical operations will be needed: addition, subtraction, multiplication, or division, pertaining to each ingredient.

Scaffolding from Prior Learning:

1. To develop rational number computation, students will be drawn upon prior knowledge of fraction operations.

2. To ensure that the students are ready for the subsequent operation, the teacher will give short revisions and illustrations of multiplying a fraction by a whole number (doubling or tripling of a fraction).

Differentiation Methods:

1. For advanced learners: Introduce more detailed problems, for example scaling for people by portions when portions cannot be divided into equal servings, for example, 7.5 people.

2. For struggling learners: As the second instructional intervention, offer more support such as visual representations like – fraction circles – and individual consultation while students are working in pairs or groups.

Critical Thinking Probing Questions:

1. What changes when different fractions are multiplied by each other about the quantity of each ingredient?

2. How is it that you are sure the scaled recipe has the right proportion?

3. What consequences can occur because of the addition of too much or too little of a component, and how can the fractions be changed?

Process Involved in the PBL Model:

1. Problem Exploration: The conceptual discussion of ideas about how to attempt to scale the recipe.

2. Problem Decomposition: Dividing a given recipe into components and defining which processes are necessary for each of them.

3. Solution Generation: Performing new measurements involving fractions and equations to find out various new measurements of the ingredients.

4. Collaboration and Presentation: Writing in groups on blackboards and then presenting to the entire class or other groups and vice versa.

Implement a plan for solving the problem. (25%)

Describe how students implement their plan to solve the problem. Describe how students are encouraged to document or record the implementation of their plan and how they evaluate whether their plan solved the problem. Describe how students are given the space to rethink their plan if the problem is not solved with the original plan. Evidence and discussion of the student products and the characteristics of the student products' connections to the problem-based learning model goals should be present in this section of your assignment.

Implement a Plan for Solving the Problem (25%)

1. Implementation of the Plan:

• Students will be writing math problems in groups so that they work with fractions, trying to solve them manually and online fraction calculators. In order for each group to share their processes and final solutions, they will be using Google Classroom or any similar platform.

1. Recording Implementation:

• Teams will make a written recipe card or a PowerPoint slide of the original and scaled recipes and the process they used to achieve the correct amounts of each ingredient. These cards will be used to keep a record of their work and help to assess the outcome of their work as well.

1. Evaluation and Reflection:

• Students will assess the differences between the final scaled recipes in terms of the quantity of certain ingredients (12 servings and 18 servings). They will contemplate whether their solutions correctly preserve such ratios as provided in the recipe.

• In case the plan fails, students are going to discover the discrepancies and modify the strategies. For instance, they may have to go back to an ingredient and measure it again using the correct fraction operation.

Evidence of Student Work:

• Recipe Cards: Illustrating scaling of ingredients as a process.

• Group Discussions: Looking back at the advantages and disadvantages.

• Presentations: Every group will discuss their final recipe with the class, and will justify the methods that were used and conclusions that were made.

Evaluate the implementation. (20%)

*Describe how students are supported in evaluating and reflecting on the implementation of their plan to solve the problem. Reflection of students' contributions to solving the problem, as well as group contributions, should be examined for what worked well and what could have been done differently. Describe how students are supported in reflecting on the benefits and challenges of their approach to solving the problem.

Evaluate the Implementation (20%)

1. Supporting Students in Reflection:

• Towards the end of the problem, students will discuss the effectiveness of their solution. They will use guiding questions to think critically about their process:

• • What do you think was the most difficult component to double?

  • In what way did your group determine as to which of them is the appropriate fraction operation to apply?

  • If your task was to increase the recipe for 24 people, how would it transform the counting?

Individual and Group Contributions:

• All students will also make personal annotations regarding contributions to solving the problem. This is a result of understanding that to enhance effective working on behalf of patients, groups will look at what they have done well and what else was possible in some other way. They shall also give feedback to each other, with emphasis on the process of solving a mathematical problem and the group work.

1. Reflection on Approach:

• The students will weigh the advantages as well as the disadvantages of their solution to the problem. The teacher will facilitate the students' reflection on how the process could have been done differently in order to arrive at a better solution and discuss how the student's method could be utilized in solving other issues.

Final Reflection Questions:

• In what way was it beneficial or disruptive to work in a group to solve the problem?

• What would you do the next time, what strategies or tools would you change?

• What do you learn from this exercise concerning the application of math in practical life?

References

• Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235-266.

• Johnson, D. W., & Johnson, R. T. (1999). Learning together and alone: Cooperative, competitive, and individualistic learning. Allyn and Bacon.

• Savery, J. R., & Duffy, T. M. (1995). Problem-based learning: An instructional model and its constructivist framework. Educational Technology, 35(5), 31-38