Objectives (5 - 7 minutes)

• Objective 1: Students will understand the concept of numerical expressions and how they are used to represent mathematical operations without the use of variables.

• Objective 2: Students will learn to evaluate numerical expressions using the order of operations (PEMDAS/BODMAS) in order to derive accurate results.

• Objective 3: Students will apply their understanding of numerical expressions to solve real-world problems involving calculations and measurements.

Secondary Objectives:

• Objective 4: Students will improve their critical thinking skills by engaging in problem-solving activities.
• Objective 5: Students will enhance their cooperative learning skills through group work and hands-on activities.

In this stage, the teacher will clearly outline these objectives to the students, ensuring they understand what they will be learning and the skills they will be developing during the lesson. The teacher will also provide a brief overview of what numerical expressions are, and their importance in mathematics.

Introduction (10 - 15 minutes)

• The teacher starts by reminding students of the basic mathematical operations such as addition, subtraction, multiplication, and division, and the order of operations (PEMDAS/BODMAS). They should also review any previous lessons related to numerical expressions.

• The teacher then presents two problem situations as a starting point for the lesson. For example,

  1. "You are shopping for school supplies and you want to buy 3 pens, each costing $2, and 2 notebooks, each costing $5. How much will you spend in total?"

  2. "Your mom bakes 4 trays of cookies. Each tray has 6 cookies. You and your siblings eat 2 cookies each. How many cookies are left?"

  These scenarios will encourage the students to start thinking about how numerical expressions can be used to solve real-life problems.

• The teacher then contextualizes the importance of numerical expressions by discussing their real-world applications. They can explain that numerical expressions are used in various fields such as engineering, computer science, business, and architecture. For instance, "Architects use numerical expressions to calculate the amount of material needed for their projects."

• To grab the students' attention, the teacher can share interesting facts or stories related to numerical expressions. For example:

  1. "Did you know that the world's longest mathematical equation contains over 200,000 variables and constants? But today, we will be focusing on numerical expressions, which do not contain any variables!"

  2. "Numerical expressions have been used since ancient times. The ancient Egyptians used numerical expressions to build their pyramids. They calculated the number of stones needed and the angle at which they should be placed using numerical expressions."

  Sharing these curiosities will help the students to see the relevance and historical context of numerical expressions in a fun and engaging way.

Development (20 - 25 minutes)

Classroom Activity 1: "Shopping Trip"

This hands-on activity simulates a shopping trip and helps students understand the concept of numerical expressions in a fun and contextualized setting.

1. The students will be divided into groups of four. Each group will receive an envelope containing cut-outs of various items with respective prices, and a shopping list. The shopping list will include tasks like "You need to buy 3 apples and 2 loaves of bread. How much do you spend?" Each task will be different for each group.

2. Each group will calculate the total shopping bill using numerical expressions. They will be required to write down the numerical expression that represents each task on the shopping list, evaluate it using the order of operations, and solve it.

3. At the end of the activity, each group will present their shopping list with the numerical expressions and the total amount spent.

4. The teacher will review the numerical expressions used by the students and correct any errors. If an error is found, the teacher will explain how the correct numerical expression should be formed and solved, reinforcing the concept of the order of operations.

Classroom Activity 2: "Trip Planner"

This is a problem-based learning activity that requires students to plan a hypothetical day trip, further applying their understanding of numerical expressions.

1. Students remain in their groups from the previous activity. This time, they are given a different scenario: they have to plan a day trip for their entire class.

2. Each group receives a package containing information about various trip options - museum visit costs, movie tickets prices, restaurant lunch costs, transportation prices, etc. The students also receive a set budget that they cannot exceed.

3. They are required to choose a combination of trip options that will consume their budget. The combination will depend on their group’s interests and the total cost the different options will accrue.

4. Students are tasked with creating numerical expressions to calculate the total cost of each possible combination. They must then evaluate these expressions to work out the most cost-effective, fun day trip.

5. At the end of this activity, each group will present their "Trip Plan" highlighting their chosen options and mathematical working.

6. The teacher will later discuss each group's planning process, illustrating how real-life numerical problem solving may involve multiple expressions before you can reach a decision.

Through these activities, students not only practice deriving and solving numerical expressions but also foster group work, decision-making, negotiation, and planning skills. Furthermore, they begin to understand the usefulness of numerical expressions in everyday life in a fun and engaging way.

Feedback (10 - 12 minutes)

• After the completion of the two activities, the teacher will initiate a group discussion. This will involve all the students and focus on the solutions or conclusions found by each group. The teacher will facilitate these discussions to ensure that each student understands the numerical expressions used and the conclusions made during the group activities.

• To promote reflective thinking, the teacher will pose questions such as, "How can we use numerical expressions to solve this problem differently?" or "What would happen if we changed this number in our numerical expression?" These questions will challenge the students to think critically and apply their understanding of numerical expressions in different contexts.

• The teacher will then assess what was learned from the group activities and how these connect with the theory. For instance, the teacher may ask, "How did your group use the order of operations to evaluate your numerical expressions?" or "How did your understanding of numerical expressions help in planning the trip or calculating the shopping bill?"

• The teacher will encourage students to share their thoughts on how they found the activities. This feedback will help the teacher understand the students' learning experiences and make adjustments to future lessons as necessary.

• At the end of the feedback session, the teacher will propose that students reflect for a minute on answers to questions such as:

  1. "What was the most important concept you learned today?"
  2. "Which questions have not yet been answered?"
  3. "What did you find challenging during today's lesson?"

• The teacher will then collect these reflections and use them to gauge the students' understanding of the lesson's content. This will also help identify any areas that need further clarification or review.

• Finally, the teacher will recap the main points of the lesson, emphasizing the importance of numerical expressions in everyday life and other fields. The teacher will also remind students that understanding and applying numerical expressions accurately is a critical skill in mathematics.

Through this feedback session, the teacher will not only assess the students' understanding of numerical expressions but also their ability to apply this knowledge in practical scenarios. The reflective questions will further enhance the students' critical thinking skills and their appreciation of the practical use of numerical expressions.

Conclusion (3 - 5 minutes)

• The teacher will begin by summarizing the key points of the lesson. They will remind the students that numerical expressions are mathematical statements that involve numbers and operations but do not contain any variables. They will also recap on the order of operations, emphasizing its importance in evaluating numerical expressions accurately.

• The teacher will then highlight how the lesson connected theory with practice and real-world applications. They will remind the students how the classroom activities helped them apply the concept of numerical expressions to solve real-life problems. For example, they had to use numerical expressions to calculate the total shopping bill and the cost of a day trip in the "Shopping Trip" and "Trip Planner" activities, respectively.

• To further enhance the students' understanding of numerical expressions, the teacher will suggest additional resources. These could include textbooks, educational websites, and math games that provide further practice on numerical expressions. For instance, the teacher could recommend a website like Khan Academy, which provides interactive lessons and exercises on numerical expressions. In addition, the teacher could suggest math games that require the use of numerical expressions, such as "Math Bingo" or "Math Jeopardy".

• Lastly, the teacher will reiterate the importance of numerical expressions in everyday life and various fields. They will explain that numerical expressions are used in shopping, planning trips, and even in professions like architecture, engineering, and computer science. The teacher will emphasize that learning numerical expressions is not just about passing exams, but also about developing essential life skills such as problem-solving, critical thinking, and decision-making.

In wrapping up the lesson, the teacher will express their hope that the students now have a deeper understanding of numerical expressions and their applications. They will also encourage the students to continue practicing and exploring numerical expressions outside of the classroom. The teacher will remind the students that mathematics is everywhere, and that understanding numerical expressions is a step towards becoming more mathematically literate and capable individuals.

Through this conclusion, the teacher will reinforce the key learning points and the relevance of numerical expressions to the students' lives. By suggesting additional resources, the teacher will provide opportunities for the students to further their understanding and practice of numerical expressions. Ultimately, this conclusion will leave the students with a clear understanding of what they have learned and how they can continue their learning journey.