Key Stage 4 Mathematics - Problem Solving and Mathematical Reasoning

Duration: 1 hour

Objectives:

• To understand the steps involved in solving mathematical problems
• To develop problem-solving skills and strategies
• To apply mathematical reasoning to real-world problems

Materials:

• Whiteboard and markers
• Handout with practice problems

Introduction (10 minutes):

• Ask students if they have solved mathematical problems before and what strategies they have used
• Explain the importance of problem-solving skills and mathematical reasoning in everyday life
• Discuss the steps involved in solving mathematical problems: understanding the problem, planning a solution, carrying out the solution, and checking the solution

Body (35 minutes):

• Provide real-world problems for students to solve in pairs or independently
• Have students discuss their strategies and solutions with each other
• Discuss common mistakes and how to avoid them
• Provide additional practice problems for students to solve and discuss with each other

Conclusion (15 minutes):

• Review the key concepts covered in the lesson
• Answer any questions students may have
• Assign homework (e.g. additional practice problems or a worksheet)
• Summarize what was learned in the lesson and what students should focus on for the next lesson

Assessment:

• Observe students during the practice problems to assess understanding
• Collect and grade the homework to see how well students have retained the material

Note: This is just a sample lesson plan, and can be adjusted to fit the needs of your students and curriculum. 

Handout: 

Problem Solving and Mathematical Reasoning Practice Problems

Instructions:

• Solve each problem using the steps involved in solving mathematical problems: understanding the problem, planning a solution, carrying out the solution, and checking the solution
• Discuss your strategies and solutions with your partner

Problem 1:

 A car travels from one city to another at a constant speed. The distance between the two cities is 300 miles, and the car takes 5 hours to complete the trip. What is the car's speed in miles per hour?

Problem 2:

A store has 40 litres of orange juice. The store wants to sell the orange juice in bottles that hold 1 liter each. How many bottles does the store need?

Problem 3: 

A right triangle has a base of 10 units and a height of 8 units. What is the length of the hypotenuse?

Problem 4: A cylinder has a height of 10 cm and a radius of 4 cm. What is the volume of the cylinder in cubic centimetres?

Problem 5: A rectangular pool has a length of 20 feet and a width of 15 feet. What is the area of the pool in square feet?

Problem 6: A company has a profit of $1000 after selling 100 units of a product. If the profit is $20 per unit, what is the cost of each unit of the product?

Note: These are just sample problems, and can be adjusted to fit the needs of your students and curriculum. The purpose of these problems is to provide opportunities for students to apply the problem-solving skills and mathematical reasoning they have learned.