Title: Solving Routine and Non-Routine Problems Involving Division with Fractions and Whole Numbers

Grade Level: 5th grade

Objective: - Students will be able to solve routine and non-routine problems involving division with fractions and whole numbers. - Students will understand the relationship between division and other operations (addition, subtraction, multiplication) when working with fractions and whole numbers.

Materials: - Whiteboard or blackboard - Markers or chalk - Worksheets with division problems involving fractions and whole numbers - Manipulatives (optional)

Procedure:

1. Introduction (5 minutes): - Begin the lesson by asking students if they know what division is and how it is different from other operations (addition, subtraction, multiplication). - Discuss the importance of division in everyday life, such as sharing equally, calculating rates, or finding the number of groups. - Explain that in this lesson, we will focus on solving problems involving division with fractions and whole numbers.

2. Review Division with Whole Numbers (10 minutes): - Remind students of the steps to solve division problems with whole numbers. - Provide a few examples on the board and solve them together as a class. - Encourage students to share their strategies for solving division problems.

3. Introduce Division with Fractions (10 minutes): - Explain that division with fractions is similar to division with whole numbers, but with a few additional steps. - Review the concept of reciprocals (flipping the numerator and denominator) and how they are used in division with fractions. - Provide examples on the board and solve them together as a class. - Emphasize the importance of simplifying fractions before dividing.

4. Solving Routine Problems (15 minutes): - Distribute worksheets with routine division problems involving fractions and whole numbers. - Instruct students to solve the problems independently, showing their work and simplifying fractions when necessary. - Circulate the classroom to provide assistance and answer any questions.

5. Solving Non-Routine Problems (15 minutes): - Introduce non-routine division problems that require critical thinking and problem-solving skills. - Provide examples on the board and guide students through the process of breaking down the problem, identifying the necessary steps, and solving it. - Encourage students to think creatively and use different strategies to solve the problems.

6. Group Activity (10 minutes): - Divide the class into small groups of 3-4 students. - Provide each group with a set of manipulatives (if available) or fraction cards. - Assign each group a division problem involving fractions and whole numbers. - Instruct the groups to work together to solve the problem using the manipulatives or fraction cards. - Encourage students to discuss their strategies and explain their reasoning to their group members.

7. Conclusion (5 minutes): - Gather the class back together and review the key concepts covered in the lesson. - Ask students to share any challenges they faced while solving the problems and how they overcame them. - Summarize the importance of division in everyday life and how it relates to other operations. - Assign homework that includes both routine and non-routine division problems involving fractions and whole numbers.

Extension Activity (optional): - Provide additional division problems for students to solve independently or in pairs. - Encourage students to create their own division problems involving fractions and whole numbers and exchange them with a partner to solve.