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Division and Multiplication Relationship
Students will be able to show understanding of the inverse relationship between multiplication and division.
- Draw a picture of 7 groups of 12 on the board and ask students to turn and share in pairs what they see and notice about the drawing. Listen for key terms such as "groups of," "multiplied," "divide," "repeated addition," etc.
- Ask students to share their ideas and write them on the board. If they haven’t given an equation, ask them to write on the board as many equations they can think of that relate to the picture (e.g., 7 x 12 = ____, ____ 7 = 12, 12 + 12 + 12 + 12 + 12 + 12 + 12 = ____). Ask students to solve for the blanks in partners if they hadn’t done so in the sharing portion.
- Circle the multiplication and division equations and rewrite them on the board stacked on top of each other. Explain that today they’ll review the inverse relationship of multiplication and division to help solve future word problems.
Explicit instruction/Teacher modeling(8 minutes)
- Define inverse operation as an operation that reverses the effect of another operation. With multiplication and division, if you multiply to get a product, you can use division to reverse the operation by dividing the product, and vice versa. The product is the answer when two or more numbers are multiplied together.
- Provide a simple multiplication and division problem using the same numbers. Model how you can change a division problem into a multiplication problem to make the division problem easier to solve.
- Highlight that converting multiplication equations to division equations is a strategy to divide by focusing on memorized or familiar multiplication facts. Check your answer using the picture representation of your choice (e.g., arrays, equal groups, tape diagrams, etc.).
Guided practice/Interactive modeling(20 minutes)
- Distribute the worksheet The Inverse Relationship of Division and read the directions. Tell students they’ll work in pairs to answer the questions and find the inverse of each of the equations.
- Conduct a multiplication fluency game in which there are two teams placed in two lines perpendicular to the board. Project the Division Facts to 100 with One-Digit Divisors exercise and have one student from each team compete to quickly convert the division equation to a multiplication problem and provide the answer. The students who get the correct answer first win a point for their team. Allow them to use whiteboards as necessary.
Independent working time(10 minutes)
- Distribute the Multiplication and Division Review worksheet and ask students to complete the top section on their own.
- Allow students to meet in partners to share their answers and correct misconceptions.
- Choose students to share any corrections they made and their process to get the right answer with the class.
- Provide a pre-lesson with simple multiplication and division problems with manipulatives and a review of vocabulary terms and their meanings.
- Allow students to practice converting equations with a common factor (e.g., 8 x 3 = 24, 9 x 3 = 27, etc.), then transition to other factors. Use a worksheet like the optional Division Facts: 9s worksheet for assistance.
- Allow students additional practice with the inverse operations of multiplication and division with the Math Crossword Puzzle worksheet. Additionally, allow them to practice division with the Division with One-Digit Divisors and Missing Factors exercise.
- Ask them to complete the word problems in the Multiplication and Division Review worksheet and show their method and equations, or create their own word problems.
- Write the following numbers on the board: 72, 9, 8. Distribute the index cards and ask students to write a multiplication and division equation using those numbers. Then, ask them to write how they know their answers are correct.
- Allow them to read their explanations to their elbow partners.
Review and closing(5 minutes)
- Choose a student to answer the following question: “How are multiplication and division inverse operations?”
- Have students turn to their elbow partner and have them discuss why it is important to understand the relationship between multiplication and division (e.g., solve unfamiliar division problems with multiplication and vice versa).
- Review some of the ideas students shared in partners with the whole class.