Multiplication and Division with Larger Numbers

Objective: 

• To understand the principles of multiplication and division with larger numbers.
• To apply these concepts to solve real-world problems.

Materials:

• Whiteboard
• markers
• number line
• multiplication tables
•  worksheets

Introduction (5 minutes):

1. Review the concepts of multiplication and division.
2. Explain the importance of understanding multiplication and division with larger numbers.

Direct Instruction (15 minutes):

1. Introduce the multiplication tables and their use in solving problems.
2. Demonstrate the process of multiplying larger numbers, using visual aids such as a number line to illustrate the concepts.
3. Explain the rules for dividing larger numbers, using examples to clarify the steps involved.

Guided Practice (15 minutes):

1. Provide worksheets for students to practice multiplying and dividing larger numbers.
2. Have students work in pairs to solve problems and compare their answers.
3. Monitor student progress and provide support as needed.

Independent Practice (10 minutes):

1. Give students an independent task to complete, such as solving real-world problems that involve multiplication and division with larger numbers.
2. Have students self-assess their work and identify any areas for improvement.

Conclusion (5 minutes):

1. Review key concepts covered in the lesson.
2. Answer any remaining questions from students.
3. Assign homework to reinforce the understanding of multiplication and division with larger numbers.

Multiplication of large numbers is the process of finding the product of two or more numbers with multiple digits. To perform the multiplication of large numbers, you need to follow these steps:

1. Align the numbers: Place the numbers one above the other, with the units digit of the bottom number lined up with the units digit of the top number.
2. Multiply each digit of the bottom number by each digit of the top number. Write each product under the corresponding digit of the top number, using one line for each digit of the bottom number.
3. Add the products: Add the products vertically, carrying over any tens digit to the next column as needed.
4. Repeat the process: Repeat the process for the next digit of the bottom number until all digits have been multiplied and added.
5. Final product: The final product is the result of multiplying the large numbers.

For example, to multiply 23 x 45, you would align the numbers, multiply each digit of the bottom number by each digit of the top number (2x4=8, 3x5=15), add the products (8+0=8, 15+10=25), and carry over the tens digit (2) to the next column, producing the final product of 1035. 

Division of large numbers is the process of finding how many times one large number (dividend) can be divided by another large number (divisor). To perform the division of large numbers, you need to follow these steps:

1. Align the dividend and divisor: Place the dividend above the divisor, with the leftmost digit of the dividend lined up with the leftmost digit of the divisor.
2. Establish the first digit of the quotient: Divide the first few digits of the dividend by the divisor to find the first digit of the quotient. This digit should be as large as possible without going over the dividend.
3. Multiply the divisor by the first digit of the quotient and write the product under the corresponding digits of the dividend.
4. Subtract the product from the dividend.
5. Repeat the process: Repeat the process for the next digit of the dividend, using the remainder as the new dividend and the divisor as the same.
6. Final quotient: The final quotient is the result of dividing the large numbers, which gives you the number of times the divisor goes into the dividend.

For example, to divide 356 by 12, you would align the numbers, divide the first digit of the dividend by the divisor (3 divided by 12) to get the first digit of the quotient (0), divide the first two digits of the dividend by the divisor (35 divided by 12) to get the first digit of the quotient (2), multiply the divisor by the first digit of the quotient (2 x 12 = 24), write the product under the corresponding digits of the dividend (356 - 24 = 332), and repeat the process with the remainder as the new dividend (332 divided by 12 = 27 with a remainder of 6), producing the final quotient of 29 with a remainder of 6.