Objectives:
Students will comprehend the concept of an algorithm and its application in solving multiplication problems.
Students will learn and practice the steps of the expanded algorithm for multiplication.
Materials:
Whiteboard/Chalkboard and markers/chalk
Visual aids (illustrations of expanded form, stacked multiplication problems)
Practice problems (for hands-on application of the expanded algorithm)
Introduction (2 minutes):
Define an algorithm as the steps taken to find the answer to a problem. Review the what the expanded form of a number is (e.g. the expanded form of 17 is 10 + 7; the expanded form of 115 is 100 + 10 + 5) Introduce the expanded algorithm for multiplication, emphasizing its reliance on the expanded form of a number.
Theocratic Connections:
N/A
Activity 1 – Understanding Expanded Algorithm (9 minutes):
Explain the concept of the expanded algorithm using the example of 24 x 7. Emphasize that when multiplying using expanded algorithm, it’s easiest to start with the numbers in the ones place first and work your way up to the highest place. (e.g. The tens is the highest place value in the 24 x 7 example)
Break down the steps:
- Write the problem: 24 x 7 = ? Then write 24 in expanded form below it in parentheses.
- Write the multiplication problem again, but write it stacked this time.
- Multiply the numbers in ones place in one color and write the answer below the line. (e.g. circle 4 x 7 with blue and write the answer (28) in blue below the line. )
- Multiply the number in the tens place by 7. (e.g. since you wrote 24 in expanded form (20 + 4) the expanded form shows students which number to multiply by 7. Since 20 is the number in the tens place, multiply 20 x 7 and write the answer (140) in red below 28, the first answer.
- Explain that these two answers are called partial products.
- Add the partial products together, to get the answer. (28 + 140 = 168)
- Explain to students that the sum of the partial products is the answer, so 24 x 7 = 168.
Model solving the problem on the board, emphasizing each step. Engage students in a guided practice session, working collaboratively on similar problems.
Activity 2 – Applying Expanded Algorithm to Larger Numbers (8 minutes):
Extend the concept to larger numbers, using the example of 734 x 3. Emphasize the importance of understanding the expanded form of a number. Also, explain that the number of partial products we will have corresponds to the number of place values in the number. Since 734 has 3, (ones, tens, and hundreds), we will end up with 3 partial products using the expanded algorithm method. Model how to solve this problem to reinforce the concept.
Break down the steps:
- Write the problem: 734 x 3 = ? Then write 734 in expanded form below it in parentheses.
- Write the multiplication problem again, but write it stacked this time.
- Multiply the numbers in ones place in a distinct color and write the answer below the line. (4 x 3 = 12 )
- Multiply the number in the tens place by 3 in a distinct color write the answer below the first answer. (30 x 3 = 90)
- Multiply the number in the hundreds place by 3 in a distinct color write the answer below the first answer. (700 x 3 = 2100)
- Add the partial products together, to get the answer. Remind students not to forget to carry the one when adding. (12 + 90 + 2100 = 2202)
- Explain to students that the sum of the partial products is the answer, so 734 x 3 = 2202.
Activity 3 – Review and Practice Problems (9 minutes):
Present practice problems on the board for students to apply the expanded algorithm. Help students practice breaking down numbers into expanded form to solve multiplication problems.
Encourage collaborative learning and peer discussions.
Conclusion (2 minutes):
Summarize key points, highlighting the importance of understanding place value in the expanded algorithm. Reinforce the idea that solving multiplication problems using the expanded algorithm involves breaking down the number into its expanded form and applying the multiplication to each place value.
Encourage regular practice to enhance proficiency in using the expanded algorithm for multiplication.
Assessment:
Informally assess student understanding through class discussions, observations during activities, and their ability to apply the expanded algorithm in solving multiplication problems.
