Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multiplication How do I multiply larger numbers? -MisconceptionsStudents often think they are multiplying by single digits. They fail to recognize the value of the digit based on its place. It is important that students do not use the standard algorithm to solve multiplication problems. Students will develop a deeper understanding of multiplication by breaking numbers apart (this is called decomposing). By using place value, the distributive property, base ten blocks, area models, and partitioning, students will be able to show their thinking and understanding of the multiplication process. The algorithm will be introduced in the 5th grade after students have developed understanding. Problem: There are 12 cookies in each batch of cookies baked by the baker. This morning the baker baked 25 batches of cookies for the bakery. What is the total number of cookies baked by the baker? OK…so we must first understand multiplication. We are not multiplying by 1 and 2. We are multiplying by 10 and 2. We are not multiplying 2 and 5 we are multiplying 20 and 5. We must consider the value of the digit based on its place. Method #1 – Partial Product In order to multiply correctly, we must multiply the tens place + the ones place of the first factor by the tens place of the second factor. 25 x 12 200 (10 x 20) 25 x 12 50 (10 x 5) We multiplied by the tens place! Once we have multiplied by the tens place, we must multiply by the ones place. We multiply the tens place + the ones place in the first factor by the ones place of the second factor. 25 x 12 40 (2 x 20) 25 x 12 10 (2 x 5) We multiplied by the ones place! Now to find the product, we need to add all the partial products together. 200 + 50 + 40 + 10 = 300 Our product is 300! Method #2 – Decompose the numbers. This is also the distributive property. 25 x 12 = (25 x 10) + (25 x 2) 250 + 50 300 So…. 25 x 12 = 300 But wait…..there is more….keep reading! The next two methods are the most used in class! Method #3 – Use expanded form. Still decomposing! Another form of the partial product (Method #1) and much easier to understand. 25 = 20 + 5 12 = 10 + 2 25 x 12 20 + 5 x 10 200 + 50 250 + + + 20 + 5 x 2 40 + 10 50 300 Method #4 – Draw an area model. Yes…it looks like a window and we are still decomposing! 5 50 10 20 200 40 x 10 + 2 200 50 10 +40 300 OR 5 50 10 10 100 20 10 100 20 x 10 + 100 100 50 10 20 + 20 300 2 **With this model, decomposing is the key. 25 can equal 20 + 5 or 10 + 10 + 5. It does not matter how the student decomposes the number as long as they try to use multiples of 100 or 10. This makes for easier multiplication.**