Download Multiplication Notes

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.**