This week in Math Workshop we have been using our understanding of 100 to build on larger numbers that are multiples of 100. In addition to relating these landmark numbers, we are also concentrating on how well we communicate our mathematical understanding to others. Below are responses from two of our students that were discussed during our Closing Meeting this past Monday with our morning class. The students in this class analyzed the work of these two students and many students either asked clarifying questions or connected this work in some way with their own work.

Ryan’s Work:

20 as a factor of 100:
In 100, there are 5 groups of 20.
In 200, there are 10 groups of 20.
In 300, there are 15 groups of 20.
In 400, there are 20 groups of 20.
and so on……….

After completing a table which reflects the information shown above, Ryan made the following statement regarding the number of groups of 20 in 300. He determined that there are 15 groups of 20 in 300.

“I know there are 15 groups of 20 in 300 because there are 5 groups of 20 in 100 so 300 ÷ 20 = 15. Because 100 ÷ 20 = 5 and 5 x 3 = 15. The 3 represents 300 and the five represents the groups of 20 in 100.”

We can make a connection to Ryan's written work by relating what he is saying back to our earlier work with multiplication clusters.

5 x 20 = 100
5 x 20 = 100
+ 5 x 20 = 100
15 x 20 = 300
(15 "groups of 20" is 300.)

Min’s Work:

10 as a factor of 100:
In 100, there are 10 groups of 10.
In 200, there are 20 groups of 10.
In 300, there are 30 groups of 10.
In 400, there are 40 groups of 10.
and so on……….

After completing a table which reflects the information shown above, he made the following statement regarding the number of groups of 10 in 300. He determined that there are 30 groups of 10 in 300.

“I know there are 30 groups of 10 in 300 because I know that 10 10’s are equal to 100 so you do 10 x 3 which equals 30 because 300 is the triple of 100 so to find how many 10’s are in 300 is to multiply 10 x 3.”

We can also make a connection to Min's written work by relating what he is saying back to our earlier work with multiplication clusters.

10 x 10 = 100
10 x 10 = 100
+10 x 10 = 100
30 x 10 = 300
(30 "groups of 10" is 300.)

Min and Ryan did a very nice job in communicating their mathematical understanding using words, numbers, and symbols. We will continue to focus on how well we communicate our mathematical understanding to others as the year progresses.