More Hungry Ants
Yesterday we started a pretty cool collaborative unit with one of the Teacher Collaborators from the University of Illinois Center for Education in Small Urban Communities. (I suppose I should point out that Urbana-Champaign, due to the population density, are classified as small urban, or sometimes micro-urban, communities, even though we are not a huge metropolis like Chicago or St. Louis. Just in case you were wondering what was up with the name of the Center.)
Today we continued on with our exploration of multiplication by building on what the students had started yesterday with their visual representations of the different arrays of one hundred hungry ants portrayed in Elinor J. Pinczes’ book of that title. I started by asking students to point out what they noticed about the arrays (1×100, 2×50, 4×25, 5×20, and 10×10). Some of the things that the students offered included that the numbers in the mathematical model corresponded with the number of groups and the number of items in the group. For example, the 4×25 array consisted of four groups (in this case columns) of twenty-five ants (in our pictures, each ant was represented by an X). Another idea brought up was that the ants could be described as being both “four columns of twenty-five” and “twenty-five rows of four” and that there were one hundred ants in all of the arrays. In other words, the students could identify both the commutative property of multiplication and the factors of a given number.
After reviewing the posters they made yesterday, the Teacher Collaborator took over and had the students create pages for a book that we are calling More Hungry Ants. While there isn’t the story/plot of the first book, the concept is similar. The students, working in their pairs, were given a variety of numbers to put into rectangular arrays. Each pair had a different number, and they were challenged to find as many arrays as possible. To help them, they were given a bag of pennies that corresponded to the number they were given. (For example, the pair working on 36 was given 36 pennies to move around on their desks.) The numbers ranged from 10 to 72. The students were able to work with their partners as I, the Teacher Collaborator, our special education teacher who works with us in the morning, and an America Reads/America Counts tutor all worked with the students to observe what they were doing and offer guidance as needed. In an effort to capture more visuals of what we are doing in the classroom, I took a few pictures today:
After the students finished with their pages for More Hungry Ants, I collected them so I can bind them at the school and have it as a math resource in the room. We wrapped up the morning with a quick “exit slip.” We wanted to see how many students could take the ideas of what we had been doing and process them without using manipulatives. The task was to create a rectangular array to represent twenty items in all. We saw all of the factor pairs represented except for 1×20. (I need to remember to point out tomorrow that it is possible to have an array of one column or one row. Just to make sure we don’t lose that multiplicative property of one!)
Day two of our Hungry Ants multiplication project went very well! The students have been receptive and open to trying new things and exploring concepts of multiplication. Tomorrow we will continue as we start to look into other ways to use multiplication, such multiplicative comparisons.