In order to develop good number sense, children need opportunities to to make sense of, and reason about, numbers. At the beginning of the school year in Second Grade, students have varied opportunities to count sets of objects by ones. As the school year progresses, most second graders shift from thinking and working primarily with ones to thinking and working with groups of ones. To help them make this shift, students have many opportunities to develop strategies for grouping and for counting by groups.
While visiting Disney’s Wilderness Lodge, our 4 year old son relied on his ability to count sets of objects by ones. However, we started to discuss and find groups of ones in order to count.
We walked around and counted by groups. For our son, the concept of a group was one that needed some reinforcement and this activity helped to further provide examples of groups for him. We found chandelier fixtures outside and inside the lobby being made up of a group of 4 lights. We used a chandelier to represent one group of 4 and counted by groups of 4 to explore that 5 chandeliers had 20 lights. Our son continued to count by ones to check my counting while I modeled grouping and counting by groups of 4s.
In the entrance way to the lobby, we found 4 lanterns with 2 lights on each lantern. We used this opportunity to discuss that we could form groups of 2 and count them in order to count to 8. This also demonstrated that 8 lights could be represented by the arrangement of 4 groups (lanterns) of 2 lights, just like outside the hotel where 5 chandeliers contained 20 lights. In the lobby of the Villas, we discussed one group of 8 being used to represent 8. Click the link to see some of our interactions.
There seemed to be different groups of numbers everywhere you looked around the resort. Here are some groups of 6 represented by a column of logs.
Researchers have linked good number sense with skills observed in students proficient in the following activities: mental calculation, computational estimation, judging the magnitude of numbers, recognizing whole-part relationships and place-value concepts, and problem solving.
This particular activity focuses and encourages counting by groups. Initially, some groups are easier to count than others so we encourage students to form groups that they can count fluently. It is recommended to first focus on contexts that encourage counting by groups of 2, 5, or 10 and then specifically on groups of 10 which serves as the base ten structure of our number system.
As an extension, focusing on the strategy of finding equal groups in the world around us can help lead to identifying the components of the multiplication operation (the number of groups, the number in each group, and the number in all of the groups). We can begin to rely and discuss physical models and other representations to support the visualization of multiplicative relationships.