September 13th, 2011
In her new book Number Sense Routines, author Jessica Shumway shares a series of routines designed to help young students internalize and deepen their facility with numbers. For the next four weeks, we are going to share four routines that will help build students’ number sense. Today’s routine — an exclusive not included in the book — is about using quick images with dot cards to build a community of learners in your classroom at the beginning of the year. Check back next Tuesday for more ideas!
Summer… a time to recharge and a wonderful time for reflection on the past school year as well as planning for the fresh start in the fall. During the summer I plan out the core classroom routines that will build a strong community of learners with my new group of students at the beginning of the school year. I hope these suggestions in the Math Quick Tips will help you do the same!
Teaching students to share ideas, listen to each other, support one another, and learn to value a variety of ideas are critical components to successful discussions in my classroom. One way to begin negotiating our norms for classroom discussions is using the Quick Images with dot cards. I love the Quick Images with dot cards because children naturally see the amounts in different ways. Using these will help you establish the norm that “we value various ideas and strategies.” For example, showing this dot card:
and then asking “how many dots did you see? How did you see the total?” will elicit responses such as “5 and 3 is 8” or “I saw 3 on top and 3 on the bottom, which is 6 then two more—in the middle—is 8 total.” Some students might count by twos to 8.
A student might say “I saw 4 and 4 which makes 8.” To encourage listening to one another, discussion, and flexibility with amounts, ask “Can someone explain what Julia saw? Show us on the dot card.” After someone restates her thinking, then ask Julia, “Is that how you saw the 4 and 4?” Emphasize all the different ways of thinking about the amount by recording equations that students describe:
3+3=6 and 2 more is 8 or 3+3+2=8
2+2+2+2=8 or 2×4=8
Then say, “look at all those different ways we made 8. Your brains think differently and we saw the amount in so many ways. How cool is that?!”
Another possible format to teach students to have math discussions is to show, then hide a dot card followed by “turn and talk” with a partner. Show and hide the following combination of dot cards…
then, ask students to turn and talk to their partner (knee-to-knee, eye-to-eye). Challenge your students and say, “see if you can figure out how your partner figured out how many dots on the card!” The colors on this dot card combination may encourage certain strategies, such as counting by threes and/or combining groups of threes. However, other students will focus on the arrangement (rather than the colors) of the groups of fours. After students discuss their process for figuring out 12 dots on the cards, ask a few students to explain what their partner did to figure it out. This teacher move encourages students to listen to one another as well as learn new ways of seeing an amount.
The beauty of Quick Images with dot cards is that it is a useful routine for setting up classroom norms and building a strong community of learners while doing important mathematics at the same time. You can use this routine to teach students to listen to each other, guide students with how to hold a respectful discussion, and value multiple ideas in one classroom. Simultaneously, students are building their number sense as they utilize their abilities to subitize, build visual sense of quantities, compare quantities, combine and separate amounts, and discuss part-part-whole relationships. During the discussions, you will likely write equations based on the children’s descriptions, so they are also seeing pictorial representations of amounts (the dot cards) connected with the symbolic representations (the equations). Students become more flexible in thinking about amounts like 8 and 12 which will help them become more efficient with composing and decomposing numbers (as well as computations and mental math!).
This routine is extremely rich and students love it! It is amazing that such a mathematically rich Number Sense Routine only takes 5 or 10 minutes at the beginning of each math lesson!!!