This year's first "Math Quest"

     
 In the Seabury primary grades we do regular inquiry-based math lessons that allow for a wide range of developmental stages to work simultaneously on the same project. Last year we called these "Math Adventures," but this year, they are  called "Math Quests," of course!
      Our first quest this year centered around place value and the book Sir Cumference and All the King's Tens, one of the wonderful series of math adventure books by Cindy Neuschwander. School Library Journal describes the plot as follows:

"Sir Cumference and his wife, Lady Di(ameter), are back in another math adventure. As the hosts of a surprise birthday party for King Arthur, the couple needs to organize a growing number of guests for events to run smoothly. After several fumbling attempts to count the crowd, Sir Cumference realizes that the simplest way to figure out the total is to group the guests into tens, hundreds, and ultimately thousands. This system allows the royal celebration to take place without a hitch, resulting in a happy ending for all."

      Like the hosts in this book, the students counted and organized the guests, represented by beans, into groups of ones, tens, and hundreds to tally up the total number of people attending King Arthur's party.  Students are usually given the option of working individually or in small groups, and the difficulty of the work is differentiated by math level - some student received hundreds or thousands of beans to count, some received smaller amounts. Once they had their beads counted, everyone participated in "making trades" at the "party pavilion" - ten tents of ones traded for one tent of tens; ten tents of tens traded for one tent of one-hundred; ten tents of one hundred traded for a tent of one thousand, etc. Everyone was asked to make an estimate of the total number of beans/party guests before starting, and when we were done counting (it took us two days of math time!) we reviewed how to make accurate estimates and how estimating helps us solve big problems quickly. 

      It is always interesting to see the new insights and understandings students build during this type of exercise. For one thing it is always fun, but more importantly, everyone does math thinking and students are always busy talking about what they are doing, what they should be doing differently, better ways to approach the problem -- generally sharing strategies and ideas. Our role as teachers is to circulate, asking questions to elicit thinking and make sure students are on track. This is one of my favorite parts of teaching math - the "a-ha" moments take place non-stop!

       During this quest, many students started counting beans one-by-one, but quickly moved into more efficient methods of counting - skip counting by 2s, 5s, and 10s. Lots of addition and multiplication took place as students tried to figure out how many more beams they had to count before they could bring them to the counting table to be added to the total. One of the students standing at the counting table was waiting to flip the thousands digit when we counted up a group of ten one-hundreds, saying "Oh - that's why it's called the thousands PLACE. I get it now." A-ha!