Wondering what a number string looks like in a classroom? Curious about the details of the routine? The following video features site co-founder Rachel Lambert teaching a group of 4th grade students at the Citizens of the World Charter School in Mar Vista, CA. These students have a wonderful classroom teacher, Hayley Roberts, who does number strings regularly with the students as part of a rigorous, inquiry-based mathematics curriculum. Hayley is off camera in Part 1 leading the students in a mathematics mindfulness exercise.
Students in this class had done lots of number strings with the open number line for addition and subtraction, as well as the array as a model for multiplication. On the previous day, the number string had been a multiplication doubling and halving string on the open number line. Today’s number string was designed to help students understand division on the open number line, focused on using equivalence as a strategy. Before you watch, you might want to anticipate how 4th graders might solve these problems, and how Rachel will represent strategies on the open number line.
2 x 50
4 x 100
100 ÷ 2
100 ÷ 4
200 ÷ 4
400 ÷ 8
800 ÷ 16
In the first segment, Rachel reminds the students of the strategies they used the day before (giving students credit), and gives the first (2 x 50) and second (4 x 25) problems.
Notice the way the classroom teacher leads her students to be mindful mathematically before they begin. This is a beautiful way to help students orient themselves to the mathematics.
In the second segment, Rachel takes more strategies for 4 x 25, and then presents the third problem, 100 ÷ 2.
In Part 3, Rachel begins by asking students if they can find an open number line that represents 100 ÷ 2. Throughout this segment, she asks students to visualize representations before she models them. This segment continues, moving fairly quickly through 100 ÷ 4 and 200 ÷ 4, before moving more slowly through 400 ÷ 8 and 800 ÷ 16. It ends with one student beginning to generalize a strategy for understanding the relationship between the dividend and the divisor in division.
In Part 3, Rachel also adds another support to the number string: context. She asks the students to imagine that the division problems represent a lottery winning beings shared by students equally. She wants this context to support them in in thinking about the relationships between the dividend, the divisor and the quotient. What happens when the amount of money in the lottery is doubled? What happens when the number of students sharing the money doubles?
Part 4 continues with another student sharing their thinking about that generalizable relationship. Like the first student, this generalization is supported by the context of the lottery.
Rachel then tries to wrap up the number string, but a student offers what they think will be the next problem: 1600 ÷ 32. Students love to predict the next problem in a number string! Although she is over her time limit, Rachel throws out what would have been the last problem if she had time: 800/16 as a fraction.
In the final part, Rachel asks students, not to solve this problem, but if they can think of any equivalent fractions for 800/16.
A couple of small points. Students use the sign for “agree” in American Sign Language to indicate that they used the same strategy as a classmate. Rachel stops the class several times for a turn and talk, particularly at moments in which they were unsure, or she was unsure how much students understood. The turn and talk gives students a chance to talk through their thinking, helping them make sense of still emerging understandings.
Finally, we present this number string not as an example of perfect practice, by any means, but as a sample of practice that can be analyzed. What did you notice? What are your questions?