How to extend a string

We are often asked about how we can “stretch” strings beyond their place as a short mental math activity in the classroom.  How can they be used as part of a formative assessment of individual kids? What might come after a string that isn’t necessarily another string? What can kids do at home that builds on the thinking and reasoning that we are developing by doing strings?

With these questions in mind, our Math in the City colleague Janan Hamm developed an example of the kind of written extension that would support students’ development of big ideas, strategies and even models.  Here it is:

A written extension after a multiplication string
A written extension after a multiplication string

Notice that this written activity follows directly from string work in class, and reminds students of two strategies that were offered by their peers.  You might even name the students who authored them. Students are asked to first notice and compare these strategies, in words.  And then use them to solve a problem they haven’t yet seen. We think that written extensions like this would give teachers lots of really good information, and be very helpful in deciding what string to do next, which students to focus on, and where to focus the instruction.

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