Building proficiency

Number strings

A number string is a set of related math problems, crafted to support students to construct big ideas about mathematics and build their own strategies (Fosnot & Dolk, 2002).

Number strings are a short (15-20 minutes) routine, using a sequence of about 6 to 8 number problems. The sequence of number problems is carefully crafted to highlight number relationships and to build specific mental strategies.

How to run a number string

The routine begins by revealing the first of the number problems for students to solve. When students have a solution strategy, they show they are ready. We suggest using thumbs up in front of their chest, as hands going up can be distracting for those still working on the problem.

The teacher chooses a student to share their solution strategy and the whole class listens to their explanation. As the student describes their thinking, you represent this for the class to see, using a specific, carefully selected representation which makes visible the mathematical focus of the number string.

A different student solution strategy is then selected, and the same process of representing student thinking is repeated. Here, the existing representation can be altered to include any new thinking to make any connections visible. Even when a student solution is incorrect, you represent their strategy while they explain their thinking, to provide opportunity for them to notice their error. Exploring and comparing the representations of different strategies in conjunction with each other allows the mathematical relationships and structures to be noticed by the students.

The role of discussion

Conversation is a critical element of a number string activity, as students are held accountable for defending their own strategies and making sense of others’. Students have a greater chance of making sense of and using the mathematical ideas that arise from other students’ work when they are made public and explicit. The teacher focuses the conversation on the mathematical relationships between the number problems in the string to engage students in discussion and complex mathematical thinking within the boundaries of structured practice. This structured practice supports students to develop a range of mental calculation strategies and deepens their understanding of mathematical models.

Discuss with your colleagues

• What daily routines do you use with your students to develop number sense? How are these routines similar to and different from this description of a number string?

 

Resources

Cathy Fosnot and colleagues have developed a number of books on number strings. Some of their new strings incorporate other areas of mathematics, including geometry, measurement and data. Learn more about Cathy's work here.

References

DiBrienza, J., & Shevell, G. (1998). Number strings: Developing computational efficiency in a constructivist classroom. The Constructivist, 13(2), 21 –25.

Fosnot, C. T., & Dolk, M. (2002). Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann Press

Lambert, R., Imm, K., & Williams, D. A. (2017). Number Strings: Daily Computational Fluency. Teaching Children Mathematics, 24(1), 48–55.