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 short (15-20 minutes) routines which use a short sequence of number problems. The sequence of problems is carefully crafted to highlight number relationships and properties, and to build specific mental strategies.
Watch this video from New Perspectives on Learning to see part of a number string being used in the classroom.
How to run a number string
The number string 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. 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 model which represents the mathematical focus of the number string.
A different student solution strategy is 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. As the students explore and compare the models of the different strategies in conjunction with each other, they begin to notice mathematical relationships and structures.
Once a few students have shared their solution strategy, the teacher moves on to the next question in the string.
The role of talk
Conversation is a critical element of number strings 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 students’ work when the ideas 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.
The use of models
By anchoring computation on well-chosen models, the teacher provides external scaffolding for problem solving that students gradually begin to internalise. Modelling is central to the process of mathematising, as models become tools for students to visualise and think about mathematical relationships.
Discuss with your colleagues:
Below are three number strings. Consider each string individually.
Number string 1 | Number string 2 | Number string 3 |
|---|---|---|
$5 + 5$ $7 + 5$ $5 + 8$ $6 + 4$ $6 + 5$ $6 + 8$ | $3 \times 4$ $3 \times 8$ $6 \times 4$ $6 \times 8$ $12 \times 4$ $3 \times 16$ | $13 \times 10$ $13 \times 2$ $13 \times 12$ $13 \times 20$ $13 \times 19$ $13 \times 22$ |
- What relationships do you notice between the different questions in each string? When students recognise these relationships, they can draw on the answers to previous questions in the string to help them work out the answers to more difficult questions that come later in the string. How might students draw on previous answers to help them answer more difficult questions?
- Each string has been carefully designed to develop particular mental strategies by highlighting mathematical properties. What property is highlighted in each string and what mental strategy does each string develop?
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.