Number Strings Primer
Number Strings: What is it?
Number Strings is a short, routine activity that engages children in mentally solving a
“string” of related equations. This task is designed to highlight efficient computation
strategies (often but not necessarily done mentally) and an understanding of the
meaning of mathematical operations. Each problem in the string is designed to build
on the thinking used to solve previous problems.
In this activity, teachers present a sequence of equations designed to encourage
students to notice a particular mathematical concept or make use of a particular
strategy. After introducing the task, the teacher gives students the first problem and
then engages students in a conversation about how they solved it, highlighting
efficient strategies and how the strategies work. These ideas are recorded on the
board, sometimes with an accompanying representation. The teacher then poses
another problem and repeats the process, usually offering three to five problems in a
session. At the end of the activity, the teacher synthesizes the strategies that
students found helpful and the mathematical goal of the lesson.
Number Strings supports students to build computational fluency by developing
understanding of the relationships between numbers and how the operations work.
For example, the sequence of equations and numbers selected in the following
number string encourage students to use a compensating or “friendly number”
strategy.
10 + 7
9 + 7
9 + 27
9 + 84
I know 10+7 is 17
9 is one less than 10. 10+7 is 17, so 9+7 is one less, 16
9 is one less than 10. 10+27 is 37, so 9+27 is one less, 36
10 + 84 is 94, so 9+84 is one less, 93
This instructional activity is a powerful tool for novices and practicing teachers in that
it has a predictable structure, engages children in rich mathematics, and can
continue to be refined and modified to pursue a broad range of mathematical goals.
Teachers with varying levels of expertise can enact this task and continue to learn
about student thinking and the mathematics involved as they engage with students
in the activity.
The Number Strings Instructional Activity is adapted by the University of Washington based on the Young
Mathematicians at Work series by Fosnot & Dolk (2001). © 2014 University of Washington. For
noncommercial use only. For commercial use please contact license@uw.edu. For all other information
contact TEDDinfo@uw.edu.
What are kids working on: What’s the math?
Teachers can select numbers and operations to suit a wide variety of mathematical
goals. Children can think about solving each equation in multiple ways, providing a
broad range of access points for a given string. Some of the ideas children might
work on in Number Strings include:
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Composing and decomposing numbers
Place value, ideas about tens and ones
Structure of the base ten system
Efficient computational strategies across the operations
Comparing strategies
The meaning of the operations
What are teachers working on: What practices of
ambitious teaching are embedded?
Number Strings is a discussion-based activity, making it a great opportunity for
teachers to work on eliciting and responding to children’s ideas. As children share
the strategies that they used to solve the equations, teachers must develop
strategies for engaging the whole class in considering those ideas, orienting
students toward one another and the math content.
Teachers must also decide, in the moment, which ideas to further pursue in order to
teach toward their instructional goal. Through careful number selection and
sequencing of equations, teachers can anticipate some of the ideas that children
might share and how they will respond. Number Talks by Sherry Parrish provides
detailed guidance in these areas.
Another important practice that teachers have an opportunity to work on in Number
Strings is representing children’s thinking. As students share how they solved the
problems, teachers must represent these ideas in a way that provides access to the
idea for the rest of the students, supports the mathematical goal of the lesson, and
honors the child’s thinking.
In addition, the Number Strings activity protocol is similar to the Quick Images
activity protocol (see Number Talks by Sherry Parrish). The similar structure of these
two activities increases the mathematical terrain that teachers can explore while
utilizing a similar protocol and embedded practices.
The Number Strings Instructional Activity is adapted by the University of Washington based on the Young
Mathematicians at Work series by Fosnot & Dolk (2001). © 2014 University of Washington. For
noncommercial use only. For commercial use please contact license@uw.edu. For all other information
contact TEDDinfo@uw.edu.
Resources
Parrish, S. (2010). Number Talks: Helping Children Build Mental Math and
Computation Strategies. Math Solutions: Sausalito, CA.
Fosnot, C. & Dolk, M. (2001). Young Mathematicians at Work: Constructing Number
Sense, Addition, and Subtraction. Heinemann; Portsmouth, NH.
Fosnot, C. & Dolk, M. (2001). Young Mathematicians at Work: Constructing
Multiplication and Division. Heinemann; Portsmouth, NH.
The Number Strings Instructional Activity is adapted by the University of Washington based on the Young
Mathematicians at Work series by Fosnot & Dolk (2001). © 2014 University of Washington. For
noncommercial use only. For commercial use please contact license@uw.edu. For all other information
contact TEDDinfo@uw.edu.