Number Strings

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A number string is a set of related math problems. Strings are often used in the earlier grades, but can be used in any grade, and the benefits of the strings are everlasting. Students work to solve strings using mental math strategies and then share their strategies with the class after being given time to sit and think about the problem. Each problem in the string is revealed one after the other, but it is extremely important to keep each problem (and its solutions) visible.

Here is an example of a string.

19 x 10 =
19 x 2 =
19 x 12 =
19 x 20 =
19 x 19 =
19 x 21 =

When doing a string, I would pose the first problem and then tell students to think about how to figure it out and answer it. It is important for students to be asked for a strategy along with a solution. I would ask them to put their thumb on their desk when they are ready. I make sure the give students plenty of “think time” for the string and stress putting the thumb on the desk instead of raising their hand so that people who haven’t had enough time feel like they can still take the time to think.

Benefits of this string:

Doubling: students can double the solution from 19 x 10 to arrive at the solution for 19 x 20.

Adding on: students can add an additional set of 19 to the solution from 19 x 20 to arrive at the solution to 19 x 21.

Chunking/Distributive property: 19 x 19 could be broken into (19 x 10) + (19 x 9). Similarly, 19 x 12 can be seen as the sum of 19 x 10 and 19 x 2.

Proportional thinking: this goes along with both the idea of doubling and chunking. Students start to see that when one factor increases by 1, the solution increases by “a set of 19”.

Besides the specific benefits listed above, strings, in general, have myriad advantages. Strings improve students’ flexibility in thinking and expose them to multiple methods/strategies for one problem. This flexibility allows students to build their fluency and confidence. The format of the strings allows quieter or slower students time to process and share their ideas or build on the ideas of their classmates. Since strings are related problems, they are designed to help students see, identify, and use patterns. This lets students use what they already know to move forward and solve different problems. Additionally, strings help model student thinking and, since the model is shown to all students, the strings help students fluidly use models to problem solve.
Additional resources for number strings:

 

Websites:
http://numberstrings.com/about/

Books:
http://www.heinemann.com/products/E01013.aspx (and other Context for Learning mini-lesson books)
http://www.heinemann.com/products/E04804.aspx
http://www.heinemann.com/products/E02662.aspx

 

Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.