Measuring for the Art Show: Addition on the Open Number Line and Subtractionis one of eight units in the Contexts for Learning Mathematics’ Investigating Number Sense, Addition, and Subtraction (K–3)
The focus of this unit is the development of the open number line model within the context of measurement. As the unit progresses, the number line is used as a model for double-digit addition strategies. The unit begins with the story of a teacher who has offered to organize an art show of children’s work as a school fund-raiser. The children have produced beautiful pieces of art and the teacher and several children set out to make signs to hang underneath each piece, listing the title of the piece, the artist’s name, and the price. They want to measure each art piece very carefully so that the sign will be exactly the same length as the piece of art. But this huge pile of work is daunting. Thankfully, the students soon figure out a solution. They sort the art by size, measure each size, and make a blueprint—a pattern strip—that will be used for cutting all the signs.
The story sets the context for a series of investigations in this unit. Children measure various sizes of art paper with connecting cubes and then place the measurements onto a long strip of adding machine paper, to be used as a blueprint or pattern for cutting the signs. As the unit progresses, lengths of fives and tens are introduced in place of the cubes and the blueprint is progressively developed into an open number line—a helpful model used as a tool to explore and represent strategies for double-digit addition.
In contrast to a number line with counting numbers written below, an “open” number line is just an empty line used to record children’s addition (and later subtraction) strategies. Only the numbers children use are recorded and the addition is recorded as leaps or jumps. For example, if a child’s strategy for adding 18 + 79 is to keep 79 whole and decompose the 18 into smaller pieces, moving to a landmark number of 80 (79 + 1 + 10 + 7), it would be recorded on the open number line.
Such representations help children move beyond tedious strategies like counting one by one to strategies such as taking leaps of ten, splitting, and using landmark numbers.
Several minilessons for addition are also included in the unit. These are structured as strings of related problems designed to guide learners more explicitly toward computational fluency with double-digit addition.
The unit culminates with an art show. Thus, as you progress through the unit, you may find it helpful to work with the art teacher in your school to collect pieces of student artwork.
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