Video: Division on the open number line in fourth grade

Wondering what a number string looks like in a classroom? Curious about the details of the routine? The following video features site co-founder Rachel Lambert teaching a group of 4th grade students at the Citizens of the World Charter School in Mar Vista, CA. These students have a wonderful classroom teacher, Hayley Roberts, who does number strings regularly with the students as part of a rigorous, inquiry-based mathematics curriculum. Hayley is off camera in Part 1 leading the students in a mathematics mindfulness exercise.

Students in this class had done lots of number strings with the open number line for addition and subtraction, as well as the array as a model for multiplication. On the previous day, the number string had been a multiplication doubling and halving string on the open number line. Today’s number string was designed to help students understand division on the open number line, focused on using equivalence as a strategy. Before you watch, you might want to anticipate how 4th graders might solve these problems, and how Rachel will represent strategies on the open number line.

2 x 50

4 x 100

100 ÷ 2

100 ÷ 4

200 ÷ 4

400 ÷ 8

800 ÷ 16


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What the kids say…..

I’ve known Rachel Carr for many, many years.  She shepherded me through that exhilarating and exhausting first year of teaching and has remained a mentor and role model ever since.  This summer Rachel attended a summer institute at Math in the City, and we got to work together again — making sense of the landscape of learning for rational number.  I am continually struck by how a teacher with so much experience and insight still considers herself a learner.

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“Stack of Bills” string

Here’s a string I designed with a team of fifth grade teachers who were looking for creative ways to encourage a multiplicative understanding of place value.  When students are reasoning additively about number, they might see 321 as equivalent to (3 x 100) + (2 x 10) + (1 x 1).  And this is very common in classrooms, and is often confused as thinking multiplicatively because it does involve some multiplication. But in essence you are splitting the number into place value parts and adding those together. When students are able to reason multiplicatively about number it looks more like this: 321 = 32.1 x 10 or 3210 ÷ 10.

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