How often do you hear, “I don’t get what they want me to do!”? Deciphering word problems can trigger bouts of unproductive struggle, but word problems are not as complex as they first seem. Did you know that there are only four or five basic types of problem situations for addition or subtraction word problems? It’s true for multiplication and division, too, no matter what kind of numbers are in the problem. Productive struggle with word problems dwells in the sense-making phase– what does it mean to understand a problem situation, in a mathematical sense? Understanding word problems is more than reading comprehension, followed by computation. Drawing, modeling, constructing, describing, and sense making happen in what we call the “Mathematizing Sandbox.” In the sandbox students pack down and build up representations, look at them from different angles, and maybe tear them back down and start all over again. Nothing is permanent in the Mathematizing Sandbox! When students “construct” the meaning of a problem, they learn that each word problem tells a tale. Acting out the story or exploring the relationships among quantities reveals “the work” each operator (+ - x ÷) can do, giving students access to the general problem situations in specific word problem contexts. Empowered to better understand word problems and to mathematize real world situations, the world of mathematical modeling and problem-based learning is a natural next step.

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When students mathematize, they learn to see situations through a mathematical lens and build from this understanding to model increasingly complex scenarios. Word problems are an important tool for helping students understand how mathematics describes situations in the world around us. More than “narrative computation,” carefully structured problems help students develop strong operation sense and learn to mathematize their world. While powerful when used well, word problems are also complicated by many different variations. Fractions, integers, and algebra can complicate things further. Even when students understand the operations well, the transition from whole numbers to new categories of values can make familiar problem structures seem new again. It is important to support students using multiple representations to find the underlying known structures and make sense of the situation.

In this session, we will share structures and strategies which build from elementary into middle grades and extend to include the full range of mathematical ideas students are expected to understand in middle school. How do we build from equal groups multiplication and multiplicative comparison into proportional reasoning? Where does the idea of sample space in probability fit in the work of multiplication? What happens to addition and subtraction when situations involve integers? These are all important parts of extending operation sense into middle grades and supporting students’ developing modeling skills.

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“My brain told me the answer.” “I don’t get what they want me to do!” Have you heard these comments from students? Why does one student seem to automatically know how to find the answer to a word problem and another doesn’t know where to start? In this session we will dive into that space between understanding what the words in a word problem say and how to calculate its answer. In that space students make sense of the actions or relationships within a word problem and then select a solution strategy that matches.