6. Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Representative IMP Year 1 Lesson:

You’re the Storyteller: From Rules to Situations (The Overland Trail), 53

Students are given a set of equations and must create a context that the equation could represent. Precision is important in this activity, as students must create a situation, clearly state what the variable represents (including units), and then find the number that will make the given equation true. Clear communication of their variables and their meaning is vital to this activity.

Representative IMP Year 2 Lesson:

How Many More People? (Small World, Isn’t it?), 389

In order to explore population growth, students must graphically represent population data over time. Students are asked to graph this data on an appropriate scale of axes. Using their graph or using algebra, they then find the average increases over different periods of time. They are then asked to look at different intervals of time in order to compare growth rates. Precision in graphing and calculating the average increase is used throughout the activity.