Get connected with like-minded individuals in the movement dedicated to innovative thinking and action to improve and advance STEM education. Sign up below for our updates on STEM events in USA and around the globe.

## 5. Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

**Representative IMP Year 1 Lesson:**

*Sublett’s Cutoff Revisited (Overland Trail), 67*

The graphing calculator is used to quickly plot data and allow students to graph various linear functions that will fit the data best. Students have been using paper and pencil methods up to this point and will discover that technology will allow them to explore more efficiently and deeply than their previous experiences. After finding the line of best fit, they use their function to make predictions regarding water consumption over a period of time.

**Representative IMP Year 2 Lesson:**

*Parabolas and Equations I and III (Fireworks), 11, 14*

Students use the graphing calculator to explore families of functions. They begin with the simple function for a parabola and then investigate what parts of the function make the graph narrower, wider, inverted, and translated in any direction. Using the investigative approach, students soon discover what each parameter does in *y = a(x)^2 +k*