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### Measuring Uncertainty

9-12

By measuring long jump results, students will discover how to determine the appropriate number of digits they should report when taking a linear measurement. Students will realize that measured numbers are never exact and researcher skill and tools can be analyzed to determine the precision of a measurement.### Analyzing the Data

9-12

In the third lesson, students identify a function that models the data. An interactive graphing tool can be used to determine a function that fits the data points.

### Do You Notice Sum-Thing?

6-8, 9-12

This lesson invites students to investigate the patterns when a "plus sign" (a cross-shaped arrangement of five squares) is placed on the board in various locations. Students will conjecture about the pattern of the five displayed numbers, the sum of the five numbers, and any other patterns that they notice. Students may also explore similar patterns when other shapes, such as a 2 × 1 rectangle, are placed on the hundreds board.### Don't Freeze the Engine

9-12

In this lesson, students will learn to read an antifreeze chart to determine the necessary mix of antifreeze and water for protection against various temperatures. Students will then numerically analyze a particular cooling system to determine how much fluid to drain in order to get the desired percent concentration of antifreeze. Finally, students will set up a system of equations to solve the same system.### Elevator Arithmetic

6-8, 9-12

Students will use vertical movement of an elevator to evaluate signed number expressions.

The idea behind the method of adding and subtracting signed integers offered in this lesson and the next is that the number of rules that students have to *memorize* and the amount of *understanding* are minimal, while the underlying concepts are not trivialized.

### Exploring Equations Further

9-12

Starting from the concrete notion of weights and balance and moving to symbolic expressions and representations of functions, this i-Math investigation has focused on some of the issues that arise along the way. In this part, this connection is extended to functions. More sophisticated tools allow for a greater diversity of investigations.### Flipping for Integers

6-8, 9-12

In this lesson, students will adapt expressions that add or subtract two signed integers.### The Brew Master

9-12

Students develop a delicious new drink by mixing various concentrations of a two-fold dilution series. Students calculate the percents of their mixtures, taste these differences, and visually observe their results.### Walk to the Movies

6-8, 9-12

In this lesson students measure their speed walking in a hallway and predicting how long it takes them to get to the local movie theater 3 miles away. This is an open-ended problem in which students must develop a strategy on how to collect the data, how to convert the data to MPH, and finally make a prediction. In addition to reasoning skills, students will practice unit conversion, prediction, proportions, and graphing.### What's the Function?

9-12

This activity allows students to look for functions within a given set of data. After analyzing the data, students should be able to determine what type of function best represents the data.