Real Math!
How can we use free manipulatives at our disposal to make math real for students?
Data Collection Process - For Teachers
 For Teachers Collecting Data As students use the manipulatives in activities, they will need to collect enough data to analyze.  In most projects, students should work with at lease one partner to ensure data is as accurate as possible.  Allow students to account for human error.  As humans, it is nearly impossible to measure anything with 100% accuracy.  For this reason, we also generally use three trials and find an average.  If our activity were to find the area of the average hand towel, students would need to measure at least three different brands and find an average.  This ensures that our measurements are as close to the mean as possible.  For the example activity, students drop Barbie three times per additional rubber band, and measure the lengths of the falls in centimeters.  Students then find an average and convert to inches. Displaying Data Once data is collected, students should find an appropriate method of display.  Some data lends itself better to bar graphs or pie charts while other data is better represented in a line graph. We look to the type of data to know the right display to choose. When we collect data that represents parts of a whole, pie charts are the best means to display the information.    When we have data that shows various numbers with no relation to each other, we are more likely to choose a bar, picture, graph.      When the data we collect has some relation, we can showcase the information best with a line graph, or continuous graph.        In 8th grade, students work with linear equations.  These equations demonstrate the pattern that occurs with a constant rate of change.  The example Barbie project emphasizes linear equations and graphs because of the constant rate at which Barbie's fall changes with each additional rubber band.     For more information on creating graphs, check out this powerpoint.

 MATH-F.8.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. MATH-F.8.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. MATH-F.8.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Use functions to model relationships between quantities. MATH-F.8.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.