Course Guide - USAID Teacher Education Project

d) Help students understand how to:1) Set the range and appropriate scale for each axis2) Label each axis and title the graph3) Plot the data points (x, y) from the chart they createde) Introduce the idea of a pattern rule that can be used to describe the change betweentwo variables.f) Introduce the concept of direct variation where the variables change at the samerate. (Note that this is often not true of situations where data is collected in the realworld.)4. Class Activitiesa) Begin by having students give examples of things that change over time. Ask howthose changes might be represented. Students may, for example, refer to the "tree"problem done in the last session where the number of blocks used changed accordingto the age of the tree.Other changes such as distance as a function of time related to speed (d= rt) or thechange in a circle's circumference as a function of its diameter [C = pi(d)] may bementioned. Note: what students often call formulas are actually pattern rules put intoequations.b) Use "The Coin Graph" activity. Do this activity as a whole class demonstrationwhile students create the same T-chart and graph.During the coin collecting activity, create a T-chart of the data, adding x and y to thenames of the two columns. Note that x is the independent variable, and y is thedependent variable.When this activity is complete, refer to the empty grid paper on which you and theywill create a graph together. Demonstrate how to set up a first quadrant coordinategraph. Note that you labeled the axes to reflect issues for this particular activity, butthat the conventional way of discussing the two axes is to call the horizontal axis xand vertical axis y.Next, ask how you should add a scale to each axis. What would be a reasonableinterval to get all the data from the T-chart onto the graph? Proceed to label the axeswith numbers.Have students come up to the graph, refer to their T-chart, and plot the points. Whenfinished, ask about a "latecomer" scenario. How would the graph look if someoneadded their coins after class was in session, extending the table and graph? What ifthis activity were done in an auditorium with many more people? How would thataffect how they might scale the graph?What about a pattern rule? What in the table and on the graph suggest one? Is thepattern rule the same for both the table and the graph?