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Building an Understanding for Linear Functions Part II

Building an Understanding for Linear Functions Part II. Jim Rahn www.jamesrahn.com james.rahn@verizon.net. Consider the sequence of cubes where each cube is set of cubes is attached at a face. The length of each edge of the cube is 2 units.

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Building an Understanding for Linear Functions Part II

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  1. Building an Understanding for Linear FunctionsPart II Jim Rahn www.jamesrahn.com james.rahn@verizon.net

  2. Consider the sequence of cubes where each cube is set of cubes is attached at a face. The length of each edge of the cube is 2 units. Complete the table for a sequence of figure cubes.

  3. Write a recursive routine for the number of visible faces. Write a recursive routine for the total visible surface area. Write a recursive routine for the total volume.

  4. Find the number of visible faces in Figure 10. Find the volume of Figure 12. Which figure has at 47 visible faces? Which figure has 68 square units of visible surface area? Will a figure have exactly 200 visible faces? Why or why not? Which figure will have a volume of 168 cubic units?

  5. Write a formula that could be used to find the number of visible faces in Figure n. Write a formula that could be used to find the visible surface area in Figure n. Write a formula that could be used to find the volume of Figure n.

  6. If the figures could be picked up and moved around find the number of visible faces in each figure.

  7. Write a recursive sequence for this information. How is it different from the previous sequence for visible faces?

  8. Time-Distance Relationships Explore time-distance relationship Write walking instructions or act out walks for a given graph Sketch graphs based on given walking instructions or table data Use an electronic device, motion sensor, and graphing calculator to collect and graph data

  9. The time-distance graphs at the right provide a lot of information about the walks they picture. Because the lines are straight and increasing means that both walkers are moving away from the motion sensor at a steady rate. The first walker starts 0.5 meters from the sensor, whereas the second walker starts 1 meter from the sensor. The first graph pictures a walker moving 3-1= 2 meters in 4-0 =4 seconds or 1/2 meter per second. The second walker covers 3.5-0.5=3 meters in 3-0=3 seconds or 1 meter per second. In the next activity you will analyze time-distance graphs and create your own graphs.

  10. Walk the Line Study one of the pictures above. Each describes a 6 second walk. The vertical axis shows 0 to 4 meters. Write a set of walking instructions for each graph. Tell where the walk begins, how fast the person walks, and whether the person walks toward or away from the motion sensor. Make a paper graph of a 6 second walk based on your instructions.

  11. Obtain a CBR (motion detector) to use with your graphing calculator to complete set of instructions. Be ready to discuss the results of your investigation.

  12. Building Understanding for the form y = b+mx

  13. Federal Minimum Wage • The chart below show the federal minimum hourly wage for 1974-1997.

  14. 1. Make a scatter plot of the data on your calculator. Describe any patterns you see in the table and/or graph. • 2. Select two points that you believe represents the steepness of the line that would pass through the data. (________, ________) and (________, ________) • Find the slope of the line between these two points.

  15. Give a real world meaning to this slope. • Use the slope you found to write an equation of the form y = mx. • Graph this equation with your scatter plot. • Describe how the line you graphed is related to the scatter plot. • What do you need to do with the line to have the line fit the data better?

  16. Run the APPS TRANFRM on your graphing calculator. Change your equation to y=B+Ax. Press WINDOW and move up to Settings. Change B to start at 0 and increase by steps of 10. Press GRAPH and notice that B=0 is printed on the screen. Use the right arrow to increase the value of B. What happens to the graph as you increase the value of B. • Continue to increase or decrease the value of B until you have a line that fits the data. Write the equation for your line.Y = _____________________ • What is the real world meaning for the y-intercept you located?

  17. Use your equation to predict what the federal minimum wage will be in 2010. Explain how you predicted the number of quarters. • Use your equation to predict when the federal minimum wage will exceed $7.00. Explain how you found your answer. • Use your equation to predict when the federal minimum wage was $1.00. Explain how you found your answer.

  18. You have seen steepness of a line can be a graphical representation of a real-world rate of change (car’s speed, walking a line). • Study the graphs at the right. • Study the equations at the side of each graph. • Match each line with one of the equations.

  19. On the first picture draw a slope triangle on line A that illustrates its slope. • Add a second slope triangle to line A that illustrates the same slope. • Add a third slope triangle to line A that illustrates the same slope.

  20. On the first picture draw a slope triangle on line D that illustrates its slope. • Add a second slope triangle to line D that illustrates the same slope. • Add a third slope triangle to line D that illustrates the same slope.

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