
ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary 
Please keep in mind that this is a research project, and there may sometimes be glitches with the interactive software. Please let us know of any problems you encounter, and include the computer operating system, the browser and version you're using, and what kind of connection you have (dialup modem, T1, cable).
Welcome to ZOOM!
Your challenge is to explore the concept of scale in mathematics and apply it to your everyday experiences. Scale is an important concept to mathematicians and people in many other fields, because it allows one to gain many different perspectives on the same thing. You may notice important things in one scale that you might not see in another.
To Do and Notice
Use the graph zooming applet to experiment with different scales of a graph.
Notice what you see and don't see depending on the view you choose. Use your experiences with the applet to answer the following questions:
 What is the point of intersection of the red and green lines? (Please write as an ordered pair.)
Zoom in so you cannot see the red line. You have just changed the scale of the graph. Notice that the minimum and maximum x and y values of the graph have changed.
 Describe what the Zoom In button does. Why does it make the red line disappear? (Hint: Consider what points are on the red line.)
 Suppose you could add a fourth Zoom button that would show the intersection of the green line on the yaxis (the "yintercept"), but not show the red line at all. What would your new button do? (Hint: What would the new scale of the graph be?)
 Bonus question: Change the equation for the blue line. Experiment with different equations until you can see your new line when the graph is in the Zoomed In position. What is the equation of your line?
Teacher Support Page I'm happy to say that everyone who tried the bonus got it right! But that makes me wonder if it was too easy...
I had a great time mentoring this week. I think it was a combination of having students who cared about the math and having a wellworded problem with an applet that worked.
I was really excited that so many of you revised your solutions this week (about 33%). The main problem you had was in being clear enough in your explanations, though most of you seemed to understand what you wanted to say. In many cases, when you revised, you made things very clear.
I guess the main problem was that people talked about what zooming in was without talking about why the red line didn't show up. Don't forget, these solutions are read by people who don't know how to solve these problems, so your clear explanations are very important!
The second problem that people had was in clearly explaining what the new zoom button would show. We felt that to make it clear, you should state what was in the center, plus how far out on the x and yaxes you could see. Some people mistakenly thought that the current zoomin button would suffice  but that doesn't show where the green line intersects the yaxis.
Thanks to all of you who participated this week. I enjoyed the interactions. Please take a look at the problems that were highlighted to see some details that you may have missed in your solutions.
 Jody

1. What is the point of intersection of the red and green lines? (Please write as an ordered pair) (20, 80) Zoom in so you cannot see the red line. You have just changed the scale of the graph! Notice that the minimum and maximum x and y values of the graph have changed. 2. Describe what the Zoom In button does. Why does it make the red line disappear? (Hint: Consider what points are on the red line). The zoom in button is used to scale down the graph. The numbers on the x and y axis become smaller, because you're looking more closely at the scale. The red line disappears because it intercepts the x oaxis at 60, and the yaxis at 60. Therefore, if you zoom out so that all you can see of the graph is points going up to 11 and negative 11, then obviously you would not be able to see the red line. 3. Suppose you could add a fourth <b>Zoom</b> button that would show the intersection of the green line on the yaxis (the "yintercept"), but not show the red line at all. What would your new button do? (Hint: What would the new scale of the graph be?) The fourth zoom button would serve to zoom in just to show the green line and where it intercepts the x and y axis, but not to the point where it would show the red line. So, if you wanted to make a new graph to only show where the green line intercepts the x and y axis and the green line itself, you would have several options. The graph would have points going up to 20 and going down 20. Like, the yaxis would have points going up to 20, and points going down to 20, so there are 40 points in between. Bonus question 4. Now change the equation for the blue line. Experiment with different equations until you can see your new line when the graph is in the Zoomed In position. What is the equation of your line? y = 9/7 x + 10

1. What is the point of intersection of the red and green lines? (Please write as an ordered pair) (20, 80) Zoom in so you cannot see the red line. You have just changed the scale of the graph! Notice that the minimum and maximum x and y values of the graph have changed. 2. Describe what the Zoom In button does. Why does it make the red line disappear? (Hint: Consider what points are on the red line). The zoom in button shows the graph more close up. Therefore the points only go up to 11 and 11 from the origin which is (0,0). The red line disappears because when the graph was 'zoomed out' the red line crosses the graph at 60 and 60. But when the graph was 'zoomed in' the graph only showed up to points 10 and 10. Thus, there is no possible way that we could've seen the red line. 3. Suppose you could add a fourth <b>Zoom</b> button that would show the intersection of the green line on the yaxis (the "yintercept"), but not show the red line at all. What would your new button do? (Hint: What would the new scale of the graph be?) The yaxis should reach up to 22 and 22. The xaxis should reach up to 22 and a little bit more and 22 and a little bit more. There can also be more options. This button should make the graph zoom in so we will only be able to see the green line and its yintercept. Since the yintercept is 20. The scale increases and decreases by 2s. Bonus question 4.Now change the equation for the blue line. Experiment with different equations until you can see your new line when the graph is in the Zoomed In position. What is the equation of your line? y = 9/7x + 10
Alex Acosta, age 15  Westside High School, Houston, TX
Lee Bobbitt, age 15  Westside High School, Houston, TX
Andy G., age 13  Georgetown Day School, Washington, DC
Julius L., age 13  Taipei American School, Taipei, Taiwan
Katie L., age 13  Taipei American School, Taipei, Taiwan
Tina L., age 13  Taipei American School, Taipei, Taiwan
KaiLing S., age 13  Taipei American School, Taipei, Taiwan
Mary S., age 13  Taipei American School, Taipei, Taiwan
Max S., age 14  Taipei American School, Taipei, Taiwan
Will S., age 15  McLean High School, McLean, VA
Michelle Shadwell, age 17  Westside High School, Houston, TX
Brian T., age 14  McLean High School, McLean, VA
Denise W., age 13  Taipei American School, Taipei, Taiwan
Grace Hsiang Wen Y., age 14  Taipei American School, Taipei, Taiwan