circumference
1) The size of circle O can be changed by dragging point A horizontally. Drag point A and observe the effect on how the circle looks. Also observe how the length of radius OA changes as you drag the point.
2) Make a conjecture on how you think the circumference of circle O will be affected as you drag point A to the left. How do you think the circumference will be affected as you drag point A to the right?
3) Click on the button, “Show Circumference”. The circumference of circle O will appear. Notice how the circumference changes as you move point A left and right. Does this verify your conjecture?
4) Imagine you plotted a point where you let the x-value be represented by the radius OA and let the y-value be equal to the circumference of circle O. Describe below how you think that point would behave as you changed the radius length of circle O.
5) Click on the button, “Show Point (radius, circumference)”. As you drag point A horizontally, observe how the plotted point changes coordinates. Is this how you expected the point to behave?
6) While observing the plotted point react to your dragging of point A, make additional conjectures below about how the graph that the collection of these plotted points would produce will look.
7) Click on the button, “Show Traced Point”. You will see how your plotted point will pass through all of the “traced points”, giving you a better idea of what this graph would look like. Does the graph look how you expected it to look? Explain anything you noticed about the graph that surprised you.
8) Now that you know a bit more about the collection of plotted points (radius, circumference), can you make any conjectures as to why the graph looks this way? Describe them below. Make note of things like the slope, intercepts, how the graph was created, and anything you know about circles and circumference when making your conjectures.
9) A calculation can be made available by clicking the “Show Calculation” button. Does this calculation confirm your beliefs about the model? Explain below why you think the given calculation makes sense or what values it reminds you of?
10) Write the formula for the circumference of a circle below? How does the graph that was created connect with that formula?