Exploring with GeoGebra New Goal: Geometry Explorations Using GeoGebra to explore Emphasis on Mathematical Practice Standards How would your students explain their work in these Explorations?

Exploration 1 Where should I live? Download the Explorations at http://faculty.ithaca.edu/dabrown/geneva/ Go to Day 3, Exploration 1 Open WhereToLive.ggb The map was created in Google Maps I took a screen shot and used the Insert Image tool

Exploration 1 Where should I live? You are planning to move to Downtown Ithaca and you want be the same distance from from home to each of Wegmans, the Farmers' Market, and your Mom's house. Figure out the best location for your new home. Without doing anything else, make a reasonable guess as to where you should live. How would you go about solving this problem? How did your solution compare with your initial guess? Anything surprise you?

Exploration 2 Using the Tools menu Create a centroid tool Construct an arbitrary triangle Construct midpoint of each side Construct each median Use the Intersect Two Objects tool to create centroid Select the centroid (only the centroid) Choose Create New Tool... in Tools menu In the dialog box, the centroid should be listed as Output Objects Click Next (the triangle vertices appear as Input Objects) Name tool (such as Centroid), check the Show in Toolbar, and click Finish Now, tool appears in toolbar. Create another triangle and use the Centroid tool.

Exploration 2 Using the Tools menu Use the centroid tool to discover a significant difference between the centroid of a triangle and the circumcenter created in Exploration 1. Create an Orthocenter Tool (recall, the orthocenter is the intersection of altitudes of a triangle) Explore the differences between the centroid, circumcenter, and orthocenter. Do they ever coincide?

Exploration 3 Where Should the Mirror Go? This young lady wants to install a mirror so that she can see her whole body in the mirror without wasting material. Use the accompanying GGB file to see the modeling power of GeoGebra and to explore questions on the next page.

Exploration 3 Where Should the Mirror Go? This young lady wants to install a mirror so that she can see her whole body in the mirror without wasting material. What is the minimum possible length of the mirror? How high up the wall should the mirror be mounted? How from the mirror should she stand?

Exploration 4 Four-bar linkage

Exploration 4 Four-bar linkage A four-bar linkage contains four links that interconnect and rotate (or not). The Frame link rigidly connects the linkage to another system. The Coupler is opposite the Frame and connects the remaining two links. The linkage may have 0, 1, or 2 links that completely rotate.

Exploration 4 Four-bar linkage Download Linkage.ggb and explore Use Construction Protocol (View Menu) to see how I built it. What conditions on the lengths of the links guarantees that at least one link fully rotates? Explore different lengths for the different links. Make the Frame the longest side and make Link2 the shortest. How are the lengths of the Frame and Link2 related to other two lengths when Link2 rotates completely? What is the motion of Link1 in this case?

Exploration 5 Nine Point Circle – from EngageNY Module 1 Go to Lesson 31 in Module 1 or Open Explorations 3 in download