HCPSS Worthwhile Math Task
Your Trip to Paris
Common Core Standard
G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
MP1:
MP2:
MP3:
MP5:
MP6:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically.
Attend to precision.
Common Core Geometry, Unit 3
The Task
Your parents call you down to the kitchen. You think you are in trouble, but instead they
surprise you. Since you have kept your grades up, even earning an “A” in French, you are going
on a family vacation to Paris this summer! They haven’t finished planning all of the details and
would like your help in determining where to stay. They want your hotel to be equidistant from
the top three places that you would like to visit.
Use the map and choose three places that you would most like to visit while in Paris. You can
choose any three attractions as long as they do not lie along the same line.
Construct where the hotel should be located in order to be equidistant from the places you chose.
On loose-leaf paper (or optional stationary), write a note to your parents justifying how you
know that you found the right location for the hotel.
Facilitator Notes
1. Distribute a copy of the map of Paris to each student.
2. Allow students a few minutes to look over the map. Share any knowledge you or they
have about the points of interest highlighted on the map. (Look for evidence of MP1 and
MP2.)
3. Provide students with construction tools: ruler, compass, patty paper, transparencies and
markers. Optional material: stationary for note to parents. (Look for evidence of MP5.)
4. You may want to have them verify their construction is accurate prior to writing the note
to their parents.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
5. Remind students that when writing the note, “justify” means that you need to tell why
you know that what you have done is correct. Simply explaining what you did is not
enough. (Look for evidence of MP3 and MP6.)
6. Have students share the locations that they chose and the note they wrote to their parents.
7. See the following site for additional support following the task:
http://illuminations.nctm.org/LessonDetail.aspx?ID=L661
Follow-Up Questions
1.
2.
3.
4.
5.
What influenced your choice of locations?
Why do you think that the instructions specified your locations could not be in a line?
What is the geometric name for the location of the hotel?
Construct the circumscribed circle.
Can you think of other “real-world” situations where you would need to locate the point
equidistant from three given non-linear points?
Extension Activities
1. Driving in Paris is very dangerous; people play bumper cars with their automobiles.
Suppose that your family is going to rent scooters to get around the city while on
vacation. Use your construction tools to find where the scooter rentals would best be
located in order to be the shortest distance from the paths connecting your points of
interest.
2. Justify why your location is the best.
Solutions
Answers will vary. Check student constructions. Students should connect their locations using a
straight edge or copy and connect the points on patty paper. Students should then be
constructing the perpendicular bisectors of at least two sides of the triangle either with a compass
or folding the patty paper. The hotel should be located at the point where the perpendicular
bisectors intersect. This point is equidistant from the vertices of the triangle.
One possible solution:
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Follow Up Question Sample Answers:
1. Answers will vary.
2. If the points were co-linear, there could not be a location equidistant from all three points
of interest. It could be closer to one or two, but not all three.
3. The circumcenter.
4. Check student constructions.
5. Answers will vary. Sample Answer: Locating the bathrooms in an amusement park
equidistant from the three most popular rides. Locating the center for a circular sink that
will pass through certain points on your counter.
Extension Activity Sample Answers:
1. Answers will vary.
2. Students should construct the incenter; by bisecting the angles, students find the point
that is equidistant from the sides of a triangle.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Your Map of Paris
http://www.parisleftbankapartment.com/?page_id=18
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
http://www.paris-architecture.info/IMAGES/paris_city_map.jpg
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.