The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.

In this unit, students learn the very basics of navigation, including the different kinds of navigation and their purposes. The concepts of relative and absolute location, latitude, longitude and cardinal directions are explored, as well as the use and principles of maps and a compass. Students discover the history of navigation and learn the importance of math and how it ties into navigational techniques. Understanding how trilateration can determine one's location leads to a lesson on the global positioning system and how to use a GPS receiver. The unit concludes with an overview of orbits and spacecraft trajectories from Earth to other planets.

This task is a reasonably straight-forward application of rigid motion geometry, with emphasis on ruler and straightedge constructions, and would be suitable for assessment purposes.

To navigate, you must know roughly where you stand relative to your designation, so you can head in the right direction. In locations where landmarks are not available to help navigate (in deserts, on seas), objects in the sky are the only reference points. While celestial objects move fairly predictably, and rough longitude is not too difficult to find, it is not a simple matter to determine latitude and precise positions. In this activity, students investigate the uses and advantages of modern GPS for navigation.

In this activity, students will learn how to read a topographical map and how to triangulate with just a map. True triangulation requires both a map and compass, but to simplify the activity and make it possible indoors, the compass information is given. Students will practice converting a compass measurement to a protractor measurement, as well as reverse a bearing direction (i.e., if they know a tree's bearing is 100 degrees from you, they can determine what bearing they are from the tree). Students will use the accompanying worksheets to take a bearing of certain landmarks and then start at those landmarks to work backwards to figure out where they are.

In this activity, students will learn how to actually triangulate using a compass, topographical (topo) map and view of outside landmarks. It is best if a field trip to another location away from school is selected. The location should have easily discernable landmarks (like mountains or radio towers) and changes in elevation (to illustrate the topographical features) to enhance the activity. A national park is an ideal location, and visiting a number of parks, especially parks with hiking trails, is especially beneficial.

Students learn how to take bearings using orienteering compasses. They also learn how to describe a bearing and find an object in the classroom using a bearing.