This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

This task shows how to inscribe a circle in a triangle using angle bisectors.

This task focuses on a remarkable fact which comes out of the construction of the inscribed circle in a triangle: the angle bisectors of the three angles of triangle ABC all meet in a point.

This task is primarily for instructive purposes but can be used for assessment as well. Parts (a) and (b) are good applications of geometric constructions using a compass and could be used for assessment purposes but the process is a bit long since there are six triangles which need to be constructed.

This task implements many important ideas from geometry including trigonometric ratios, important facts about triangles, and reflections. As a result, it is recommended that this task be undertaken relatively late in the geometry curriculum.

This task provides an opportunity for students to apply triangle congruence theorems in an explicit, interesting context.

This problem introduces the circumcenter of a triangle and shows how it can be used to inscribe the triangle in a circle. It also shows that there cannot be more than one circumcenter.

In this task students are asked to label negative numbers on a numberline and then answer questions about which are greater or less than.

Given two bank interest rate scenarios, students will compare returns, write an expression for a balance, and create a table of values for the balances.

This division task asks studnets to consider the conceptual understanding of something usually taught as a rote procedure. To be successful with this task, students must make sense of the procedure and how place value is represented and abbreviated within it.

Students will use the graph (for example, by marking specific points) to illustrate the statements in (a) and (d). If possible, label the coordinates of any points you draw.

The purpose of this task is to help students learn to read information about a function from its graph, by asking them to show the part of the graph that exhibits a certain property of the function. The task could be used to further instruction on understanding functions, or as an assessment tool with the caveat that it requires some amount of creativity to decide how to best illustrate some of the statements.

This problem provides an opportunity to experiment with modeling real data. Populations are often modeled with exponential functions and in this particular case we see that, over the last 200 years, the rate of population growth accelerated rapidly, reaching a peak a little after the middle of the 20th century and now it is slowing down.

This task rquires students to determine if linear functions would be useful to model relationships presented in a data table.

This task lets students explore the differences between linear and non-linear functions. By contrasting the two, it reinforces properties of linear functions. The task lends itself to an extended discussion comparing the differences that students have found and relating them back to the equation and the graph of the two functions.

This task could serve as an introduction to polynomials or as an application after students are familiar with this type of function.

This task illustrates several components of standard F-BF.B.4.c: Find Inverse Functions. Here, instead of presenting two functions and asking the students to decide which one is invertible, students are asked to complete a table of input-output pairs for the functions in such a way that one of the functions is invertible and the other one is not.