Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

An art gallery is holding a special exhibition of small watercolors. The exhibition will be held in a rectangular room that is 22 meters long and 20 meters wide with entrance and exit doors each 2 meters wide as shown below. Two security cameras are fixed in corners of the room, with the resulting video being watched by an attendant from a remote control room. The security cameras give at any instant a "scan beam" of 30o. They rotate backwards and forwards over the field of vision, taking 20 seconds to complete one cycle.

For a function that models a relationship between two quantities, students will interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

The purpose of this task is to study an example of a function which varies discretely over time.

The First National Bank has just been robbed (the position of the bank on the map is marked). The clerk pressed the silent alarm to the police station. The police immediately sent out police cars to establish road blocks at the major street junctions leading out of town. Additionally, 2 police cars were dispatched to the bank.

|The bank manager is trying to improve customer satisfaction by offering better service. Management wants the average customer to wait less than 2 minutes for service and the average length of the queue (length of the waiting line) to be 2 persons or fewer. The bank estimates it serves about 150 customers per day. The existing arrival and service times are given in the tables below

This task asks students to analyze a set of data from a physical context, choose a model that reasonably fits the data, and use the model to answer questions about the physical context.

This task asks students to analyze a set of data from a physical context, choose a model that reasonably fits the data, and use the model to answer questions about the physical context.

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

Almost everyone will seek health care at some point in life. In an emergency, an individual will most likely go to the closest hospital, but for non-emergencies we may have a choice of where to seek treatment.

Although it's only November, you need to start planning for your 2021 summer job. You have a variety of choices this year and want to determine your "best" choice. You pose this problem for your team of math friends:

Several cities in the US are starting bike share programs. Riders can pick up and drop off a bicycle at any rental station. These bicycles are typically used for short trips within the city center, either one-way or roundtrip. The idea is to help people get around town on a bike instead of a car. Those making longer trips (such as commuting to work) are likely to use their own bikes. Some of the challenges are how to determine where to locate the rental stations, how many bikes to have at each station, how/where to add new locations as the program grows, how many bikes to move to another location and when (time of day, day of week).

This task examines linear models for the boiling point of water as a function of elevation. Two sets of data are provided and each is modeled quite well by a linear function.

The purpose of this task is to give students experience working with simple exponential models in situations where they must evaluate and interpret them at non-integer inputs.

A number of communities (campuses, towns, cities, etc.) around the world have proposed and enacted plastic water bottle bans in some form.

In 2013 the small town of Concord, Massachusetts (population approximately 19,000) became the first town or city in the United States to ban the sale of single-serving Polyethylene terephthalate (PET) bottles less than or equal to 1 liter (34 ounces) containing water which is non-sparkling and non-flavored (in other words, plain water)[1]. The sale of water in bottles of any size made of other types of plastic or other materials, as well as PET bottles of flavored or sparkling water, soda, tea, juices, and other non-plain water beverages, regardless of size, is allowed[2]. See attached FAQ document.

Open Middle provides math problems that have a closed beginning, a closed end, and an open middle. This means that there are multiple ways to approach and ultimately solve the problems. Open middle problems generally require a higher Depth of Knowledge than most problems that assess procedural and conceptual understanding.

This student interactive, from Illuminations, allows students to create a customized box plot as well as display pre-set box plots.

This task is for instructional purposes only and builds on ''Building an explicit quadratic function.'' First, it is vital that students have worked through ''Building an explicit quadratic function'' before undertaking this task.

This task is intended for instruction and to motivate the task Building a General Quadratic Function. This task assumes that the students are familiar with the process of completing the square.