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.

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.

TuvaLabs Data Stories provide resources for teachers to engage students in rich discourse about an interesting topic and then allows students to come to conclusions using mathematical reasoning and tools.

In this task students are asked to write expressions about the relation to the price of oil and gas mileage.

A regional city has had lots of problems with gangs and violence over the years. The mayor, chief of police, and city council need your help. Data are available for the following: Incidents of violence, Homicides, Assaults, Regional Population (Census data), Unemployment, Unemployment rate, High School enrollment, High school drop outs, Graduation rate, Drop out rate, Prison population, Released on parole, Parole violations, Percent of parole violations, and Juvenile Inmates. Analyze and model these data to give the city a plan to reduce violence. After you complete your analysis and model, prepare a news release for the mayor briefly outlining your proposals that recommend a campaign strategy to curb the violence.

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses.

The purpose of this task is for students to encounter negative exponents in a natural way in the course of learning about exponential functions.

Taraxacum officinale, commonly referred to as the dandelion, is a plant native to Eurasia that can now be found worldwide[1]. This plant is easily identifiable by its bright yellow flowers (Figure 1) and its distinctive “puffball” seed head (Figure 2). Each seed from this head is attached to a parachute-like structure, known as a 'pappus', which facilitates wind dispersal[2]

This task provides concrete experience with exponential decay. It is intended for students who know what exponential functions are, but may not have much experience with them, perhaps in an Algebra 1 course.

The goal of this task is to critically analyze several possible definitions for parallel lines.

The purpose of this task is to critically examine some different possible definitions of what it means for two lines to be perpendicular.

The goal of this task is to compare and contrast the visual intuition we have of reflections with their technical mathematical definition.

The goal of this task is to encourage students to be precise in their use of language when making mathematical definitions.

The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.

The goal of this task is to look at the impact of outliers on two important statistical measures of center: the mean and the median.

The design of airline terminals varies widely. The sketches below show airline terminals from several cities. The designs are quite dissimilar. Some involve circular arcs; others are rectangular; some are quite irregular. Which is optimal for operations? Develop a mathematical model for airport design and operation. Use your model to argue for the optimality of your specified design. Explain how it would operate.

The goal of this task is to interpret the mathematics behind a famous story from ancient mythology, giving rise to linear and quadratic expressions which model the story.

The goal of this task is to study the impact of dilations on distances between points.

The purpose of this Illustrative Mathematics task is to illustrate through an absurd example the fact that in real life quantities are reported to a certain level of accuracy, and it does not make sense to treat them as having greater accuracy.

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.