This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

This task starts with an exploration of the graphs of two functions whose expressions look very similar but whose graphs behave completely differently.

This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas.

This task addresses an important issue about inverse functions. In this case the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted.

This task requires students to recognize the graphs of different (positive) powers of x.

This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is. It is effective after students have graphed parabolas in vertex form, but have not yet explored graphing other forms.

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting. More generally, the idea of the lesson could be used as a template for a project where students develop a questionnaire, sample students at their school and report on their findings.

This is a challenging Illustrative Mathematics task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them.

In this task, students will calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

In this task, students are given a scenario and different graphs that could describe the relationship of the quantities in the situation, the height of a flag as a function of time.

In this task, students are given a scenario and different graphs that could describe the relationship of the quantities in the situation, the height of a flag as a function of time.

The goal of this task is to compare a transformation of the plane (translation) which preserves distances and angles to a transformation of the plane (horizontal stretch) which does not preserve either distances or angles.

During events at your school, students operate a concession stand to raise money in support of student activities. Your team is in charge of the concession stand for this year. Your team will sell food and other items at the stand. There are 10 monthly events this year.

Gas prices fluctuate significantly from week to week. Consumers would like to know whether to fill up the tank (gas price is likely to go up in the coming week) or buy a half tank (gas price is likely to go down in the coming week).

Consider the following cases:

Consumer drives 100 miles per week
Consumer drives 200 miles per week
Assume:

Gas tank holds 16 gallons and average mileage is 25 miles/gallon => 400 miles/tank
Consumer buys gas once a week

The price of copper fluctuates. Between 2002 and 2011, there were times when its price was lower than $1.00 per pound and other times when its priace was higher than $4.00 per pound. Copper pennies minted between 1962 and 1982 are 95% copper and 5% zinc by weight, and each penny weighs 3.11 grams. At what price per pound of copper does such a penny contain exactly one cent worth of copper?

The equations in this task are intentionally very simple; the point of the task is not to test technique in solving equations, but to encourage students to reason about them.

Consider the following major league baseball parks: Atlanta Braves, Colorado Rockies, New York Yankees, California Angles, Minnesota Twins, and Florida Marlins.

Each field is in a different location and has different dimensions. Are all these parks "fair"? Determine how fair or unfair is each park. Determine the optimal baseball "setting" for major league baseball.

This task can be used as a quick assessment to see if students can make sense of a graph in the context of a real world situation. The task could also be used to generate a group discussion on interpreting functions given by graphs.

The purpose of this Illustrative Mathematics task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into their solutions.

The goal of this task is to interpret the graph of a rational function and use the graph to approximate when the function takes a given value.