This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

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.

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

In this math activity, learners are challenged to create aluminum foil boats that will hold plastic bears until the boats sink. The lesson serves as a fun, hands-on way to collect data. Data from two attempts is collected and used to make two class box-and-whisker plots with some surprising results. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

The PhET project at the University of Colorado creates "fun, interactive, research-based simulations of physical phenomena." This particular one deals with Beer's Law. "The thicker the glass, the darker the brew, the less the light that passes through." Make colorful concentrated and dilute solutions and explore how much light they absorb and transmit using a virtual spectrophotometer! The simulation is also paired with a teachers' guide and related resources from PhET. The simulation is also available in multiple languages.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

In this 8-lesson unit students use buttons to explore logical and numerical relationships that form the conceptual basis for understanding addition and subtraction operations. Topics include counting, ordinal numbers (and relative position), classification (attributes), relationships between numbers, addition of sets, commutativity of addition, sums to 10, fact families (including subtraction), three models of subtraction ("take away", comparative, missing addend), and bar graphs. Includes student activity sheets and a link to an online graphing applet.

This activity is a scientific investigation focusing on inquiry after using the Foss Water Kit. The students will pose a question, create a procedure and produce a poster showing their findings.

Study of an area of current interest in theoretical computer science. Topic varies from term to term. This course is a study of Behavior of Algorithms and covers an area of current interest in theoretical computer science. The topics vary from term to term. During this term, we discuss rigorous approaches to explaining the typical performance of algorithms with a focus on the following approaches: smoothed analysis, condition numbers/parametric analysis, and subclassing inputs.

This activity will allow students to see light bending. The students will be able to calculate the amount of bend or refraction that occurs with various mediums.

In this optics activity, learners discover that when they rotate a special black and white pattern called a Benham's Disk, it produces the illusion of colored rings. Learners experiment with the speed of rotation and direction of rotation to observe varying patterns. Use this activity to explain to learners how our eyes detect color and how different color receptors in the eye respond at different rates.

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

Demonstrate Bernoulli's Principle using balloons and and pop cans. Real world concept of lift can be applied to an airplane demonstration.

This article provides a brief discussion of the importance of teaching students to analyze data and representations of data as well as two resources that can help teachers implement these strategies into their instruction.

This Cyberchase video segment features Bianca, who must figure out the fastest route to a movie premiere.

In this card game students play in pairs to practice recognizing the biggest number.

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

This task asks students to glean contextual information about bird eggs from a collection of measurements of said eggs organized in a scatter plot. In particular, students are asked to identify a correlation and use it to make interpolative predictions, and reason about the properties of specific eggs via the graphical presentation of the data.

This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.

In this Illuminations lesson plan students explore the use of variables as they solve for the weights of objects using information presented in pictures. Learners model situations that involve adding and subtracting whole numbers, using objects, pictures, and symbols. A student activity sheet is available and downloadable (pdf).