Students conduct a simple experiment to see how the water level changes in a beaker when a lump of clay sinks in the water and when the same lump of clay is shaped into a bowl that floats in the water. They notice that the floating clay displaces more water than the sinking clay does, perhaps a surprising result. Then they determine the mass of water that is displaced when the clay floats in the water. A comparison of this mass to the mass of the clay itself reveals that they are approximately the same.

Students bury various pieces of trash in a plotted area of land outside. After two to three months, they uncover the trash to investigate what types of materials biodegrade in soil.

This task operates at two levels. In part it is a simple exploration of the relationship between speed, distance, and time. Part (c) requires understanding of the idea of average speed, and gives an opportunity to address the common confusion between average speed and the average of the speeds for the two segments of the trip. At a higher level, the task addresses N-Q.3, since realistically neither the car nor the bus is going to travel at exactly the same speed from beginning to end of each segment; there is time traveling through traffic in cities, and even on the autobahn the speed is not constant. Thus students must make judgements about the level of accuracy with which to report the result.

This task provides a good entry point for students into representing quantities in contexts with variables and expressions and building equations that reflect the relationships presented in the context.

In this activity, students will make their own finger signs for the numbers from zero to ten. Students will relate each finger sign to its numeral and then explore number sentences using the calculator.

Statistics is the study of variability. Students who understand statistics need to be able to identify and pose questions that can be answered by data that vary. The purpose of this task is to provide questions related to a particular context (a jar of buttons) so that students can identify which are statistical questions. The task also provides students with an opportunity to write a statistical question that pertains to the context.

There are two aspects to fluency with division of multi-digit numbers: knowing when it should be applied, and knowing how to compute it. While this task is very straightforward, it represents the kind of problem that sixth graders should be able to recognize and solve relatively quickly.

The emphasis in this task is on the progression of equations, from two that involve different values of the sales tax, to one that involves the sales tax as a parameter. It is designed to foster the habit of looking for regularity in solution procedures, so that students don't approach every equation as a new problem but learn to notice familiar types.

Students are taught to look for patterns in solving mathematical problems. Starting in the lower grades, they learn that math problems can be decomposed and recomposed without its value changing (the distributive property). In these videos, you'll see teachers demonstrating how ratios, percentages, and fractions can have very similar meanings but depending on the context, they might choose one strategy over another. Students can use this knowledge to simplify and solve more difficult mathematical problems in higher grades.

Chefs at Gaines Street Pies explain how they make their pizzas and why all of their pizzas are similar circles. [4:13]

[Free Registration/Login Required] This is a formative assessment task where students are asked to estimate the population of Utah based on information given about its population density and the perimeter of its state boundaries. Samples of student responses and possible misconceptions are provided along with questions to help students clarify their thinking and deepen their understanding.

[Free Registration/Login Required] This is a formative assessment task where students are asked to use geometric solids to model each of four tent shapes on a worksheet and use mathematical language to describe them. Samples of student responses and possible misconceptions are provided along with questions to help students clarify their thinking and deepen their understanding.

In this Cyberchase video segment, the CyberSquad must estimate the measurements of Spout the Whale in order to find a cage that will fit him.Ű_í_

In this video segment from Cyberchase, Inez and Lucky figure out how to keep track of the number of clones as they continue to multiply.

This interactive exercise focuses on using the Pythagorean Theorem to calculate distance and plotting points on a Cartesian grid.

This short video and interactive assessment activity is designed to teach fourth graders about using greater than and less than.

This task is intended for instructional (rather than assessment) purposes, providing an opportunity to discuss technology as it relates to irrational numbers and calculations in general. The task gives a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

In this video tutorial, the instructor demonstrates how to determine how to calculate the area of a rectangle and assess knowledge with a quiz. [3:01]

Use different size triangle to determine how to solve for the area in this video lesson. Take quiz to check understanding. [3:41]