The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred.
Fundamentals of characterizing and recognizing patterns and features of interest in numerical data. Basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. Decision theory, statistical classification, maximum likelihood and Bayesian estimation, non-parametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research.
This short video and interactive assessment activity is designed to teach third graders about division patterns within the multiplication table.
This short video and interactive assessment activity is designed to teach fourth graders about patterns in division by 6, 7, 8, 9, 11, 12.
The goal of this task is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table.
This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.
This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes.
This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.
This word problem requires students to use addition and subtraction and think about money.
This short video and interactive assessment activity is designed to teach third graders about perimeter in grid.
This short video and interactive assessment activity is designed to teach third graders about perimeter of squares and rectangles.
This short video and interactive assessment activity is designed to teach second graders an overview of perimeter.
These word problems represent the "Add To" contexts for addition and subtraction.
This interactive Flash animation allows students to explore size estimation in one, two and three dimensions. Multiple levels of difficulty allow for progressive skill improvement. In the simplest level, users estimate the number of small line segments that can fit into a larger line segment. Intermediate and advanced levels offer feature games that explore area of rectangles and circles, and volume of spheres and cubes. Related lesson plans and student guides are available for middle school and high school classroom instruction. Editor's Note: When the linear dimensions of an object change by some factor, its area and volume change disproportionately: area in proportion to the square of the factor and volume in proportion to its cube. This concept is the subject of entrenched misconception among many adults. This game-like simulation allows kids to use spatial reasoning, rather than formulas, to construct geometric sense of area and volume. This is part of a larger collection developed by the Physics Education Technology project (PhET).
Students learn about the basic principles of electromicrobiology—the study of microorganisms’ electrical properties—and the potential that these microorganisms may have as a next-generation source of sustainable energy. They are introduced to one such promising source: microbial fuel cells (MFCs). Using the metabolisms of microbes to generate electrical current, MFCs can harvest bioelectricity, or energy, from the processes of photosynthesis and cellular respiration. Students learn about the basics of MFCs and how they function as well as the chemical processes of photosynthesis and cellular respiration
This task requires students to answer questions about the structure of an expression.
The objective of this lesson is to illustrate how a common everyday experience (such as playing pool) can often provide a learning moment. In the example chosen, we use the game of pool to help explain some key concepts of physics. One of these concepts is the conservation of linear momentum since conservation laws play an extremely important role in many aspects of physics. The idea that a certain property of a system is maintained before and after something happens is quite central to many principles in physics and in the pool example, we concentrate on the conservation of linear momentum. The latter half of the video looks at angular momentum and friction, examining why certain objects roll, as opposed to slide. We do this by looking at how striking a ball with a cue stick at different locations produces different effects.
The purpose of this task is for students to select 2 numbers from a set of 3 that sum to 9. The task can be completed for sums equaling any number. Teachers may choose to ask students to write the simple equations they select.
This is a choral counting activity that can be easily adjusted as students learn higher numbers.
This task requires students to use functions to calculate how to best benefit from a pizza promotion.