This web resource is an interactive way to help students visually understand why the area of a circle is r x r x pi.
The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.
In this real world problem students solve questions based on the relationship between production costs and price.
This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.
This real world task requires students to answer questions about equations for calculating compound interest.
This task asks students to use similarity to solve a problem in a context that will be familiar to many, though most students are accustomed to using intuition rather than geometric reasoning to set up the shot.
Students will use Numbers to create a bar graph with the data given. Students will then use Pages to make generalizations about the data.
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 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.
This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.
In this task, output is given from a computer-generated simulation, generating size-100 samples of data from an assumed school population of 2000 students under hypotheses about the true distribution of yes/no voters.
The purpose of this task is to assess a student's ability to compute and interpret an expected value. Notice that interpreting expected value requires thinking in terms of a long-run average.
This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.
The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.
This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''
This is the first of a series of task aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function.
This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.
This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.
This task is intended for instruction and to motivate "Building a general quadratic function.''
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.