The task provides an opportunity for students to engage in Mathematical Practice Standard 4: Model with mathematics.
The purpose of this task is to give students experience in using simulation to determine if observed results are consistent with a given model (in this case, the Ňjust guessingÓ model). Part (i) also addresses the role of random assignment in the design of an experiment and assesses understanding of this concept.
This task involves two aspects of statistical reasoning: providing a probabilistic model for the situation at hand, and defining a way to collect data to determine whether or not the observed data is reasonably likely to occur under the chosen model. When guessing between two choices, there is no reason to suspect that one outcome is more likely than the other. Thus, a model that assumes the two outcomes to be equally likely (such as flipping a coin) is appropriate.
This task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task models a satellite orbiting the earth in communication with two control stations located miles apart on earthsŐ surface.
The context of this task is a familiar one: a cold beverage warms once it is taken out of the refrigerator. Rather than giving the explicit function governing this warmth, a graph is presented along with the general form of the function. Students must then interpret the graph in order to understand more specific details regarding the function.
Observe what happens to an image when the scale changes. This interactive exercise focuses on visually comparing multiplicative and additive relationships.
This task allows students to think about and discuss sampling methods.
The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.
This task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the busines
This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).
This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?
This task provides a concrete geometric setting in which to study rigid transformations of the plane. It is important for students to be able to visualize and execute these transformations and for this purpose it would be beneficial to have manipulatives and it will important that the students be able to label the vertices of the hexagon with which they are working.
This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.
The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions. The task is designed to encourage students to communicate their findings in a narrative/report form in context Đ not just simply as a computed number.
This lesson is to be used at the end of the year or unit to help students make a digital story to show what the have learned that year or unit in math. It could be converted an used with any subject matter.
In this Cyberchase video segment, the CyberSquad learns what happens to the area of a rectangle when the shape enclosed by the perimeter changes.
This problem is a quadratic function example. The other tasks in this set illustrate F.BF.1a in the context of linear (Kimi and Jordan), exponential (Rumors), and rational (Summer Intern) functions.
The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever _AXB is a right angle.
The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.
Total solar eclipses are quite rare, so much so that they make the news when they do occur. This task explores some of the reasons why. Solving the problem is a good application of similar triangles