In this lesson, students understand the term sampling variability in the context of estimating a population mean. Students understand that the standard deviation of the sampling distribution of the sample mean offers insight into the accuracy of the sample mean as an estimate of the population mean.

In this lesson, students understand the term sampling variability in the context of estimating a population mean. Students understand that the standard deviation of the sampling distribution of the sample mean conveys information about the anticipated accuracy of the sample mean as an estimate of the population mean.

Given data from a statistical experiment with two treatments, students create a randomization distribution. Students use a randomization distribution to determine if there is a significant difference between two
treatments.

Given data from a statistical experiment with two treatments, students create a randomization distribution. Students use a randomization distribution to determine if there is a significant difference between two treatments.

In this lesson, students carry out a statistical experiment to compare two treatments. Given data from a statistical experiment with two treatments, students create a randomization distribution. Students use a randomization distribution to determine if there is a significant difference between two
treatments.

In this lesson, students carry out a statistical experiment to compare two treatments. Given data from a statistical experiment with two treatments, students create a randomization distribution. Students use a randomization distribution to determine if there is a significant difference between two
treatments.

In this lesson, students write an exponential function that represents the amount of water in a tank after ?? seconds if the height of the water doubles every 10 seconds. Students discover Euler’s number ?? by numerically approaching the constant for which the height of water in a tank equals the rate of change of the height of the water in the tank. Students calculate the average rate of change of a function.

Students will extend their study of functions to include function notation and the concepts of domain and range by exploring examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.

The purpose of this task is to extend student understanding of log properties and using the properties to write equivalent expressions. In the beginning of the task, students are given values of a few log expressions and asked to use log properties and known values of log expressions to find unknown values. This is an opportunity to see how the known log values can be used and to practice using logarithms and substitution. In the second part of the task, students are asked to determine if the given equations are always true (in the domain of the expression), sometimes true, or never true. This gives students an opportunity to work through some common misconceptions about log properties and to write equivalent expressions using logs.

The purpose of this task is to develop students’ understanding of logarithmic expressions and to make sense of the notation. In addition to evaluating log expressions, student will compare expressions that they cannot evaluate explicitly. They will also use patterns they have seen in the task and the definition of a logarithm to justify some properties of logarithms.

Using the formulas for arc length and area of a sector developed in the previous task, in this task students use proportional reasoning to calculate the ratio of arc length to radius to define a constant of proportionality for any given angle intercepting arcs of concentric circles. This constant provides an alternative way of measuring the angle: radians.

Students will use data from a random sample to estimate a population mean, calculate and interpret margin of error in context, and know the relationship between sample size and margin of error in the context of estimating a population mean.

Margin of error is first developed visually and then estimated by twice the standard deviation of the sampling distribution of the sample proportion.

Students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in context. Students know the relationship between sample size and margin of error in the context of estimating a population proportion.

Students will create a poster (1 each per student in the group) that explains a circle theorem or property. Student Groups will use a 360 degree camera to create a virtual museum where they use a photo overlay of their poster and an attached audio file to explain their theorem/property.

Students will learn to use mathematical models to represent real life situations. In particular, they will use tables and equations to represent the relationship between the number of revolutions made by a "driver" and a "follower" (two connected gears in a system), and they will explain the significance of the radii of the gears in regard to this relationship.

Adapted from mathematicsvisionproject.com’s Material Overview:
The Mathematics Vision Project (MVP) was created as a resource for teachers to implement the Common Core State Standards (CCSS) using a task-based approach that leads to skill and efficiency in mathematics by first developing understanding. The MVP approach develops the Standards of Mathematical Practice through experiential learning. Students engage in mathematical problem solving, guided by skilled teachers, in order to achieve mathematical proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. The MVP authors created a curriculum where students do not learn solely by either “internalizing what a teacher or book says or, on the other hand, solely by inventing mathematics on their own.”
The MVP classroom experience begins by confronting students with an engaging problem and allows them to grapple with solving it. As students’ ideas emerge, take form, and are shared, the teacher deliberately orchestrates the student discussions and explorations toward a focused math goal. Students justify their own thinking while clarifying, describing, comparing, and questioning the thinking of others leading to refined thinking and mathematical fluency. What begin as ideas become concepts that lead to formal, traditional math definitions and properties. Strategies become algorithms that lead to procedures supporting efficiency and consistency. Representations become tools of communication which are formalized as mathematical models. Students learn by doing mathematics.

Use remotely sensed data to estimate and measure the area of (center-pivot irrigation) crop circles.

The purpose of this task is to examine how changing the parameters in a function of the form ℎ(#) = & sin(*#) + , affects the corresponding graph of the function. Students will make connections between the parameters in the equation, the description of the motion of the Ferris wheel, and the amplitude, period and midline of the graph. The midline, which lies halfway between the maximum and minimum points of the graph, depends upon the height of the center of the Ferris wheel and is represented by the value of the parameter d. The amplitude, or distance from the midline to the maximum and minimum points of the graph, depends upon the radius of the Ferris wheel and is represented by the value of the parameter a. The period, or interval before the graph repeats itself, depends upon the length of time of one complete revolution of the wheel. The parameter b represents the angular speed of the wheel—given in terms of degrees per second for this scenario—and is found by dividing 360° by the amount of time it takes to make one complete revolution. Students will observe that the graph is periodic—the rider returns to the same height every 20 seconds. Students should also note the characteristic shape of a sinusoidal graph—the smooth turns rather than sharp points at the maximum and minimum values, for example—and be able to justify the constantly changing slope of the graph in terms of the horizontal and vertical components of motion one experiences when riding on a Ferris wheel.