This task has students approach a function via both a recursive and an algebraic definition, in the context of a famous game of antiquity that they may have encountered in a more modern form. The content underlying the algebra is the sum of the first n natural numbers (also known as the nth triangular number.
Material Type: Activity/Lab
This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.
Material Type: Activity/Lab
This task addresses the first part of standard F-BF.3: ŇIdentify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).Ó Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.
Material Type: Activity/Lab
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.
Material Type: Activity/Lab
In this task students use algebraic methods to determine whether each of the functions is odd, even, or neither.
Material Type: Activity/Lab
This task has students explore the relationship between the three parameters a, b, and c in the equation f(x)=ax2+bx+c and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.
Material Type: Activity/Lab
This task has students explore the relationship between the three parameters a, h, and k in the equation f(x)=a(x−h)2+k and the resulting graph. There are many possible approaches to solving each part of this problem, especially the first part. We outline some of them here (which overlap heavily in places), applied to the top left graph, and then only give the final answers in the solution provided.
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: SCREEN I In science class, some students dropped a basketball and allowed it to bounce. They measured and recorded the highest point of each bounce. ht...
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: SCREEN I In science class, some students dropped a basketball and allowed it to bounce. They measured and recorded the highest point of each bounce. ht...
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a table showing the approximate boiling point of water at different elevations: Elevation (meters above sea level)Boiling Point (degrees Celsi...
Material Type: Activity/Lab
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below are population estimates for the larger metropolitan areas of Paris (France), Shenzhen (China), and Lagos (Nigeria) for each decade between 1950 ...
Material Type: Activity/Lab
In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Material Type: Activity/Lab
This real world task requires students to compare differing interest rates.
Material Type: Activity/Lab
This task gives a variet of real-life contexts which could be modeled by a linear or exponential function. The key distinguishing feature between the two is whether the change by equal factors over equal intervals (exponential functions), or by a constant increase per unit interval (linear functions).
Material Type: Activity/Lab
This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting. More generally, the idea of the lesson could be used as a template for a project where students develop a questionnaire, sample students at their school and report on their findings.
Material Type: Activity/Lab
The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions. The solution should directly compare the center, spread, and shape of the two distributions and comment on the high outlier in the northbound data set.
Material Type: Activity/Lab
In this task students design a plan to conduct a random sample of the students in their school to estimate the proportion of students who think their parents are strict.
Material Type: Activity/Lab
The following are some common methods of data collection in statistical studies that involve people.
Material Type: Activity/Lab
The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of raandom assingment to experimental groups in an experiment.
Material Type: Activity/Lab
This task addresses many standards regarding the description and analysis of bivariate quantitative data, including regression and correlation. Students should recognize that the pattern shown is one of a strong, positive, linear association, and thus a correlation coefficient value near +1 is plausible. Students should also be able to interpret the slope of the least-squares line as an estimated increase in y per unit change in x (and thus for a 3 unit increase in x, students should expect an estimated increase in y that equals 3 times the model's slope value).
Material Type: Activity/Lab
