The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.
This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.
This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.
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 aspects of the task and its potential use.
This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere. Students who are given this task must be familiar with the formula for the volume of a cylinder, the formula for the volume of a cone, and CavalieriŐs principle.
The goal of this task is to provide examples for comparing two fractions by finding a benchmark fraction which lies in between the two.
This task deals with a student error that may occur while students are completing F-IF Average Cost.
The purpose of the task is to explicitly identify a common error made by many students, when they make use of the "identity" f(x+h)=f(x)+f(h). A function f cannot in general be distributed over a sum of inputs.
This task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.
Students develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.
For this task, Minitab software was used to generate 100 random samples of size 16 from a population where the probability of obtaining a success in one draw is 33.6% (Bernoulli). Given that multiple samples of the same size have been generated, students should note that there can be quite a bit of variability among the estimates from random samples and that on average, the center of the distribution of such estimates is at the actual population value and most of the estimates themselves tend to cluster around the actual population value.
This task helps students broaden and deepen their understanding of the equals sign and equality.
In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.
This task could be used in instructional activities designed to build understandings of fraction division. With teacher guidance, it could be used to develop knowledge of the common denominator approach and the underlying rationale.
This task asks students to write and interpret a given expression.
This real world word problem requires students to use equations and functions.
This problem is the fifth in a series of seven about ratios. In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates. The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.
This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex.
This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.
This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Every problem requires students to understand what ratios are and apply them in a context. The problems build in complexity and can be used to highlight the multiple ways that one can reason about a context involving ratios.