Illustrative Mathematics
Illustrative Mathematics: F if Which Function?
For this task, students are presented with a graph and asked to identify the functions that could be represented by it and explain their thinking. The task addresses knowledge related to interpreting forms of functions derived by...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Gianna's Job
Students use ratios and rates to answer two questions in this performance task.
Illustrative Mathematics
Illustrative Mathematics: F if How Is the Weather?
For this task, students are presented with three graphs that show solar radiation as a function of time. They are asked to match each graph to the corresponding description of the weather during the day. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F if Interpreting the Graph
In this task, students are asked to label points on the graph of a function that illustrate several statements. Aligns with F-IF.A.
Illustrative Mathematics
Illustrative Mathematics: F if Pizza Place Promotion
For this task, young scholars investigate the price of pizza at a new restaurant, how to get the best deal, and what equations represent the functions. Aligns with F-IF.B.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Overlapping Squares
Students use ratio and rate to answer this performance task: The data transfer rate of an Internet connection is the rate in bytes per second that a file can be transmitted across the connection. Data transfer is typically measured in...
Illustrative Mathematics
Illustrative Mathematics: 6.rp Data Transfer
Students use unit rates to answer two questions in this real-world math performance task.
Illustrative Mathematics
Illustrative Mathematics: F if Identifying Graphs of Functions
For this task, students are presented with four function equations and four graphs of functions showing -2 less than or equal to x, which is less than or equal to +2. They are asked to match each function to the corresponding graph and...
Illustrative Mathematics
Illustrative Mathematics: F if Warming and Cooling
Students are presented with a graph showing temperature over a period of 20 hours and are asked to read and interpret the graph. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F if Influenza Epidemic
Students are presented with a graph showing the spread of an influenza epidemic through a city. They are asked to read and interpret the graph and the equation for its function. Aligns with F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: 6.rp Mixing Concrete
Students use ratio and rate to answer this performance task: A mixture of concrete is made up of sand and cement in a ratio of 5 : 3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix?
Illustrative Mathematics
Illustrative Mathematics: 6.rp Currency Exchange
Students use ratio and rate to answer this performance task: Joe was planning a business trip to Canada, so he went to the bank to exchange $200 U.S. dollars for Canadian dollars (at a rate of $1.02 CDN per $1 US). On the way home from...
Illustrative Mathematics
Illustrative Mathematics: F if Domains
In this task, students are asked to list the operations that must be performed on a variable to find the solution to each function, explain restrictions placed on the domain, and state the domain. Aligns with F-IF.A.1.
Illustrative Mathematics
Illustrative Mathematics: F if Cell Phones
This task about cell phones shows whether students can interpret function notation. Aligns with F-IF.A.2.
Illustrative Mathematics
Illustrative Mathematics: F if Oakland Coliseum
For this task, students are asked to find the domain and range of a linear function in the context of ticket sales at the Oakland Coliseum. Aligns with F-IF.B.5.
Illustrative Mathematics
Illustrative Mathematics: F if Points on a Graph
This task will help students understand the difference between between independent and dependent variables. Aligns with F-IF.A.1.
Illustrative Mathematics
Illustrative Mathematics: F if Parabolas and Inverse Functions
This task assumes an understanding of the relationship between functions and equations. Students try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, then the...
Illustrative Mathematics
Illustrative Mathematics: F if Running Time
This task provides an application of polynomials in computing. Students are asked to calculate the running time of algorithms for loading images of different sizes. They then graph the running time polynomials and decide which is more...
Illustrative Mathematics
Illustrative Mathematics: F Bf 1,000 Is Half of 2,000
This task is about an online mathematics organization that is trying, over a four-year period, to generate 2,000 math problems that cover all grades. This real-life modeling task could serve as a summative exercise that draws on many...
Illustrative Mathematics
Illustrative Mathematics: F if Model Airplane Acrobatics
In this task, a model airplane pilot is practicing flying her airplane in a big loop for an upcoming competition. The task could serve as an introduction to periodic functions and as a lead-in to sinusoidal functions. By visualizing the...
Illustrative Mathematics
Illustrative Mathematics: F Bf Invertible or Not?
For this task, students are asked to complete a table of input-output pairs for two functions in such a way that one of the functions is invertible and the other one is not. Aligns with F-BF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F Bf Rainfall
In this task, students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given...
Illustrative Mathematics
Illustrative Mathematics: F Bf Latitude
For this task, students are presented with data about latitude and the percentage of the Earth's surface north of each latitude line. They are to use this data to sketch a graph, analyze it, and build an understanding of an invertible...
Illustrative Mathematics
Illustrative Mathematics: F Bf Skeleton Tower
This problem is a quadratic function example where students analyze how many cubes are used to build a multi-dimensional tower of different heights. Aligns with F-BF.A.1.