Illustrative Mathematics
Illustrative Mathematics: F Tf, F if as the Wheel Turns
In this task, students use trigonometric functions to model the movement of a point around a wheel and through space. Students also interpret features of graphs in terms of the given real-world context. Aligns with F-TF.B.5 and F-IF.B.4.
Illustrative Mathematics
Illustrative Mathematics: F if Average Cost
In this task, young scholars must calculate the average cost for a DVD recording for different numbers of DVDs and explain why the cost levels off as the number of DVDs goes up. Aligns with F-IF.B.4 and F-IF.B.5.
Illustrative Mathematics
Illustrative Mathematics: F if a Sse Modeling London's Population
In this task, students are shown a table of population data for the city of London and are asked to explore whether a linear, quadratic, or exponential function would be appropriate to model relationships within the data. They are next...
Illustrative Mathematics
Illustrative Mathematics: F if Throwing Baseballs
In this task about the height of baseballs thrown into the air, students are asked to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out...
Illustrative Mathematics
Illustrative Mathematics: F if Logistic Growth Model, Explicit Version
For this task, students are presented with a graph showing the growth of the U.S. population from 1790 to 1940 and are given the equation for a logistic function for it. They are asked to use the equation and the graph to find the...
Illustrative Mathematics
Illustrative Mathematics: F if Logistic Growth Model, Abstract Version
For this task, young scholars are presented with an equation for a logistic growth model and are asked to analyze it. They are then questioned about a graph showing bacterial population growth. Next, they must use information from...
Illustrative Mathematics
Illustrative Mathematics: F if Telling a Story With Graphs
For this task, students are presented with three weather-related graphs - on temperature, solar radiation, and precipitation. They are asked to describe the function represented in each graph and tell a more detailed story using...
Illustrative Mathematics
Illustrative Mathematics: F if How Is the Weather?
For this task, learners 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 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: 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,if the Canoe Trip, Variation 1
In this task about canoeing, learners must analyze paddling speed and current speed, which are working against each other, to determine how long a canoe trip would take. They write expressions and analyze characteristics of the graph...
Illustrative Mathematics
Illustrative Mathematics: F Bf,if the Canoe Trip, Variation 2
In this task about canoeing, paddling speed, and current speed, students examine how long a trip would take at different speeds. They write a function equation, graph their equation, and explain their thinking. The primary purpose of the...