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.
Illustrative Mathematics
Illustrative Mathematics: F Bf.3 Transforming the Graph of a Function
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. There is no formula for the function so the focus is on...
Illustrative Mathematics
Illustrative Mathematics: F Bf Building a Quadratic Function From F(x) = X^2
This is the first of a series of tasks aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function. Here the student works with an explicit function and studies the impact of additive...
Illustrative Mathematics
Illustrative Mathematics: F Bf Summer Intern
For this task, students write expressions that describe the relationship between quantities and ketch and analyze its graph. The task is about a worker at an aquarium who must dilute saltwater to a specified concentration of salt. Aligns...
Illustrative Mathematics
Illustrative Mathematics: F Bf Medieval Archer
In this task about archery, students investigate the effects on a function of replacing f(x) with f(x+k). Aligns with F-BF.B.3.
Illustrative Mathematics
Illustrative Mathematics: F Bf Compounding With a 100% Interest Rate
In the problem presented here, a man understands that money invested in an account where the interest is compounded semi-annually gives a better return than if it was compounded annually. He wonders how much interest can be earned by...
Illustrative Mathematics
Illustrative Mathematics: F Bf Compounding With a 5% Interest Rate
In the problem presented here, money is invested in an account and its owner understands that interest compounded semi-annually gives a better return than interest compounded annually. He wonders how much interest can be earned by...
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 Building Explicit Quadratic Function: Composition
For this task, students work through the steps and operations involved in the composition of an explicit quadratic function. The task assumes that the students are familiar with the process of completing the square. Aligns with F-BF.B.3...
Illustrative Mathematics
Illustrative Mathematics: F Bf Lake Algae
In this task, students analyze the amount of algae growing on the surface of a lake. The purpose of the task is to introduce students to exponential growth. Instead of giving a starting value and asking for subsequent values, it gives an...
Illustrative Mathematics
Illustrative Mathematics: F Bf Temperature Conversions
In this task involving temperature conversions, young scholars compose and solve functions. Unit conversion problems provide a rich source of examples for the composition of functions and for inverses. Aligns with F-BF.A.1.c and F-BF.B.4.a.
Illustrative Mathematics
Illustrative Mathematics: F Bf Flu on Campus
In this task, students analyze data about the number of students being infected during an influenza outbreak. The purpose of this problem is to have students compose functions using tables of values only. Aligns with F-BF.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Bf Graphs of Compositions
This task addresses an important issue about inverse functions. In this case, the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted. Aligns with F-BF.A.1.c.
Illustrative Mathematics
Illustrative Mathematics: F Bf Exponentials and Logarithms Ii
The purpose of this task is to help students see that the definition of the logarithm as an exponent results in an inverse relationship between the exponential and logarithm functions with the same base. This prepares them to think about...
Illustrative Mathematics
Illustrative Mathematics: F Bf Exponentials and Logarithms I
The purpose of this task is to help students see the "why" behind properties of logs that are familiar but often just memorized (and quickly forgotten or misremembered). The task focuses on the verbal definition of the log, helping...
Illustrative Mathematics
Illustrative Mathematics: F Bf, a Sse Building a General Quadratic Function
This task is a followup to the one called 'Building an explicit quadratic function.' In this one, learners follow the same process with a general quadratic function. The operations take place in the opposite order and the goal is to find...
Illustrative Mathematics
Illustrative Mathematics: F Bf a Sum of Functions
For this task, students are asked to sketch a graph that represents the addition of two other functions. They must first analyze the two graphs presented and complete the problem without any formulas being given. Aligns with F-BF.A.1.b.
Illustrative Mathematics
Illustrative Mathematics: F Bf Susita's Account
In this task, students write an equation for the amount of money in a checking account when money is deposited and withdrawn regularly, and use it to calculate the balance at a certain time. This task asks students to determine a...
Illustrative Mathematics
Illustrative Mathematics: Choral Counting Ii
Using a 100 chart, students will chant the counting sequence starting with one to one hundred. Variations can include skip counting, counting from various numbers other than one, and counting backward.
Illustrative Mathematics
Illustrative Mathematics: Favorite Ice Cream Flavor
The purpose of this task is for students to represent and interpret categorical data. As a class, students will answer a question with three possible answers and construct a bar graph with the responses. Multiple discussion questions and...