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, students 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, students 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, learners analyze data about the number of students being infected during an influenza outbreak. The purpose of this problem is to have learners 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 young scholars 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, students 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, young scholars 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...
Illustrative Mathematics
Illustrative Mathematics: F Bf Temperatures in Degrees Fahrenheit and Celsius
In this task involving temperature conversions, students construct a linear function given two input-output pairs, investigate the inverse of a linear function, and reason about quantities and/or solving a linear equation. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: Weather Graph Data
The purpose of this task is for students to represent and interpret weather data, as well as answer questions about the data they have recorded. Student worksheets and recording sheet are included.
Illustrative Mathematics
Illustrative Mathematics: Comparing Numbers
This task is a fun partner game in which students practice making two-digit numbers, decide which is greater, and write the appropriate comparison symbolically.
Illustrative Mathematics
Illustrative Mathematics: F Bf,if the Canoe Trip, Variation 2
In this task about canoeing, paddling speed, and current speed, learners 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...
Illustrative Mathematics
Illustrative Mathematics: F Bf Kimi and Jordan
In this problem, students compare the different incomes and allowances of two young people to see who has earned more in a set period of time, when they will be equal, and what happens if one gets a raise or loses their allowance. Aligns...
Illustrative Mathematics
Illustrative Mathematics: F Bf Us Households
For this task, students are asked to find a linear function which models the number of households in the U.S. as a function of the year. They are also to construct and use an inverse function to model the context, and interpret their...
Illustrative Mathematics
Illustrative Mathematics: F Bf Identifying Even and Odd Functions
In this task, students are presented with four functions and must determine whether each is odd, even, or neither. Includes a GeoGebra worksheet that can be used by the instructor to demonstrate the material. Aligns with F-BF.B.3.