Illustrative Mathematics
Illustrative Mathematics: Buttons Odd and Even
The purpose of this task is for young scholars to determine whether a set of objects (up to 20) has an odd or even number of elements. Students will also write an equation to express an even number as a sum of two equal addends and an...
Illustrative Mathematics
Illustrative Mathematics: Hitting the Target Number
The purpose of this task is to help learners develop flexible strategies for adding and subtracting within 20. Students will pick 5 number cards from pre-made cards labeled 1-10. Then, another student will pick a "target number" between...
Illustrative Mathematics
Illustrative Mathematics: Building Toward Fluency
The purpose of this task is to promote certain addition strategies that will help students learn to fluently add and subtract within 20. Students will use a number line or magnetic cubes to solve addition problems. Students will be asked...
Illustrative Mathematics
Illustrative Mathematics: Saving Money 2
The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. A problem is given that will contain multiple solutions, this allows students to think...
Illustrative Mathematics
Illustrative Mathematics: Delayed Gratification
You won first place at your school Science Fair and have 2 choices for your prize!! The purpose of this task is for learners to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to...
Illustrative Mathematics
Illustrative Mathematics: Number of the Day
Repeatable, daily activities are one of the best ways to instill the counting sequence for children. This activity requires a 100 chart which can be made or purchased. Students will count the "Number of the Day" beginning with 1 on the...
Illustrative Mathematics
Illustrative Mathematics: Pencil and a Sticker
The following problem is posed to the class: A pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together? The solution with explanation is included on this site.
Illustrative Mathematics
Illustrative Mathematics: F if Yam in the Oven
The purpose of this task is to give young scholars practice interpreting statements using function notation. The problem is about a baked yam whose temperature is changing as it cools. Aligns with F-IF.A.2.
Illustrative Mathematics
Illustrative Mathematics: F if the Customers
This is a beginning instructional activity on the concept of functions. The context is a business that has a database of customer names and phone numbers in a table and students must decide if a function is involved. Aligns with F-IF.A.1...
Illustrative Mathematics
Illustrative Mathematics: F if Using Function Notation Ii
The purpose of the task is to explicitly identify a common error made by many students in function notation, when they make use of the "identity" f(x + h) = f(x) + f(h). Aligns with F-IF.A.2.
Illustrative Mathematics
Illustrative Mathematics: F if Using Function Notation I
This task deals with a student error that may occur where learners misinterpret function notation. Aligns with F-IF.A.1.
Illustrative Mathematics
Illustrative Mathematics: F if Average Cost
In this task, students 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 Bank Account Balance
This task introduces the concept of a step function. It is about the changing balance in a bank account as money is deposited and removed. Aligns with HSF-IF.C.7.b.
Illustrative Mathematics
Illustrative Mathematics: F If.3 Snake on a Plane
In a video game called Snake, a player moves a snake through a square region in the plane, trying to eat the white pellets that appear. This task has young scholars approach a function via both a recursive and an algebraic definition, in...
Illustrative Mathematics
Illustrative Mathematics: F if Graphing Rational Functions
In this task, students interact with a Desmos app by moving sliders and making observations about features of the graphs and the structures of the expressions of the functions. Aligns with F-IF.C.7.d.
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, a Rei Springboard Dive
This problem is about the changing height of a diver en route to the water. It gives students experience translating questions about a real-world context into mathematical questions about a quadratic function and then answering those...
Illustrative Mathematics
Illustrative Mathematics: F if Graphs of Power Functions
In this task, students are asked to sketch and label the graphs of different (positive) powers of x. Aligns with F-IF.C.7.c.
Illustrative Mathematics
Illustrative Mathematics: F if the Random Walk
In this task, a person moves left or right one unit on a life-sized number line based on the toss of a coin. The task involves interpreting a function in a non-standard context and provides an opportunity to compute some probabilities in...
Illustrative Mathematics
Illustrative Mathematics: F if Temperature Change
In this task, students examine the average rate of change of the temperature in Tucson, Arizona hours after midnight. Aligns with F-IF.B.6.
Illustrative Mathematics
Illustrative Mathematics: F if.c Analyzing Graphs
For this task, students are presented with four different equations and asked to match them with their graphs, then respond to questions about the characteristics of the constants. Aligns with F-IF.C.
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: Making a Clock
Learning to tell time is a skill that needs to be practiced often in the classroom. In this activity, the students sit in a large arc/rainbow in order to make a giant clock to practice telling time. Instructions for making the clock,...
Illustrative Mathematics
Illustrative Mathematics: Overlapping Rectangles
The purpose of this task is to give young scholars an opportunity to compose and decompose polygons to make rectangles. The students will be shown a picture and are asked to count how many rectangles they see. Explanations and examples...