Illustrative Mathematics
Illustrative Mathematics: Origami Stars
The purpose of this task is to present students with a situation in which they need to divide a whole number by a unit fraction in order to find a solution. Calculating the number of origami stars that Avery and Megan can make...
Illustrative Mathematics
Illustrative Mathematics: Painting a Room
The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number. Determining the amount of paint that Kulani needs for each wall illustrates an...
Illustrative Mathematics
Illustrative Mathematics: 5.nf Standing in Line
The purpose of this task is for students to solve a problem in context that can be solved in different ways, but in particular by dividing a whole number by a unit fraction. Aligns with 6.NS.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Rectangle Perimeter 3
The purpose of this task is to ask young scholars to write expressions and to consider what it means for two expressions to be equivalent. Aligns with 6.EE.A.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Seven to the What?!?
At first glance, this might seem like an impossible problem because the number $7^{2011}$ is much too large to evaluate even with a calculator. It requires a starting point, and, to many, such a starting point might not be obvious....
Illustrative Mathematics
Illustrative Mathematics: 7.rp Two School Dance
The purpose of this task is to see how well students students understand and reason with ratios. This task was adapted from problem #14 on the 2011 American Mathematics Competition (AMC) 8 Test. Aligns with 7.RP.A.3. The site provides a...
Illustrative Mathematics
Illustrative Mathematics: 7.rp,ee Gotham City Taxis
The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. The site includes a task and the solution.
Illustrative Mathematics
Illustrative Mathematics: Painting a Wall
The purpose of this task is for students to find the answer to a question in context that can be represented by fraction multiplication. This task is appropriate for either instruction or assessment depending on how it is used and where...
Illustrative Mathematics
Illustrative Mathematics: 7.rp the Price of Bread
The purpose of this task is for students to calculate the percent increase and relative cost in a real-world context. This task is part of a set collaboratively developed with Money as You Learn, an initiative of the President's Advisory...
Illustrative Mathematics
Illustrative Mathematics: The Value of Education
The purpose of this task is for students to add, subtract, multiply, and divide decimal numbers in a real-world context. The weekly income earned by each person in the task is the median weekly income for their education level, but they...
Illustrative Mathematics
Illustrative Mathematics: 6.ee,ns,rp; 8.ee,f Pennies to Heaven
The goal of this task is to give students a context to investigate large numbers and measurements. Students need to fluently convert units with very large numbers in order to successfully complete this task. The total number of pennies...
Illustrative Mathematics
Illustrative Mathematics: Seeing Is Believing
The purpose of this task is to help students see that 4x(9+2) is four times as big as (9+2). Though this task may seem very simple, it provides students and teachers with a very useful visual for interpreting an expression without...
Illustrative Mathematics
Illustrative Mathematics: Dividing by One Half
This task requires students to recognize both "number of groups unknown" (part (a)) and "group size unknown" (part (d)) division problems in the context of a whole number divided by a unit fraction. It also addresses a common...
Illustrative Mathematics
Illustrative Mathematics: 6 Sp.2,5d Electoral College
In addition to providing a task that relates to other disciplines (history, civics, current events, etc.), this task is intended to demonstrate that a graph can summarize a distribution as well as provide useful information about...
Illustrative Mathematics
Illustrative Mathematics: 5.nf Banana Pudding
The purpose of this task is to provide students with a concrete situation they can model by dividing a whole number by a unit fraction. Aligns with 5.NF.B.7.
Illustrative Mathematics
Illustrative Mathematics: 6.g Polygons in the Coordinate Plane
The purpose of this task is for young scholars to practice plotting points in the coordinate plane and finding the areas of polygons. This task assumes that students already understand how to find areas of polygons by decomposing them...
Illustrative Mathematics
Illustrative Mathematics: Salad Dressing
The purpose of this task is to have students add fractions with unlike denominators and divide a unit fraction by a whole number. This accessible real-life context provides students with an opportunity to apply their understanding of...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Watch Out for Parentheses
This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses. Aligns with 6.EE.A.
Illustrative Mathematics
Illustrative Mathematics: 6.ee,rp 7.ee,rp Anna in d.c.
The purpose of this task is to give students an opportunity to solve a multi-step percentage problem that can be approached in many ways. Because the tax and tip in this problem are a fixed percentage of the cost of the meal, the total...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Busy Day
This problem can be solved using simple arithmetical reasoning but is also naturally represented by a simple equation. Thus, it provides a good entry point for students into representing quantities in contexts with variables and...
Illustrative Mathematics
Illustrative Mathematics: 5.nf How Many Marbles?
This task is intended to complement "5.NF How many servings of oatmeal?" and "7.RP Molly's run.'' All three tasks address the division problem 4/13 but from different points of view. Aligns with 5.NF.B.7.b.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Morning Walk
This task presents a straight forward question that can be solved using an equation in one variable. The numbers are complicated enough so that it is natural to set up an equation rather than solve the problem in one's head. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: 7.rp Tax and Tip
This site provides a problem with completed solutions for that problem. This problem covers the topic of sales tax and tips. The problem aligns with 7.RP.A.3.
Illustrative Mathematics
Illustrative Mathematics: 7.rp Walk a Thon 2
The purpose of this task is for students to translate information about a context involving constant speed into information presented in a table and to find the time it takes to travel a unit distance as well as the distance traveled per...