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 learners 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 learners 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 students 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 into...
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...
Illustrative Mathematics
Illustrative Mathematics: N q.a.1 and N q.a.3: Felicia's Drive
This task requires students to make some sensible approximations of the amount of gas needed for a drive. They must choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Aligns with N-Q.A.1 and...
Illustrative Mathematics
Illustrative Mathematics: 4.g the Geometry of Letters
Letters can be thought of as geometric figures. Aligns with 4.G.A.1.
Illustrative Mathematics
Illustrative Mathematics: 4.nf Explaining Fraction Equivalence With Pictures
The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example. Part (c) should be approached as a discussion before students are asked to write an...
Illustrative Mathematics
Illustrative Mathematics: 4.nf Using Benchmarks to Compare Fractions
Melissa gives her classmates the following explanation for comparing fractions.
Illustrative Mathematics
Illustrative Mathematics: Rounding to Tenths and Hundredths
The purpose of this task is for students to use the position of a number on the number line to round the number without knowing its exact value. Though this task deals most directly with rounding, it also requires students to understand...
Illustrative Mathematics
Illustrative Mathematics: 7.rp Proportionality
This lesson plan explores how to recognize and represent proportional relationships between quantities.
Illustrative Mathematics
Illustrative Mathematics: G Mg Hexagonal Pattern of Beehives
Beehives are made of walls, each of the same size, enclosing small hexagonal cells where honey and pollen are stored and bees are raised. This problem examines some of the mathematical advantages of the hexagonal tiling in a beehive....
Illustrative Mathematics
Illustrative Mathematics: G Mg Toilet Roll
Picture a roll of toilet paper; assume that the paper in the roll is very tightly rolled. Assuming that the paper in the roll is very thin, find a relationship between the thickness of the paper, the inner and outer radii of the roll,...
Illustrative Mathematics
Illustrative Mathematics: G Mg How Many Cells Are in the Human Body?
About how many cells are in the human body? The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. Aligns with G-MG.A.2.