Illustrative Mathematics
Illustrative Mathematics: 6.ee Equivalent Expressions
In this problem, we have to transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent. Common mistakes are addressed, such as not distributing the 2 correctly. Aligns...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Distance to School
This task asks learners to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible. Aligns with 6.EE.A.2.
Illustrative Mathematics
Illustrative Mathematics: 6.ee
The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow. Students who are just learning about...
Illustrative Mathematics
Illustrative Mathematics: 6.g Same Base and Height, Variation 2
This is the second version of a task asking students to find the areas of triangles that have the same base and height. This presentation is more abstract as students are not using physical models. They still determine the area of each...
Illustrative Mathematics
Illustrative Mathematics: Making S'mores
The purpose of this instructional task is to motivate a discussion about adding fractions and the meaning of the common denominator. The different parts of the task have young scholars moving back and forth between the abstract...
Illustrative Mathematics
Illustrative Mathematics: Finding Common Denominators to Subtract
Part (a) of this task asks students to use two different denominators to subtract fractions. The purpose of this is to help students realize that any common denominator will work, not just the least common denominator. Part (b) does not...
Illustrative Mathematics
Illustrative Mathematics: How Much Pie?
The purpose of this task is to help students see the connection between a/b and a/b in a particular concrete example. The relationship between the division problem 3/8 and the fraction 3/8 is actually very subtle. Aligns with 5.NF.B.3.
Illustrative Mathematics
Illustrative Mathematics: Jog a Thon
The purpose of this task is to present students with a situation where it is natural to add fraction with unlike denominators; it can be used for either assessment or instructional purposes. Aligns with 5.NF.A.1.
Illustrative Mathematics
Illustrative Mathematics: Finding Common Denominators to Add
Part (a) of this task asks young scholars to find and use two different common denominators to add the given fractions. The purpose of this question is to help students realize that they can use any common denominator to find a solution,...
Illustrative Mathematics
Illustrative Mathematics: Mixed Numbers With Unlike Denominators
The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting. The two primary ways one can expect students to add are converting the mixed...
Illustrative Mathematics
Illustrative Mathematics: Egyptian Fractions
One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. Aligns with 5.NF.A.1.
Illustrative Mathematics
Illustrative Mathematics: How Many Servings of Oatmeal?
This task provides a context for performing division of a whole number by a unit fraction. This problem is a "How many groups?'' example of division: the "groups'' in this case are the servings of oatmeal and the question is asking how...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Chocolate Bar Sales
n this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Log Ride
In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities. There are two solutions...
Illustrative Mathematics
Illustrative Mathematics: Bowling for Numbers
The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Aligns with 5.OA.A.1.
Illustrative Mathematics
Illustrative Mathematics: Folding Strips of Paper
The purpose of this task is to provide students with a concrete experience they can relate to fraction multiplication. Perhaps more importantly, the task also purposefully relates length and locations of points on a number line, a common...
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 young scholars 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...