Illustrative Mathematics
Illustrative Mathematics: 5.nf Comparing a Number and a Product
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: Picturing Factors in Different Orders
The purpose of this task is to help students picture the multiplicative structure of the number 30 in different ways. Some of this structure is easier to communicate using grouping symbols, as it is easier to interpret...
Illustrative Mathematics
Illustrative Mathematics: 6.g Base and Height
The purpose of this task is to help students understand what is meant by a base and its corresponding height in a triangle and to be able to correctly identify all three base-height pairs. Aligns with 6.G.A.1.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Fishing Adventures 1
This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Young scholars write and solve inequalities, and represent the solutions...
Illustrative Mathematics
Illustrative Mathematics: To Multiply or Not to Multiply?
Many real world problems appear similar. Even when children might know what operation to choose when the problem only involves whole numbers, they often are confused with fractions. It is also important for students to know that 18x25 is...
Illustrative Mathematics
Illustrative Mathematics: Video Game Scores
Standard 5.OA.2 asks students to "Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them." This task asks students to exercise both of these complementary skills,...
Illustrative Mathematics
Illustrative Mathematics: Words to Expressions 1
This problem allows students to see words that can describe the expression from part (c) of "5.OA Watch out for Parentheses." Additionally, the words (add, sum) and (product, multiply) are all strategically used so that the student can...
Illustrative Mathematics
Illustrative Mathematics: Watch Out for Parentheses 1
This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have different results due to the placement of parentheses. It helps students see the purpose of using parentheses....
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 students 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 young scholars 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...
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 students moving back and forth between the abstract representation...
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 students 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, not...
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 young scholars 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...
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...