Illustrative Mathematics
Illustrative Mathematics: Calculator Trouble
Even though young scholars can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: 5.nf Fundraising
This task asks students to multiply rational numbers. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: 5.nf Grass Seedlings
For the sake of this commentary, let R be the height of Rual's seedlings (of course students do not need to use a letter to represent any number in this task). Student must compare the size of each of two products (112xR, and 34xR) to...
Illustrative Mathematics
Illustrative Mathematics: Comparing Products
The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. Aligns with 5.OA.A.2.
Illustrative Mathematics
Illustrative Mathematics: Half of a Recipe
This is the third problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. Aligns with 5.NF.B.6.
Illustrative Mathematics
Illustrative Mathematics: Running to School
This is the easiest problem in a series of three tasks involving fraction multiplication that can be solved with pictures or number lines. Aligns with 5.NF.B.6.
Illustrative Mathematics
Illustrative Mathematics: Converting Fractions of a Unit Into a Smaller Unit
Note that in each of these problems we are given a set of a specified size and a specified number of subsets into which it is to be divided. The questions ask the student to find out the size of each of the subsets. Students are not...
Illustrative Mathematics
Illustrative Mathematics: What Is 23/5?
When a division problem involving whole numbers does not result in a whole number quotient, it is important for students to be able to decide whether the context requires the result to be reported as a whole number with remainder (as...
Illustrative Mathematics
Illustrative Mathematics: 5.nf Running a Mile
Young scholars complete a task in which they need to use fraction multiplication. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: Tenths and Hundredths
The purpose of this task is for students to explore the relationship between tenths and hundredths (as well as the relationship between tens and hundreds).
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 learners 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. Students 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 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: 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.