Illustrative Mathematics
Illustrative Mathematics: Making Cookies
This tasks lends itself very well to multiple solution methods. Students may learn a lot by comparing different methods. Students who are already comfortable with fraction multiplication can go straight to the numeric solutions given...
Illustrative Mathematics
Illustrative Mathematics: Multiplying Decimals by 10
The purpose of this task is to help students understand and explain why multiplying a decimal number by 10 shifts all the digits one place to the left. This understanding builds on work around place-value that students have done with...
Illustrative Mathematics
Illustrative Mathematics: Using Operations and Parentheses
The purpose of this task is to give students a chance to work creatively with three of the four fundamental arithmetic operations (addition, subtraction, and multiplication). It is well suited for helping students develop fluency with...
Illustrative Mathematics
Illustrative Mathematics: 7.rp.3 Lincoln's Math Problem
The purpose of this task is for students to solve a multi-step problem involving simple interest. The Aligns with 7.RP.A.3. The task provides both a problem and the solution.
Illustrative Mathematics
Illustrative Mathematics: Measuring Cups
This task could form part of a classroom activity where students are encouraged to find as many different ways as possible to make different fractions such as 1/12 and then share their methods. While measuring cups would be helpful to...
Illustrative Mathematics
Illustrative Mathematics: Calculator Trouble
Even though students 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: Which Number Is It?
The purpose of this task is to help young scholars understand the fact that the value of a digit in one place is ten times the value of the same digit in the place to the right. Aligns with 5.NBT.A.1.
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....