Illustrative Mathematics
Illustrative Mathematics: 6.ee Triangular Tables
This task provides a good opportunity for group work and class discussions where students generate and compare equivalent expressions. In class discussion, students should be asked to connect the terms of an expression with quantities...
Illustrative Mathematics
Illustrative Mathematics: Reasoning About Multiplication
This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and...
Illustrative Mathematics
Illustrative Mathematics: 5.nf Do These Add Up?
This task addresses common errors that students make when adding fractions. Aligns with 5.NF.A.2.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Rectangle Perimeter 2
This task is a natural follow up for task Rectangle Perimeter 1. After thinking about and using one specific expression for the perimeter of a rectangle, they now extend their thinking to equivalent expressions for the same quantity....
Illustrative Mathematics
Illustrative Mathematics: 6.ee Firefighter Allocation
In this students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Rectangle Perimeter 1
This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. They then have to use the expression to evaluate the perimeter for specific values of the...
Illustrative Mathematics
Illustrative Mathematics: Connor and Makayla Discuss Multiplication
The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and use this burgeoning understanding of fraction multiplication to make sense of the commutative property of multiplication in...
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 young scholars 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...
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 young scholars synthesize what they have learned about multiplication in previous grades. Aligns with 5.OA.A.2.
Illustrative Mathematics
Illustrative Mathematics: Valentine Marbles
Explore estimation through this lesson designed to engage students.
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 young scholars to be able to decide whether the context requires the result to be reported as a whole number with remainder...
Illustrative Mathematics
Illustrative Mathematics: 5.nf Running a Mile
Students 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 learners 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.