This task has students experiment with the operations of addition and multiplication, as they relate to the notions of rationality and irrationality.

In this ordering task each number has at most 3 digits so that students have the opportunity to think about how digit placement affects the size of the number.

In this task students must place 4-digit numbers into order from smallest to greatest and greatest to smallest.

The purpose of this task is to extend students' understanding of fraction comparison.

In this task students compare numbers less than 100 to benchmark numbers and learn to build an understanding of the relative magnitude of numbers.

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.

This challenging problem and brainteaser gives students an opportunity to compose and decompose polygons to make rectangles.

The purpose of this task is to provide students an opportunity to use mathematics addressed in different standards in the same problem.

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 students are in their understanding of fraction multiplication.

The purpose of this task is to provide students with a situation in which it is natural for them to divide a unit fraction by a non-zero whole number.

This high level task is an example of applying geometric methods to solve design problems and satisfy physical constraints. This task is accessible to all students. In this task, a typographic grid system serves as the background for a standard paper clip.

This task assumes students have an understanding of the relationship between functions and equations. Using this knowledge, the students are prompted to try to solve equations in order to find the inverse of a function given in equation form: when no such solution is possible, this means that the function does not have an inverse.

The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.

The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred.

The goal of this task is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table.

This simple conceptual task focuses on what it means for a number to be a solution to an equation, rather than on the process of solving equations.

This task provides a context where it is appropriate for students to subtract fractions with a common denominator; it could be used for either assessment or instructional purposes.

This task allows students to reason about the relative costs per pound of the two fruits without actually knowing what the costs are. Students who find this difficult may add a scale to the graph and reason about the meanings of the ordered pairs. Comparing the two approaches in a class discussion can be a profitable way to help students make sense of slope.

This word problem requires students to use addition and subtraction and think about money.