The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions.

In this interactive activity adapted from Anneberg Learner’s Teaching Math Grades 3–5, compare fractions on number lines to determine which class of students wins bubble-gum-blowing contests.

This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them. This task is meant to generate classroom discussion related to comparing fractions. Particularly important is that students understand that when you compare fractions, you implicitly always have the same whole.

This task is appropriate for assessing student's understanding of differences of signed numbers. Because the task asks how many degrees the temperature drops, it is correct to say that "the temperature drops 61.5 degrees." However, some might think that the answer should be that the temperature is "changing -61.5" degrees. Having students write the answer in sentence form will allow teachers to interpret their response in a way that a purely numerical response would not.

The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.

The purpose of this task is to assess studentsŐ understanding of multiplicative and additive reasoning.

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades.

This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.

Students must calculate the volume of a cone in this real world task.

This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.

The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task.

The purpose of the task is for students to compare signed numbers in a real-world context.

The focus of this task is on understanding that fractions, in an explicit context, are fractions of a specific whole. In this problem there are three different wholes: the medium pizza, the large pizza, and the two pizzas taken together.

Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one.

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.

In this task students are required to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.

In this task students are required to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers.

This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.

Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.