This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of the (elliptical) orbit of a planet around the sun: The sun is at point $A$, point $P$ is where the planet is closest to the sun d...

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

The coffee cooling experiment is a popular example of an exponential model with immediate appeal. The model is realistic and provides a good context for students to practice work with exponential equations.

This number after bingo activity increases student flexibility with the number sequence and their ability to start counting sequences at various points.

This number line up activitiy gets students out of their seats and helps reinforce the counting sequence.

This activity is played in pairs and gives students practice reading numbers out loud and tracing them.

Students learn the connection between the counting sequence and experience from their daily lives in this daily activity. It also helps give students a sense of how "many" each number is.

The primary purpose of this task is to illustrate that the domain of a function is a property of the function in a specific context and not a property of the formula that represents the function. Similarly, the range of a function arises from the domain by applying the function rule to the input values in the domain. A second purpose would be to illicit and clarify a common misconception, that the domain and range are properties of the formula that represent a function.

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

This game game supports students in counting forward and can be adjusted to support backward counting.

This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction.

The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers.

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.