This lesson discusses how to identify sets of numbers as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

This site teaches Quantities to High Schoolers through a series of 116 questions and interactive activities aligned to 4 Common Core mathematics skills.

This site teaches The Complex Number System to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.

This site teaches The Real Number System to High Schoolers through a series of 1090 questions and interactive activities aligned to 8 Common Core mathematics skills.

This site teaches Vector and Matrix Quantities to High Schoolers through a series of 2195 questions and interactive activities aligned to 16 Common Core mathematics skills.

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.

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

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 is a very open-ended task designed for students to develop some of the basic ideas surrounding exponential growth. While implementations will vary (as discussed below), the core idea is that each fold of the piece of paper doubles the height of the stack. Combined with an estimate of the original thickness of the paper and the distance to the moon, this is enough information to deduce the minimum number of folds to get there. The solution uses the estimate of 0.1 mm for the thickness of paper and 385,000 km for the distance to the moon.

In this activity about light and reflection, learners use a special device called a Mirage Maker䋢 to create an illusion. What they perceive as an object is really an image in space, created by two concave mirrors. Learners will be surprised when they try to grab the object on the mirror and there's nothing there! Activity includes a light-ray diagram to help explain how the image is created.

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.

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 requires students to answer questions about the structure of an expression.

This task requires students to use functions to calculate how to best benefit from a pizza promotion.

This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.

This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.

To plot an inequality, such as x>3, on a number line, first draw a circle over the number (e.g., 3). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in. Finally, draw a line going from the circle in the direction of the numbers that make the inequality true.

This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.

This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.