Students prove that linear functions grow by equal differences over equal intervals. They will prove this for equal intervals of length one unit, and note that in this case the equal differences have the same value as the slope.

Linear functions grow by equal differences over equal intervals. In this task students prove the property in general (for equal intervals of any length).

In this task students prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Examples in this task is designed to help students become familiar with this language "successive quotient". Depending on the students's prior exposure to exponential functions and their growth rates, instructors may wish to encourage students to repeat part (b) for a variety of exponential functions and step sizes before proceeding to the most general algebraic setting in part (c).

This task helps students understand the meaning of the equal sign and to use it appropriately.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.

The purpose of this task is to apply knowledge about triangles to calculate the sine and cosine of 30 and 60 degrees.

In this problem students must transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent.

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.

This task is designed for the student to apply geometric concepts in modeling situations.

The purpose of this task is to give students an opportunity use quantitative and graphical reasoning to detect an error in a solution. The equations have been chosen so that finding the exact solution requires significant calculation so that it is easy to make an error.

The task is designed to show that random samples produce distributions of sample means that center at the population mean, and that the variation in the sample means will decrease noticeably as the sample size increases. Random sampling (like mixing names in a hat and drawing out a sample) is not a new idea to most students, although the terminology is likely to be new.

The goal of this Illustrative Mathematics task is to use properties of exponents for whole numbers in order to explain how expressions with fractional exponents are defined.

The purpose of this Illustrative Mathematics task is to study the rules of exponents in the context of trying to make sense of a very interesting mathematical expression.