An important property of linear functions is that they grow by equal differences over equal intervals. In this task students 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.

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.

This purpose of this task is for students to understand how to partition shapes into equal pieces. This task starts students with concrete representations of the shapes that they can fold and cut, so that later they will understand more abstract representations like diagrams and symbols. Part one provides students with opportunities to manipulate paper shapes, folding them to create equal parts.

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. 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.

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

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 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.

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.

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 purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.

The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.

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.

This problem illustrates how an exponentially increasing quantity eventually surpasses a linearly increasing quantity.

In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

This problem shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large.

The purpose of this task is twofold: first using technology to study the behavior of some exponential and logarithmic graphs and secondly to manipulate some explicit logarithmic and exponential expressions. Although not asked in the task body, the teacher may wish to prompt students to explain why the two graphs behave as they do as the base b varies: that is, a larger value of b between 1 and 2 makes the exponential graph grow faster and the logarithmic graph grow more slowly as x increases.

The task provides a reasonably straight-forward introduction to interpreting the parameters of an exponential function in terms of a modeling context. In general, an exponential function f(t)=ab^t has two parameters. The parameter a is interpreted as the starting value (when t represents time), and b represents the growth rate -- the amount the quantity is multiplied by each time the value of t is incremented by 1.