This goal of this task is to give students familiarity using the formula for the area of a circle while also addressing measurement error.

This task addresses the first part of standard F-BF.3: ŇIdentify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k (both positive and negative).Ó Here, students are required to understand the effect of replacing x with x+k, but this task can also be modified to test or teach function-building skills involving f(x)+k, kf(x), and f(kx) in a similar manner.

This task would be ideal to help students develop mental strategies to think about division during instruction. Jillian's strategy is often referred to as using "compatible numbers." Jillian is using a relationship that she can easily find: 140 divided by 7 is 20 or 20 sets of 7 is 140.

This classroom task gives students the opportunity to prove a surprising fact about quadrilaterals: that if we join the midpoints of an arbitrary quadrilateral to form a new quadrilateral, then the new quadrilateral is a parallelogram, even if the original quadrilateral was not.

This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles. The solution provided (among other possibilities) uses the SAS trial congruence theorem, and the fact that opposite sides of parallelograms are congruent.

The first two parts of this task ask students to interpret the meaning of signed numbers and reason based on that meaning in a context where the meaning of zero is already given by convention.

In this task students are asked to write two expressions from verbal descriptions and determine if they are equivalent. The expressions involve both percent and fractions. This task is most appropriate for a classroom discussion since the statement of the problem has some ambiguity.

The purpose of this task is to emphasize the use of the Remainder Theorem (a discussion of which should obviously be considered as a prerequisite for the task) as a method for determining structure in polynomial in equations, and in this particular instance, as a replacement for division of polynomials.

The purpose of this task is to help students realize there are different ways to add mixed numbers and is most appropriate for use in an instructional setting.

This task assumes students are familiar with mixing problems. This approach brings out different issues than simply asking students to solve a mixing problem, which they can often set up using patterns rather than thinking about the meaning of each part of the equations.

In order to solve this problem, students must assume that if you mix a cubic foot of sand with a cubic foot of cement, you will have 2 cubic feet of mix.

The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.

This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.

This counting activity is done in pairs and helps reinforce the concepts of greater than, less than, and equal to.

This task presents a straight forward question that can be solved using an equation in one variable. The numbers are complicated enough so that it is natural to set up an equation rather than solve the problem in one's head.

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation.