This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents, precisely the language being used in standard A-SSE.B.3.

Students are asked to consider the expression that arises in physics as the combined resistance of two resistors in parallel. However, the context is not explicitly considered here. The task is good general preparation for problems more specifically aligned to either A-SSE.1 or A-SSE.2.

The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.

The purpose of this task is to give students practice in reading, analyzing, and constructing algebraic expressions, attending to the relationship between the form of an expression and the context from which it arises. The context here is intentionally thin; the point is not to provide a practical application to kitchen floors, but to give a framework that imbues the expressions with an external meaning.

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.

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.

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PROMT Online Translator does not offer as many languages as other translators. The list is limited to about 22 languages so far. But it does have other nice features. For instance, it makes use of automatic language detection and even choose a topic for the translation.

You can then copy, paste, check the spelling, or access a dictionary. There is also a virtual keyboard so if you are using the site on a tablet, for example, popping in your words or sentences is simple. PROMT also offers translation software that you can purchase and download. Interestingly, free online website translator is also available as an Apple or Android app.

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

This task compares the usefulness of different forms of a quadratic expression. Students have to choose which form most easily provides information about the maximum value, the zeros and the vertical intercept of a quadratic expression in the context of a real world situation. Rather than just manipulating one form into the other, students can make sense out of the structure of the expressions.

This question provides students with an opportunity to see expressions as constructed out of a sequence of operations: first taking the square root of n, then dividing the result of that operation into s. Students studying statistics encounter the expression in this question as the standard deviation of a sampling distribution with samples of size n when the distribution from which the sample is taken has standard deviation s.

The purpose of this task is to identify the structure in the two algebraic expressions by interpreting them in terms of a geometric context. Students will have likely seen this type of process before, so the principal source of challenge in this task is to encourage a multitude and variety of approaches, both in terms of the geometric argument and in terms of the algebraic manipulation.

Parts (d) and (e) of this task constitute a very advanced application of the skill of making use of structure: in (d) students are being asked to use the defining property of even and odd functions to manipulate expressions involving function notation. In (e) they are asked to see the structure in the system of two equations involving functions.

This task is not about computing the final price of the shirt but about using the structure in the computation to make a general argument.

This task illustrates A-SSE.1a because it requires students to identify expressions as sums or products and interpret each summand or factor.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.

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