This problem involves solving a system of algebraic equations from a context: …

This problem involves solving a system of algebraic equations from a context: depending how the problem is interpreted, there may be one equation or two.

This task is a somewhat more complicated version of "Accurately weighing pennies …

This task is a somewhat more complicated version of "Accurately weighing pennies I'' as a third equation is needed in order to solve part (a) explicitly. Instead, students have to combine the algebraic techniques with some additional problem-solving (numerical reasoning, informed guess-and-check, etc.)

This unit was created as an introductory/review unit for Algebra II to …

This unit was created as an introductory/review unit for Algebra II to allow for a review of main concepts needed to progress in Algebra II. However, it could also be used in Algebra I to introduce for the first time real numbers; number operations; and equations, expressions, and inequalities.

This task presents a simple but mathematically interesting game whose solution is …

This task presents a simple but mathematically interesting game whose solution is a challenging exercise in creating and reasoning with algebraic inequalities. The core of the task involves converting a verbal statement into a mathematical inequality in a context in which the inequality is not obviously presented, and then repeatedly using the inequality to deduce information about the structure of the game.

The primary purpose of this task is to illustrate certain aspects of …

The primary purpose of this task is to illustrate certain aspects of the mathematics described in the A.SSE.1. The task has students look for structure in algebraic expressions related to a context, and asks them to relate that structure to the context. In particular, it is worth emphasizing that the task requires no algebraic manipulation from the students.

This task does not actually require that the student solve the system …

This task does not actually require that the student solve the system but that they recognize the pairs of linear equations in two variables that would be used to solve the system. This is an important step in the process of solving systems.

This task is the last in a series of three tasks that …

This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.EE.8 to 7.EE.4 to A-REI.12.

This task is designed to make students think about the meaning of …

This task is designed to make students think about the meaning of the quantities presented in the context and choose which ones are appropriate for the two different constraints presented. In particular, note that the purpose of the task is to have students generate the constraint equations for each part (though the problem statements avoid using this particular terminology), and not to have students solve said equations.

In the middle grades, students have lots of experience analyzing and comparing …

In the middle grades, students have lots of experience analyzing and comparing linear functions using graphs, tables, symbolic expressions, and verbal descriptions. In this task, students may choose a representation that suits them and then reason from within that representation.

Students will use data about the cooling time of coffee to create …

Students will use data about the cooling time of coffee to create an exponential regression and make estimates about how long the coffee needs to cool to reach a certain temperature.

This task assumes students are familiar with mixing problems. This approach brings …

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.

This is a simple exercise in creating equations from a situation with …

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.

The purpose of this task is to provide an opportunity for students …

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

This task asks students to determine a recursive process from a context. …

This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.

The purpose of this task is to give students practice writing a …

The purpose of this task is to give students practice writing a constraint equation for a given context. Instruction accompanying this task should introduce the notion of a constraint equation as an equation governing the possible values of the variables in question.

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