This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

The purpose of this task is to have students think about the meaning of multiplying a number by a fraction, and to use this understanding of fraction multiplication to make sense of the commutative property of multiplication in the case of fractions.

Students are introduced to the idea of improving efficiency by examining a setting that is familiar to many teenagers fast food restaurants. More specifically, they learn about the concepts of trade-offs, constraints, increasing efficiency and systems thinking. They consider how to improve efficiency in a struggling restaurant through delegating tasks, restructuring employee responsibilities and revising a floor plan, all while working within limitations and requirements. Finally, students summarize and defend their suggested changes in argumentative essays.

The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

In this activity, students use a variety of materials to design and create headphones that absorb sound.

The objective of this subject is to understand the nature of manufacturing process variation and the methods for its control. First, a general process model for control is developed to understand the limitations a specific process places on the type of control used. A general model for process variation is presented and three methods are developed to minimize variations: Statistical Process Control, Process Optimization and in-process Feedback Control. These are considered in a hierarchy of cost-performance tradeoffs, where performance is based on changes in process capability.

This task is for instruction purposes. Part (b) is subtle and the solution presented here uses a "dynamic" view of triangles with two side lengths fixed. This helps pave the way toward what students will see later in trigonometry but some guidance will likely be needed in order to get students started on this path.

Standard 8.NS.1 requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of choice of representation. For example, 0.333 and 1/3 are two different ways of representing the same number.

This task gives students word problems with a given a set of a specified size and a specified number of subsets. The questions ask the student to find out the size of each of the subsets.

This task provides an opportunity to work on the Standard for Mathematical Practice 3 Construct Viable Arguments and Critique the Reasoning of Others.

Students learn about using renewable energy from the Sun for heating and cooking as they build and compare the performance of four solar cooker designs. They explore the concepts of insulation, reflection, absorption, conduction and convection.

While the task as written does not explicitly use the term "unit rate," most of the work students will do amounts to finding unit rates. A recipe context works especially well since there are so many different pair-wise ratios to consider.

Students learn the meaning of preservation and conservation and identify themselves and others as preservationists or conservationists in relation to specific environmental issues. They use Venn diagrams to clarify the similarities and differences in viewpoints. They see how an environmental point-of-view affects the approach to an engineering problem.

In this activity, students examine how to grow plants the most efficiently. They imagine that they are designing a biofuels production facility and need to know how to efficiently grow plants to use in this facility. As a means of solving this design problem, they plan a scientific experiment in which they investigate how a given variable (of their choice) affects plant growth. They then make predictions about the outcomes and record their observations after two weeks regarding the condition of the plants' stem, leaves and roots. They use these observations to guide their solution to the engineering design problem. The biological processes of photosynthesis and transpiration are briefly explained to help students make informed decisions about planning and interpreting their investigation and its results.

Students write poems using rhyme and meter as they come to understand the mechanical concept of rhythm, based on the principle of oscillation, in a broader biological and cultural context, as seen in dance and sports, poetry and other literary forms, and communication in general. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

Students learn about the many types of expenses associated with building a bridge. Working like engineers, they estimate the cost for materials for a bridge member of varying sizes. After making calculations, they graph their results to compare how costs change depending on the use of different materials (steel vs. concrete). They conclude by creating a proposal for a city bridge design based on their findings.

Students design a simple behavioral survey, and learn basic protocol for primary research, survey design and report writing. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

Students practice counting sequences by standing in a circle and counting one by one.