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.

This is a cooperative learning exerise that allows students to learn about comparative advantage and the gains from trade.

In this activity, learners conduct an oxidation experiment that turns old pennies bright and shiny. Learners soak 20 dull, dirty pennies in a bowl of salt and vinegar for five minutes. They rinse half the pennies with water, then compare the rinsed pennies to the unrinsed after all pennies sit and dry for about an hour. Learners also observe what happens when they submerge a screw and nail in the liquid compared to a nail only half-way submerged.

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.

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions.

Working in small groups, students determine how 18 items are included in GDP (or if they are excluded.) Cards turned over one at a time encourage participation by all group members.

This task gives students another way to practice counting and gain fluency with connecting a written number with the act of counting. This task should be introduced by the teacher and would then be a good independent center.

The most engaging way to practice counting with students is to have them count meaningful things in their lives. Since five-year-olds are very focused on themselves this is easily done by allowing them to count themselves, their friends and objects within the classroom that relate to their daily lives.