The purpose of this task is to assess studentsŐ understanding of multiplicative and additive reasoning.

The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades.

This task can be used to either build or assess initial understandings related to rational approximations of irrational numbers.

Many students will not know that when comparing two quantities, the percent decrease between the larger and smaller value is not equal to the percent increase between the smaller and larger value. Students would benefit from exploring this phenomenon with a problem that uses smaller values before working on this one.

In the everyday electrical devices we use calculators, remote controls and cell phones a voltage source such as a battery is required to close the circuit and operate the device. In this hands-on activity, students use batteries, wires, small light bulbs and light bulb holders to learn the difference between an open circuit and a closed circuit, and understand that electric current only occurs in a closed circuit.

In a multi-week experiment, students monitor the core temperatures of two compost piles, one control and one tended, to see how air and water affect microbial activity. They daily aerate and wet the "treated" pile and collect 4-6 weeks' worth of daily temperature readings. Once the experiment is concluded, students plot and analyze their data to compare the behavior of the two piles. They find that the treated pile becomes hotter, an indication that more microbes are active and releasing heat. Through this activity, students see that microbes play a role in composting and how composting can be used as a carbon management process.

With the help of simple, teacher-led demonstration activities, students learn the basic concepts of heat transfer by means of conduction, convection, and radiation. Students then apply these concepts as they work in teams to solve two problems. One problem requires that they maintain the warm temperature of one soda can filled with water at approximately body temperature, and the other problem is to cause an identical soda can of warm water to cool as much as possible during the same thirty-minute time interval. Students design their solutions using only common, everyday materials. They record the water temperatures in their two soda cans every five minutes, and prepare line graphs in order to visually compare their results to the temperature of an unaltered control can of water.

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

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

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.

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 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 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.

These games support student development of number sense and the concept of mathematical operations

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.