The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

While not a full-blown modeling problem, this task does address some aspects of modeling as described in Standard for Mathematical Practice 4. Also, students often think that time must always be the independent variable, and so may need some help understanding that one chooses the independent and dependent variable based on the way one wants to view a situation.

In this task students must interpret a function in relation to a given problem.

The purpose of this task is to assess understanding of how study design dictates whether a conclusion of causation is warranted. This study was observational and not an experiment, which means that it is not possible to reach a cause-and-effect conclusion.

Students review the what they have learned throughout the five lessons in this unit. This includes a review of many types of engineers, reminding students of the various everyday products, structures and processes they design and create in our world.

Students further their understanding of the engineering design process while combining mechanical engineering and bioengineering to create an automated medical device. During the activity, students are given a fictional client statement and are required to follow the steps of the design process to create medical devices that help reduce the workload for hospital workers and increase the quality of patient care.

Students apply the concepts of conduction, convection and radiation as they work in teams to solve two challenges. One problem requires that they maintain the warm temperature of one soda can filled with water at approximately human 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 30-minute time period. Students design their engineering solutions using only common everyday materials, and test their devices by recording the water temperatures in their two soda cans every five minutes.

Students gain first-hand experience on how friction affects motion. They build a hovercraft using air from a balloon to levitate a craft made from a compact disc (CD), learning that a bed of air under an object significantly reduces the friction as it slides over a surface.

Students learn about friction and its effects on motion by building model hovercrafts.

This task is designed as an assessment item. It requires students to use information in a two-way table to calculate a probability and a conditional probability. Although the item is written in multiple choice format, the answer choices could be omitted to create a short-answer task.

These three lessons are part of the overall unit called, "How does my Cambodian Culture Affect Who I Am as a Student?" In the lessons, students will compare their Cambodian school culture to that of the United States. They will address the similarities and differences and will discuss the preconceived notions they had about school in America and how their culture affects who they are as students in the American school system.The lessons are geared for newcomers (ESL students) from Cambodia to the United States, grades 5-8. Their language proficiency is at various levels so instruction should be differentiated.

Student teams design and conduct quality-control experiments to test the reliability of several ultraviolet protection factors. Students use UV-detecting beads in their experimental designs to test the effectiveness of various types of sunscreens and sunblock. For example, they might examine zinc oxide nanoparticles versus traditional organic sun protection factors. UV intensity is quantitatively measured by UVA and UVB Vernier sensors, and students record and graph their results. By designing and conducting this experiment, students compare various substances, while learning about quality control.

To learn how friction affects motion, students explore how different textures provide varying amounts of friction to objects moving across them. They build a tool to measure the amount of friction between a note card and various surfaces by measuring the distance that a rubber band stretches. They experiment with a range of materials to determine which provides the least/most friction.

Students learn about porosity and permeability and relate these concepts to groundwater flow. They use simple materials to conduct a porosity experiment and use the data to understand how environmental engineers decide on the placement and treatment of a drinking water well.

In this activity using a balance scale students practice weighing items to see how heavy they are. Cubes are used in the balance as units of measure so students may easily count them.

Students work in pairs to measure length by lining up cubes along the longest side of an item. They count and record length by counting the number of cubes.

This task uses student generated data to assess standard 7.SP.7. This task could also be extended to address Standard 7.SP.1 by adding a small or whole class discussion of whether the class could be considered as a representative sample of all students at your school.

The purpose of this task is for students to apply the concepts of mass, volume, and density in a real-world context. There are several ways one might approach the problem, e.g., by estimating the volume of a person and dividing by the volume of a cell.

These two fraction division tasks use the same context and ask ŇHow much in one group?Ó but require students to divide the fractions in the opposite order. Students struggle to understand which order one should divide in a fraction division context, and these two tasks give them an opportunity to think carefully about the meaning of fraction division.

This task gives children an opportunity to subtract a three-digit number including a zero that requires regrouping. The solutions show how students can solve this problem before they have learned the traditional algorithm.