The problem deals with a rational expression which is built up from operations arising naturally in a context: adding the volumes of the fertilizer and the water, and dividing the volume of the fertilizer by the resulting sum. Thus it encourages students to see the expression as having meaning in terms of numbers and operations, rather than as an abstract arrangement of symbols.

Students learn about the separation techniques of sedimentation and centrifugation and investigate whether blood is a homogeneous or a heterogeneous mixture. Working in groups as if they are biomedical researchers, they employ the scientific method and make observations about the known characteristics of urine, milk and blood. They probe further by analyzing research on the properties and fractionation modes of blood. As students learn about certain strange characteristics with the fractionation behavior of blood, they formulate hypotheses on the unique nature of blood. Using provided materials —olive oil, tomato juice and petroleum jelly—they design an experiment and construct a blood model. They test their hypotheses by conducting experiments on the blood model, and then propose theories for the nature of blood as a mixture—arriving at the theory of mixture dualism in blood—that blood is a complex mixture system. An activity-guiding handout and PowerPoint® presentation are provided for this student-directed, project-based activity.

As students are learning about substances, mixtures, and solutions, they will participate in several experiments that involve chemical reactions using regular household products. Some experiments will produce gas or create something that will grow. Students will work in groups of 2-3 students to make a car move using the result of a chemical reaction from combining two or more household substances. They will present their project to the class.

Students learn about life-cycle assessment and how engineers use this technique to determine the environmental impact of everyday products and processes. As they examine what’s involved in making and consuming cupcakes, a snack enjoyed by millions of people every year, students learn about the production, use and disposal phases of an object’s life cycle. With the class organized into six teams, students calculate data for each phase of a cupcake’s life cycle—wet ingredients, dry ingredients, baking materials, oven baking, frosting, liner disposal—and calculate energy usage and greenhouse gases emitted from making one cupcake. They use ratios and fractions, and compare options for some of the life-cycle stages, such as different paper wrapper endings (disposal to landfills or composting) in order to make a life-cycle plan with a lower environmental impact. This activity opens students’ eyes to see the energy use in the cradle-to-grave lives of everyday products. Pre/post-quizzes, worksheets, activity cards, Excel® workbook and visual aids are provided.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

Students learn about the advantages and disadvantages of the greenhouse effect. They construct their own miniature greenhouses and explore how their designs take advantage of heat transfer processes to create controlled environments. They record and graph measurements, comparing the greenhouse indoor and outdoor temperatures over time. Students are also introduced to global issues such as greenhouse gas emissions and their relationship to global warming.

Students use provided materials to design and build prototype artificial heart valves. Their functioning is demonstrated using water to simulate the flow of blood through the heart. Upon completion, teams demonstrate their fully functional prototypes to the rest of the class, along with a pamphlet that describes the device and how it works.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

Many children may have heard of black holes and already have the understanding that they are ‘bottomless wells’. If something falls into a black hole, it is impossible for it to escape—even light cannot escape and is swallowed. The lack of light is how black holes get their name. These objects are mysterious and interesting, but they are not easy to explain. This activity will allow children to visualize, and therefore help them decompose, the concepts of space-time and gravity, which are integral to understanding these appealing objects.

Students investigate the ways in which ancient technologies six types of simple machines and combinations are used to construct modern buildings. As they work together to solve a design problem (designing and building a modern structure), they brainstorm ideas, decide on a design, and submit it to a design review before acquiring materials to create it (in this case, a mural depicting it). Emphasis is placed on cooperative, creative teamwork and the steps of the engineering design process.

Students make Moebius strips and use them to demonstrate the interconnectedness of an environment. They explore the natural cycles water, oxygen/carbon dioxide, carbon, nitrogen that exist within the environment.

Students are challenged to use computer-aided design (CAD) software to create “complete” 3D-printed molecule models that take into consideration bond angles and lone-pair positioning. To begin, they explore two interactive digital simulations: “build a molecule” and “molecule shapes.” This aids them in comparing and contrasting existing molecular modeling approaches—ball-and-stick, space-filling, and valence shell electron pair repulsion (VSEPR)—so as to understand their benefits and limitations. In order to complete a worksheet that requires them to draw Lewis dot structures, they determine the characteristics and geometries (valence electrons, polar bonds, shape type, bond angles and overall polarity) of 12 molecules. They also use molecular model kits. These explorations and exercises prepare them to design and 3D print their own models to most accurately depict molecules. Pre/Post quizzes, a step-by-step Blender 3D software tutorial handout and a worksheet are provided.

Students work as engineers to learn about the properties of molecules and how they move in 3D space through the use of LEGO MINDSTORMS(TM) NXT robotics. They design and build molecular models and use different robotic sensors to control the movement of the molecular simulations. Students learn about the size of atoms, Newman projections, and the relationship of energy and strain on atoms. This unique modular modeling activity is especially helpful in providing students with a spatial and tactile understanding of how molecules behave.

This task asks students to solve a problem in a context involving constant speed. This task provides a transition from working with ratios involving whole numbers to ratios involving fractions.

This task is designed to help students focus on the whole that a fraction refers to. It helps students to realize that two different fractions can describe the same situation depending on what you choose to be the whole.

Students learn the physical properties of sound, how it travels and how noise impacts human health—including the quality of student learning. They learn different techniques that engineers use in industry to monitor noise level exposure and then put their knowledge to work by using a smart phone noise meter app to measure the noise level at an area of interest, such as busy roadways near the school. They devise an experimental procedure to measure sound levels in their classroom, at the source of loud noise (such as a busy road or construction site), and in between. Teams collect data using smart phones/tablets, microphones and noise apps. They calculate wave properties, including frequency, wavelength and amplitude. A PowerPoint® presentation, three worksheets and a quiz are provided.

Students learn about the Earth's only natural satellite, the Moon. They discuss the Moon's surface features and human exploration. They also learn about how engineers develop technologies to study and explore the Moon, which also helps us learn more about the Earth.

This counting activity is done in pairs and helps reinforce the concepts of greater than, less than, and equal to.

This task presents a straight forward question that can be solved using an equation in one variable. The numbers are complicated enough so that it is natural to set up an equation rather than solve the problem in one's head.

Students learn why and how motion occurs and what governs changes in motion, as described by Newton's three laws of motion. They gain hands-on experience with the concepts of forces, changes in motion, and action and reaction. In an associated literacy activity, students design a behavioral survey and learn basic protocol for primary research, survey design and report writing.