These word problems represent the "Add To" contexts for addition and subtraction.
Through a series of four lessons, students are introduced to many factors that affect the power output of photovoltaic (PV) solar panels. Factors such as the angle of the sun, panel temperature, specific circuit characteristics, and reflected radiation determine the efficiency of solar panels. These four lessons are paired with hands-on activities in which students design, build and test small photovoltaic systems. Students collect their own data, and examine different variables to determine their effects on the efficiency of PV panels to generate electrical power.
Students download the software needed to create Arduino programs and make sure their Arduino microcontrollers work correctly. Then, they connect an LED to the Arduino and type up and upload programs to the Arduino board to 1) make the LED blink on and off and 2) make the LED fade (brighten and then dim). Throughout, students reflect on what they've accomplished by answering questions and modifying the original programs and circuits in order to achieve new outcomes. A design challenge gives students a chance to demonstrate their understanding of actuators and Arduinos; they design a functioning system using an Arduino, at least three actuators and either a buzzer or toy motor. For their designs, students sketch, create and turn in a user's manual for the system (text description, commented program, detailed hardware diagram). Numerous worksheets and handouts are provided.
This task requires students to answer questions about the structure of an expression.
In this activity, students will learn about Newton's 2nd Law of Motion. They will learn that the force required to move a book is proportional to the weight of the book. Engineers use this relationship to determine how much force they need to move an airplane.
The purpose of this task is for students to select 2 numbers from a set of 3 that sum to 9. The task can be completed for sums equaling any number. Teachers may choose to ask students to write the simple equations they select.
This is a choral counting activity that can be easily adjusted as students learn higher numbers.
Students learn about a fascinating electromechanical coupling called piezoelectricity that is being employed and researched around the world for varied purposes, often for creative energy harvesting methods. A PowerPoint(TM) presentation provides an explanation of piezoelectric materials at the atomic scale, and how this phenomenon converts mechanical energy to electrical energy. A range of applications, both tested and conceptual, are presented to engage students in the topic. Gaining this background understanding prepares students to conduct the associated hands-on activity in which they create their own small piezoelectric "generators."
Students are introduced to prosthetics history, purpose and benefits, main components, main types, materials, control methods, modern examples including modern materials used to make replacement body parts and the engineering design considerations to develop prostheses. They learn how engineers and medical doctors work together to improve the lives of people with amputations and the challenges faced when designing new prostheses with functional and cosmetic criteria and constraints. A PowerPoint(TM) presentation and two worksheets are provided.
This task requires students to use functions to calculate how to best benefit from a pizza promotion.
This task can be implemented in a variety of ways. For a class with previous exposure to properties of perpendicular bisectors, part (a) could be a quick exercise in geometric constructions, and an application of the result. Alternatively, this could be part of an introduction to perpendicular bisectors, culminating in a full proof that the three perpendicular bisectors are concurrent at the circumcenter of the triangle, an essentially complete proof of which is found in the solution below.
This is a simple exercise in creating equations from a situation with many variables. By giving three different scenarios, the problem requires students to keep going back to the definitions of the variables, thus emphasizing the importance of defining variables when you write an equation. In order to reinforce this aspect of the problem, the variables have not been given names that remind the student of what they stand for. The emphasis here is on setting up equations, not solving them.
What do plants need? Students examine the effects of light and air on green plants, learning the processes of photosynthesis and transpiration. Student teams plant seeds, placing some in sunlight and others in darkness. They make predictions about the outcomes and record ongoing observations of the condition of the stems, leaves and roots. Then, several healthy plants are placed in glass jars with lids overnight. Condensation forms, illustrating the process of transpiration, or the release of moisture to the atmosphere by plants.
The purpose of this task is to have students add mixed numbers with like denominators. This task illustrates the different kinds of solution approaches students might take to such a task.
After a brief history of plastics, students look more closely as some examples from the abundant types of plastics found in our day-to-day lives. They are introduced to the mechanical properties of plastics, including their stress-strain relationships, which determine their suitability for different industrial and product applications. These physical properties enable plastics to be fabricated into a wide range of products. Students learn about the different roles that plastics play in our lives, Young's modulus, and the effects that plastics have on our environment. Then students act as industrial engineers, conducting tests to compare different plastics and performing a cost-benefit analysis to determine which are the most cost-effective for a given application, based on their costs and measured physical properties.
In this unit, students learn the very basics of navigation, including the different kinds of navigation and their purposes. The concepts of relative and absolute location, latitude, longitude and cardinal directions are explored, as well as the use and principles of maps and a compass. Students discover the history of navigation and learn the importance of math and how it ties into navigational techniques. Understanding how trilateration can determine one's location leads to a lesson on the global positioning system and how to use a GPS receiver. The unit concludes with an overview of orbits and spacecraft trajectories from Earth to other planets.
This task is part of a series presenting important foundational geometric results and constructions which are fundamental for more elaborate arguments. They are presented without a real world context so as to see the important hypotheses and logical steps involved as clearly as possible.
This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
To gain a better understanding of the roles and functions of components of the human respiratory system and our need for clean air, students construct model lungs that include a diaphragm and chest cavity. They see how air moving in and out of the lungs coincides with diaphragm movement. Then student teams design and build a prototype face mask pollution filter. They use their model lungs to evaluate their prototypes to design requirements.
Students learn how a bill becomes law in the U.S. Congress and research legislation related to global warming.