Students construct rockets from balloons propelled along a guide string. They use this model to learn about Newton's three laws of motion, examining the effect of different forces on the motion of the rocket.
WNBA athletes discuss attendance at basketball games in terms of percentages in this video segment from TV 411. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
By taking a look at the energy of motion all around us, students learn about the types of energy and their characteristics. They first learn about the two simplest forms of mechanical energy: kinetic and potential energy, as illustrated by pendulums and roller coasters. They come to understand that energy can change from one form into another, and be described and determined by equations. Through the example of a waterwheel, the concepts of and differences between work and power are explained and calculated. Conservation of momentum and collisions are explored, with analogies to popular sports (billiards, baseball, golf), and how elastic and inelastic collisions are considered in the games' design. To show another energy transformation concept, the behavior of energy dissipating into heat by means of friction is presented. Students learn to recognize static friction, kinetic friction and drag, how they work, and how to calculate frictional force. A final lesson integrates the energy of motion concepts, showing how they are interconnected in everyday applications such as skateboards, scooters, roller coasters, trains, cars, planes, trucks and elevators. Through numerous hands-on activities, students swing pendulums, use plastic two-liter bottles to construct model waterwheels, bounce different types of balls, use weights to generate friction data, and roll balls down ramps to collide into cups.
The CyberSquad solves the problem of giving equal parts of two apples to Cerberus, the three headed dog of Greek mythology, in this video from Cyberchase. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.
In this Cyberchase video segment, Shari Spotter gets help from the CyberSquad in doubling a recipe for crumpets. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
Middle level students will collect times as they run the 100 meter dash. These times will be depicted through various graphic representations (bar, circle, histogram). Times will be compared to current world records for the 100 meters. Students will decide which Math class ran fastest and support that choice in short essay form. They will also try to determine the faster gender based on the data collected. This lesson plan is a unit filled with related lesson plans. One or two parts of this project could be completed as a stand-alone lesson, or the entire set of activities and extensions could be completed for an involved, integrated unit.
Commercial fishing nets often trap "unprofitable" animals in the process of catching target species. In this activity, students experience the difficulty that fishermen experience while trying to isolate a target species when a variety of sea animals are found in the area of interest. Then the class discusses the large magnitude of this problem. Students practice data acquisition and analysis skills by collecting data and processing it to deduce trends on target species distribution. They conclude by discussing how bycatch impacts their lives and whether or not it is an important environmental issue that needs attention. As an extension, students use their creativity and innovative skills to design nets or other methods, theoretically and/or through hands-on prototyping, that fisherman could use to help avoid bycatch.
The purpose of this task is to show three problems that are set in the same kind of context, but the first is a straightforward multiplication problem while the other two are the corresponding "How many groups?" and "How many in each group?" division problems.
Building on their fifth grade experiences with operations on decimal numbers, sixth grade students should find the task to be relatively easy. The emphasis here is on whether students are actually fluent with the computations, so teachers could use this as a formative assessment task if they monitor how students solve the problem.
In this video segment from Cyberchase, the CyberSquad replaces a piece of track to get the Madre Bonita Express to the Mother's Day harvest. ***Access to Teacher's Domain content now requires free login to PBS Learning Media.
Students solve decimal multiplication and division problems related to the basic fact 3 × 7 = 21.Students match cards that represent word problems, visual models, and numerical solutions to problems that include the numbers 0.8 and 0.2 for all four operations.Key ConceptsNo new mathematics is introduced in this lesson. Students apply their knowledge about decimal operations.Goals and Learning ObjectivesUse reasoning and mental math to solve problems.Solve word problems involving simple addition, subtraction, multiplication, and division with decimals.
In the previous lesson, students learned how to divide a decimal by a whole number. They also saw that multiplying both the dividend and the divisor by the same power of 10 does not change the quotient. In this lesson, students integrate these two understandings to find the quotient of two decimals. They see that to divide a number by a decimal, they can simply multiply both the dividend and divisor by a power of 10 so that both numbers are whole numbers. Doing so makes it simpler to use long division, or another method, to find the quotient. Students then practice using this principle to divide decimals in both abstract and contextual situations.
Groundwater is one of the largest sources of drinking water, so environmental engineers need to understand groundwater flow in order to tap into this important resource. Environmental engineers also study groundwater to predict where pollution from the surface may end up. In this lesson, students will learn how water flows through the ground, what an aquifer is and what soil properties are used to predict groundwater flow.
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A penny is about $\frac{1}{16}$ of an inch thick. In 2011 there were approximately 5 billion pennies minted. If all of these pennies were placed in a s...
Students are introduced to the differences between acids and bases and how to use indicators, such as pH paper and red cabbage juice, to distinguish between them.
Demonstrations explain the concepts of energy forms (sound, chemical, radiant [light], electrical, atomic [nuclear], mechanical, thermal [heat]) and states (potential, kinetic).
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.
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 use their knowledge of scales and areas to determine the best locations in Alabraska for the underground caverns. They cut out rectangular paper pieces to represent caverns to scale with the maps and place the cut-outs on the maps to determine feasible locations.