In this video segment from Cyberchase, Harry has a fixed budget for clothing, so he must figure out what combination of jackets and pants he can buy with $100.
Students examine random variables and distributions. Topics explored are probability distributions, and discrete and continuous random variables. The tutorial investigates the statistics concepts through class notes and examples. Review exercises and a chapter quiz are included.
Use this activity to explore forces acting on objects, practice graphing experimental data, and introduce the algebra concepts of slope and intercept of a line. A wooden 2 x 4 beam is set on top of two scales. Students learn how to conduct an experiment by applying loads at different locations along the beam, recording the exact position of the applied load and the reaction forces measured by the scales at each end of the beam. In addition, students analyze the experiment data with the use of a chart and a table, and model/graph linear equations to describe relationships between independent and dependent variables.
The CyberSquad tries to figure out how Hackerë_í__ cyberfrog moves when its various buttons are pressed, in this video from Cyberchase.
In this video from Cyberchase, the CyberSquad must figure out the new input/output pattern on Hackerë_í__ larger cyberfrog.
Students explore the use of wind power in the design, construction and testing of "sail cars," which, in this case, are little wheeled carts with masts and sails that are powered by the moving air generated from a box fan. The scientific method is reviewed and reinforced with the use of controls and variables, and the engineering design process is explored. The focus of the activity is on renewable energy, as well as the design, testing and redesign of small cars made from household materials. The activity (and an extension worksheet) includes the use of kinematic equations using distance, time traveled and speed to enforce exponents and decimals.
In this lesson and its associated activity, students conduct a simple test to determine how many drops of each of three liquids can be placed on a penny before spilling over. The three liquids are water, rubbing alcohol, and vegetable oil; because of their different surface tensions, more water can be piled on top of a penny than either of the other two liquids. However, this is not the main point of the activity. Instead, students are asked to come up with an explanation for their observations about the different amounts of liquids a penny can hold. In other words, they are asked to make hypotheses that explain their observations, and because middle school students are not likely to have prior knowledge of the property of surface tension, their hypotheses are not likely to include this idea. Then they are asked to come up with ways to test their hypotheses, although they do not need to actually test their hypotheses. The important points for students to realize are that 1) the tests they devise must fit their hypotheses, and 2) the hypotheses they come up with must be testable in order to be useful.
Most of the flavoring in gum is due to the sugar or other sweetener it contains. As gum is chewed, the sugar dissolves and is swallowed. After a piece of gum loses its flavor, it can be left to dry at room temperature and then the difference between its initial (unchewed) mass and its chewed mass can be used to calculate the percentage of sugar in the gum. This demonstration experiment is used to generate new questions about gums and their ingredients, and students can then design and execute new experiments based on their own questions.
This site defines and discusses the ideal gas law. The concept of state variables is explained and the various state variables are identified. Links to further information is available.
Using this tutorial, you'll learn how to solve a formula for a variable and how to solve word problems involving formulas.
Visualize solutions to one variable equations by performing a balancing act. This interactive exercise focuses on linear equations and mathematical reasoning to show how one variable equations need to stay balanced to be solved correctly then you get to model your own problems and solve.
Students become proficient at manipulating and solving single-variable linear equations and inequalities, and using them to model and interpret contextual situations.
Learn about the competitive sport of fencing along with the resulting mathematical problems and equivalent expressions that help determine the number of matches played per tournament in this video from the Center for Asian American Media. This resource is part of the Math at the Core: Middle School Collection. [2:23]
This site consists of interactive lessons on a multitude of math topics including sets, drawing plane and coordinate system, variables, equations, and functions. You may also view this Vienna University site in German.
Students design, build and test model race cars made from simple materials (lifesaver-shaped candies, plastic drinking straws, Popsicle sticks, index cards, tape) as a way to explore independent, dependent and control variables. They measure the changes in distance travelled with the addition of mass to the vehicles. Students also practice the steps of the engineering design process by brainstorming, planning, building, testing, and improving their "mint-mobiles."
Students venture into the Expressions and Equations domain, using variables to represent unknown or changing quantities, and using properties of operations to investigate equivalent expressions.
Students conduct an experiment to determine how varying the composition of a construction material affects its strength. They make several adobe bricks with differing percentages of sand, soil, fibrous material and water. They test the bricks for strength by dropping them onto a concrete surface from progressively greater heights. Students graph the experiment results and use what they learn to design their own special mix that maximizes the bricks' strength. During the course of the experiment, students learn about variables (independent, dependent, control) and the steps of the engineering design process.
Students are introduced to the physics concepts of air resistance and launch angle as they apply to catapults. This includes the basic concepts of position, velocity and acceleration and their relationships to one another. They use algebra to solve for one variable given two variables.
Examine how one innovator is working to improve the way concert pianos are designed and tuned. This video focuses on the balance that needs to occur in an ideally tuned piano key and explores how David Stanwood calculated the balance range through data analysis of measurements and ratios, taking math out of the classroom and into real world problem solving.
Find the next hit movie based on trends by structuring and analyzing data in a spreadsheet. Time to complete: 6-9 hours