Whole numbers are no better than any others! Practice plotting values on the number line as a passionate activist rises up and demands equity for all numbers, including fractions and decimals.
You want a projectile to fly as far as possible, at which angle should you launch it? We'll start with formulas for the initial velocity. Created by Sal Khan.
Two besotted rulers must embrace proportional units in order to unite their lands. It takes mathematical reasoning to identify the problem, and solution, when engineers from Queentopia and Kingopolis build a bridge to meet in the middle of the river.
Teaching market structures in a microeconomics class? These slides present graphs related to perfect competition, the market structure in which there are many buyers and sellers of an identical product and there are no barriers to enter or exit the market. The slides illustrate firms' short-run decisions.
In this activity, learners work in groups to determine the mass and volume of four samples: glass marbles, steel washers or nuts, pieces of pine wood, and pieces of PVC pipe. Learners then plot the data points on a large class graph of mass vs. volume to discover that data points for a particular material form a straight line, the slope of which gives the density of the material.
Plotting projectile displacement, acceleration, and velocity as a function of time. Created by Sal Khan.
Students observe four different classroom setups with objects in motion (using toy cars, a ball on an incline, and a dynamics cart). At the first observation of each scenario, students sketch predicted position vs. time and velocity vs. time graphs. Then the classroom scenarios are conducted again with a motion detector and accompanying tools to produce position vs. time and velocity vs. time graphs for each scenario. Students compare their predictions with the graphs generated by technology and discuss their findings. This lesson requires assorted classroom supplies, as well as motion detector technology.
Using position-time graphs and number lines to find displacement and distance traveled.
In this lesson, through various examples and activities, exponential growth and polynomial growth are compared to develop an insight about how quickly the number can grow or decay in exponentials. A basic knowledge of scientific notation, plotting graphs and finding intersection of two functions is assumed.
A preparation for MAT 201 and the physical sciences. Students study principles, properties, and
applications of functions and their graphs. They revisit functions introduced in MAT 107 and expand
their knowledge of them. The course focuses heavily on circular trigonometric functions and introduces
conic sections. Laboratory activities place particular emphasis on the use of functions to model real
problems. Computers and/or graphing calculators are used to enhance the study of mathematics.
Prerequisites: A grade of C- or better in MAT 107 or a score of 71 or higher on the College Level Math
placement test; ENG 090 and ENG 094 (COL 090), or satisfactory placement test scores.
A work in progress, this FlexBook is an introduction to theoretical probability and data organization. Students learn about events, conditions, random variables, and graphs and tables that allow them to manage data.
Figuring out the horizontal displacement for a projectile launched at an angle. Created by Sal Khan.
Visualizing position, velocity and acceleration in two-dimensions for projectile motion.
This lesson aims to help students with quadratic functions y = ax2 + bx + c. This is the next step after linear functions bx + c. The lesson begins with three quadratics and their graphs (three parabolas): y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y. The particular example y = x2 – 2x could be repeated by the teacher, for emphasis. The lesson will take more than one class period (and this is deserved!). The breaks allow time to consider parabolas starting with -x2 and opening downward. A physical path would be one (dangerous?) activity.
Graphing energy versus position for a block accelerated by a spring and stopped by friction.
This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).
This task requires graphing time and distance.
Students gather data by timing runners over 5 m intervals. Using that data, students graph distance and velocity over time.
The evil Scaleo has escaped from prison and is transforming the length, width, and height of objects until they become useless – or dangerous. Who can put things right? Superheroine Scale Ella uses the power of scale factor to foil the villain.
Place and Location are two of the five themes of geography and a natural starting point for a study of the Arctic and Antarctica. Location answers the question, "Where am I?" while the study of place asks, "What kind of a place is it?" and, "How does this place connect to my hometown?" This issue of Beyond Penguins and Polar Bears examines how you can introduce the Arctic and Antarctica and use science, geography, literacy, and technology to help your students compare and contrast these two dramatically different areas as well as their own home. Get ready for an adventure as you and your students develop your polar sense of place!
Beyond Penguins and Polar Bears is an online professional development magazine for elementary teachers which focuses on preparing teachers to teach polar science concepts in an already congested curriculum by integrating inquiry-based science with literacy teaching. Such an integrated approach can increase students' science knowledge, academic language, reading comprehension, and written and oral discourse abilities.