In this video David quickly explains each 2D motion concept and does a quick example problem for each concept. Keep an eye on the scroll to the right to see where you are in the review. Created by David SantoPietro.
Figuring how long it takes an A380 to take off given a constant acceleration. Created by Sal Khan.
CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.
Students will use images, U.S. Census Bureau data, and interactive maps to visualize and calculate arithmetic (population), agricultural, and physiological densities at local, regional, and national scales. They will also transfer their calculations to bar graphs.
The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.
Sal explains how to draw free body diagrams when forces are applied at an angle. How to find horizontal and vertical components of an angled force using trigonometry.
CK-12 Middle School Math Concepts for seventh grade provides a complete textbook. It presents topics including algebraic thinking, patterns, decimals, decimal operations, fractions, fraction operations, integers, integer operations, ratios, rates, proportions, percents, percent applications, equations, solving equations, inequalities, functions, graphing functions, geometry, plane geometry, solid geometry, area, perimeter, surface area, volume, statistics including mean, median, mode and range, graphing and types of graphs, and probability.
This task provides the opportunity for students to reason about graphs, slopes, and rates without having a scale on the axes or an equation to represent the graphs. Students who prefer to work with specific numbers can write in scales on the axes to help them get started.
Lesson Delivery: Students will collect weather data for a given city/town from a weather website to analyze and create a graph that displays the change in temperature over a time period (one or twq weeks). Useful Sites: Create a Graph: https://nces.ed.gov/nceskids/createagraph/Default.aspx Weather Data: https://www.weather.gov/wrh/climate
n addition to providing a task that relates to other disciplines (history, civics, current events, etc.), this task is intended to demonstrate that a graph can summarize a distribution as well as provide useful information about specific observations.
This task is the second in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically.
This task is the last in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions graphically. The progression of the content standards is 6.EE.8 to 7.EE.4 to A-REI.12.
David explains how to use a force vs. time graph to find the change in momentum and solves an example problem to find the final velocity of a spaceship. Created by David SantoPietro.
Sal draws a free body diagram for a box held stationary against a wall with a force at an angle theta.
Student teams use sensorsâmotion detectors and accelerometersâto collect walking gait data from group members. They import their collected position and acceleration data into Excel® for graphing and analysis to discover the relationships between position, velocity and acceleration in the walking gaits. Then they apply their understanding of slopes of secant lines and Riemann sums to generate and graph additional data. These activities provide practice in the data collection and analysis of systems, similar to the work of real-world engineers.
This task requires students to recognize the graphs of different (positive) powers of x. There are several important aspects to these graphs. First, the graphs of even powers of x all open upward as x grows in the positive or negative direction. The larger the even power, the flatter these graphs look near 0 and the more rapidly they increase once the distance of x from 0 excedes 1.
This exploration can be done in class near the beginning of a unit on graphing parabolas. Students need to be familiar with intercepts, and need to know what the vertex is.
How to solve for the horizontal displacement when the projectile starts with a horizontal initial velocity. We also explain common mistakes people make when doing horizontally launched projectile problems. Created by David SantoPietro.
The goal of this task is to get students to focus on the shape of the graph of the equation y=ex and how this changes depending on the sign of the exponent and on whether the exponential is in the numerator or denominator. It is also intended to develop familiarity, in the case of f and k, with the functions which are used in logistic growth models, further examined in ``Logistic Growth Model, Explicit Case'' and ``Logistic Growth Model, Abstract Verson.''
Students will examine data on the number of immigrants in the United States, to create bar graphs and line graphs with appropriate scales. Students will then compare and analyze their graphs to draw conclusions about the data.