This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

Based on knowledge of the unit Circles, students see how sinusoids (Sine and coSine waves) get their shapes.

Sal draws a free body diagram for a box held stationary against a wall with a force at an angle theta.

This task complements ``Seven Circles'' I, II, and III. This is a hands-on activity which students could work on at many different levels and the activity leads to many interesting questions for further investigation.

This task provides an opportunity to model a concrete situation with mathematics. Once a representative picture of the situation described in the problem is drawn (the teacher may provide guidance here as necessary), the solution of the task requires an understanding of the definition of the sine function. When the task is complete, new insight is shed on the ``Seven Circles I'' problem which initiated this investigation as is noted at the end of the solution.

In this lesson, students will investigate error. As shown in earlier activities from navigation lessons 1 through 3, without an understanding of how errors can affect your position, you cannot navigate well. Introducing accuracy and precision will develop these concepts further. Also, students will learn how computers can help in navigation. Often, the calculations needed to navigate accurately are time consuming and complex. By using the power of computers to do calculations and repetitive tasks, one can quickly see how changing parameters likes angles and distances and introducing errors will affect their overall result.

Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.

Presentation Slides for 17th Annual Massachusetts Colleges Online  Conference on eLearning, June 2nd, 2022.

Figuring out the components of the force due to gravity that are parallel and perpendicular to the surface of an inclined plane. Created by Sal Khan.

KiteModeler was developed in an effort to foster hands-on, inquiry-based learning in science and math. KiteModeler is a simulator that models the design, trimming, and flight of a kite. The program works in three modes: Design Mode, Trim Mode, or Flight Mode. In the Design Mode (shown below), you pick from five basic types of kite designs. You can then change design variables including the length and width of various sections of the kite. You can also select different materials for each component. When you have a design that you like, you switch to the Trim Mode where you set the length of the bridle string and tail and the location of the knot attaching the bridle to the control line. Based on your inputs, the program computes the center of gravity and pressure, the magnitude of the aerodynamic forces and the weight, and determines the stability of your kite. With a stable kite design, you are ready for Flight Mode. In Flight Mode you set the wind speed and the length of control line. The program then computes the sag of the line caused by the weight of the string and the height and distance that your kite would fly. Using all three modes, you can investigate how a kite flies, and the factors that affect its performance.

Brigitte Tennis uses the visual aid of spraying water from one point of a triangle to illustrate to her students opposite and adjacent sides. She then beats out a rhythm on drums to teach her students the mnemonic device SOH-CAH-TOA for finding sine, cosine, and tangent.

This task is closely related to very important material about similarity and ratios in geometry.

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.

This is a booklet containing 37 space science mathematical problems, several of which use authentic science data. The problems involve math skills such as unit conversions, geometry, trigonometry, algebra, graph analysis, vectors, scientific notation, and many others. Learners will use mathematics to explore science topics related to Earth's magnetic field, space weather, the Sun, and other related concepts. This booklet can be found on the Space Math@NASA website.

A PBL project I did in my HS physics and math classes to allow students voice & choice in the design of a maker space my school was building. It followed the Buck Institute model and allowed students to prove mastery in a varitey of learning targets per topics in both courses (probability, geometry, functions, algebra, and trig in geometry and force, energy, electricity & magnetism, etc. in physics). Please feel free to remix this project to suit your own needs.

A PBL project I did in my HS physics and math classes to allow students voice & choice in the design of a maker space my school was building. It followed the Buck Institute model and allowed students to prove mastery in a varitey of learning targets per topics in both courses (probability, geometry, functions, algebra, and trig in geometry and force, energy, electricity & magnetism, etc. in physics). Please feel free to remix this project to suit your own needs.

This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.

The purpose of this task is to engage students in an open-ended modeling task that uses similarity of right triangles, and also requires the use of technology.