Spatial visualization is the study of two- and three-dimensional objects and the practice of mental manipulation of objects. Spatial visualization skills are important in a range of subjects and activities like mathematics, physics, engineering, art and sports! In this lesson, students are introduced to the concept of spatial visualization and measure their spatial visualization skills by taking the provided 12-question quiz. Following the lesson, students complete the four associated spatial visualization activities and then re-take the quiz to see how much their spatial visualization skills have improved.

Working as a team, students discover that the value of pi (3.1415926...) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot chassis draws a circle on the ground as the robot travels the programmed circular path. Students measure the circle's circumference and diameter and calculate pi by dividing the circumference by the diameter. They discover the pi and circumference relationship; the circumference of a circle divided by the diameter is the value of pi.

Students learn about one-axis rotations, and specifically how to rotate objects both physically and mentally to understand the concept. They practice drawing one-axis rotations through a group exercise using cube blocks to create shapes and then drawing those shapes from various x-, y- and z-axis rotation perspectives on triangle-dot paper (isometric paper). They learn the right-hand rule to explore rotations of objects. A worksheet is provided. This activity is part of a multi-activity series towards improving spatial visualization skills.

Students use latex tubes and bicycle pumps to conduct experiments to gather data about the relationship between latex strength and air pressure. Then they use this data to extrapolate latex strength to the size of latex tubing that would be needed in modern passenger sedans to serve as hybrid vehicle accelerators, thus answering the engineering design challenge question posed in the first lesson of this unit. Students input data into Excel spreadsheets and generate best fit lines by the selection of two data points from their experimental research data. They discuss the y-intercept and slope as it pertains to the mathematical model they generated. Students use the slope of the line to interpret the data collected. Then they extrapolate with this information to predict the latex dimensions that would be required for a full-size hydraulic accumulator installed in a passenger vehicle.

Students complete an exercise showing logarithmic relationships and examine how to find the linear regression of data that does not seem linear upon initial examination. They relate number of BMD scanners to time.

Students are challenged to design and program Arduino-controlled robots that behave like simple versions of the automated guided vehicles engineers design for real-world applications. Using Arduino microcontroller boards, infrared (IR) sensors, servomotors, attachable wheels and plastic containers (for the robot frame), they make "Lunch-Bots." Teams program the robots to meet the project constraints—to follow a line of reflective tape, make turns and stop at a designated spot to deliver a package, such as a sandwich or pizza slice. They read and interpret analog voltages from IR sensors, compare how infrared reflects differently off different materials, and write Arduino programs that use IR sensor inputs to control the servomotors. Through the process, students experience the entire engineering design process. Pre/post-quizzes and coding help documents are provided.

Students measure the relative intensity of a magnetic field as a function of distance. They place a permanent magnet selected distances from a compass, measure the deflection, and use the gathered data to compute the relative magnetic field strength. Based on their findings, students create mathematical models and use the models to calculate the field strength at the edge of the magnet. They use the periodic table to predict magnetism. Finally, students create posters to communicate the details their findings. This activity guides students to think more deeply about magnetism and the modeling of fields while practicing data collection and analysis. An equations handout and two grading rubrics are provided.

The goal of this maker challenge is to demystify sensors, in particular the ambient light sensor, and to map its readings visually. In today’s world, we make sense of the environment around us by filling it with sensors, and we use output devices to display real-time data in a meaningful way. Take any smartphone as an example. Aside from the embedded camera and microphone, a number of other sensors collect a wide range of data. Depending upon the model, these sensors may collect data on proximity, motion, ambient light, moisture, compass, and touch. Some of these data are directly visualized through an app, while many operate internally and without a user interface, just below the surface of the screen. In order to become more familiar with the technology that we use (and often take for granted) on a daily basis, your challenge is to assemble a light sensor circuit, observe its readings using the Arduino Serial Monitor, and then create your own unique visualization by interfacing with the Processing software. Students learn how to use calibration and smoothing to capture a better picture of the data. Afterwards, they share their visualizations with the entire class. The time required for this challenge depends on students’ prior knowledge of Arduino and Processing software. Background resources for beginners help students get up to speed on microcontroller hardware and offer additional challenges for intermediate and advanced users.

Graph theory is a visual way to represent relationships between objects. One of the simplest uses of graph theory is a family tree that shows how different people are related. Another application is social networks like Facebook, where a network of "friends" and their "friends" can be represented using graphs. Students learn and apply concepts and methods of graph theory to analyze data for different relationships such as friendships and physical proximity. They are asked about relationships between people and how those relationships can be illustrated. As part of the lesson, students are challenged to find the social graph of their friends. This prepares students for the associated activity during which they simulate and analyze the spread of disease using graph theory by assuming close proximity to an infected individual causes the disease to spread.

Students learn about slope, determining slope, distance vs. time graphs through a motion-filled activity. Working in teams with calculators and CBL motion detectors, students attempt to match the provided graphs and equations with the output from the detector displayed on their calculators.

Course description: This course provides algebra, quantitative reasoning, and problem solving skills needed in Math 105, 106, 107, and in other college courses in programs not requiring calculus.

Students apply high school-level differential calculus and physics to the design of two-dimensional roller coasters in which the friction force is considered, as explained in the associated lesson. In a challenge the mirrors real-world engineering, the designed roller coaster paths must be made from at least five differentiable functions that are put together such that the resulting piecewise curving path is differentiable at all points. Once designed mathematically, teams build and test small-sized prototype models of the exact designs using foam pipe wrap insulation as the roller coaster track channel with marbles as the ride carts.

This course was originally developed for the Open Course Library project.  The text used is Math in Society, edited by David Lippman, Pierce College Ft Steilacoom.  Development of this book was supported, in part, by the Transition Math Project and the Open Course Library Project. Topics covered in the course include problem solving, voting theory, graph theory, growth models, finance, data collection and description, and probability.

Driving Question: How can we as 7th grade math students use surface area to make a mug that retains heat for the longest amount of time possible?

Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT -based activity. They measure the position of an oscillating platform using a ultrasonic sensor and perform statistical analysis to determine the mean, mode, median, percent difference and percent error for the collected data.

Students learn the metric units engineers use to measure mass, distance (or length) and volume. They make estimations using these units and compare their guesses with actual values. To introduce the concepts, the teacher needs access to a meter stick, a one-liter bottle, a glass container that measures milliliters and a gram scale.

Students learn about the statistical analysis of measurements and error propagation, reviewing concepts of precision, accuracy and error types. This is done through calculations related to the concept of density. Students work in teams to each measure the dimensions and mass of five identical cubes, compile the measurements into small data sets, calculate statistics including the mean and standard deviation of these measurements, and use the mean values of the measurements to calculate density of the cubes. Then they use this calculated density to determine the mass of a new object made of the same material. This is done by measuring the appropriate dimensions of the new object, calculating its volume, and then calculating its mass using the density value. Next, the mass of the new object is measured by each student group and the standard deviation of the measurements is calculated. Finally, students determine the accuracy of the calculated mass by comparing it to the measured mass, determining whether the difference in the measurements is more or less than the standard deviation.

Students learn how volume, viscosity and slope are factors that affect the surface area that lava covers. Using clear transparency grids and liquid soap, students conduct experiments, make measurements and collect data. They also brainstorm possible solutions to lava flow problems as if they were geochemical engineers, and come to understand how the properties of lava are applicable to other liquids.

Through investigating the nature, sources and level of noise produced in their environment, students are introduced to the concept of noise pollution. They learn about the undesirable and disturbing effects of noise and the resulting consequences on people's health, as well as on the health of the environment. They use a sound level meter that consists of a sound sensor attached to the LEGO® NXT Intelligent Brick to record the noise level emitted by various sources. They are introduced to engineering concepts such as sensors, decibel (dB) measurements, and sound pressure used to measure the noise level. Students are introduced to impairments resulting from noise exposure such as speech interference, hearing loss, sleep disruption and reduced productivity. They identify potential noise pollution sources, and based on recorded data, they classify these sources into levels of annoyance. Students also explore the technologies designed by engineers to protect against the harmful effects of noise pollution.

After conducting the associated activity, students are introduced to the material behavior of elastic solids. Engineering stress and strain are defined and their importance in designing devices and systems is explained. How engineers measure, calculate and interpret properties of elastic materials is addressed. Students calculate stress, strain and modulus of elasticity, and learn about the typical engineering stress-strain diagram (graph) of an elastic material.