A plot of luminosity vs. time is a ‘light curve’. In this laboratory, we will use a light curve to determine the diameter of two stars in a binary system.  --------------------------------------- Distant Nature: Astronomy Exercises 2016 by Stephen Tuttle under license "Creative Commons Attribution Non-Commercial Share Alike".

Students analyze the relationship between wheel radius, linear velocity and angular velocity by using LEGO(TM) MINDSTORMS(TM) NXT robots. Given various robots with different wheel sizes and fixed motor speeds, they predict which has the fastest linear velocity. Then student teams collect and graph data to analyze the relationships between wheel size and linear velocity and find the angular velocity of the robot given its motor speed. Students explore other ways to increase linear velocity by changing motor speeds, and discuss and evaluate the optimal wheel size and desired linear velocities on vehicles.

Learners examine the basic types of dimensioning including unidirectional and aligned systems, and linear, aligned, angled, arrowless, chain, datum, chart, tabular, radius, diameter, typical, and reference dimensions.

Mending is an important part of archaeology, as it can be used to establish relationships between different parts of an archaeological site. This resource is a tutorial detailing how to perform a ceramic mending activity with your students. Use it to support Maryland Math Standard 7.G.B.4-6 for grade 7 by focusing on the mending of round ceramics and determining their circumference or diameter from pieces. If you evaluate this resource or use it, please consider responding to this short (4 question) survey bit.ly/3rw0WQY

Students learn about the engineering design process and how it is used to engineer products for everyday use. Students individually brainstorm solutions for sorting coins and draw at least two design ideas. They work in small groups to combine ideas and build a coin sorter using common construction materials such as cardboard, tape, straws and fabric. Students test their coin sorters, make revisions and suggest ways to improve their designs. By designing, building, testing and improving coin sorters, students come to understand how the engineering design process is used to engineer products that benefit society.

Students drop water from different heights to demonstrate the conversion of water's potential energy to kinetic energy. They see how varying the height from which water is dropped affects the splash size. They follow good experiment protocol, take measurements, calculate averages and graph results. In seeing how falling water can be used to do work, they also learn how this energy transformation figures into the engineering design and construction of hydroelectric power plants, dams and reservoirs.

Working individually or in groups, students explore the concept of stress (compression) through physical experience and math. They discover why it hurts more to poke themselves with mechanical pencil lead than with an eraser. Then they prove why this is so by using the basic equation for stress and applying the concepts to real engineering problems.

Students work as engineers and learn to conduct controlled experiments by changing one experimental variable at a time to study its effect on the experiment outcome. Specifically, they conduct experiments to determine the angular velocity for a gear train with varying gear ratios and lengths. Student groups assemble LEGO MINDSTORMS(TM) NXT robots with variously sized gears in a gear train and then design programs using the NXT software to cause the motor to rotate all the gears in the gear train. They use the LEGO data logging program and light sensors to set up experiments. They run the program with the motor and the light sensor at the same time and analyze the resulting plot in order to determine the angular velocity using the provided physics-based equations. Finally, students manipulate the gear train with different gears and different lengths in order to analyze all these factors and figure out which manipulation has a higher angular velocity. They use the equations for circumference of a circle and angular velocity; and convert units between radians and degrees.

Adam Savage walks through two spectacular examples of profound scientific discoveries that came from simple, creative methods anyone could have followed -- Eratosthenes' calculation of the Earth's circumference around 200 BC and Hippolyte Fizeau's measurement of the speed of light in 1849. A quiz, thought provoking question, and links for further study are provided to create a lesson around the 7-minute video. Educators may use the platform to easily "Flip" or create their own lesson for use with their students of any age or level.

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.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

Find the area of triangles and special quadrilaterals.
Use nets composed of triangles and rectangles in order to find the surface area of solids.
Find the volume of right rectangular prisms.
Solve proportions.

Lesson Flow

After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
The unit ends with a unit examination and project presentations.

Students will measure the circumference and diameter of round things in the classroom and discover the ratio pi. They will see that the ratio of a circle's circumference to its diameter can be used to solve for the circumference when the diameter is known.Key ConceptsStudents have seen circles before, but have not analyzed the relationships between parts of a circle. The ratio of the circumference to the diameter is pi, about 3.14 or about 227. Students see that all of the objects they measure have this ratio (or close, depending on accuracy) and that the ratio is true for all circles. Students also see that the ratio can be used to solve for the circumference of a circle if the diameter (or radius) is known.GoalsMeasure round things looking for similarities.Find the ratio of the circumference to the diameter of those round things.Find a formula to find the circumference of a circle.SWD: Make sure students understand these domain-specific terms:It may be helpful to preteach these terms to students with special needs. If possible, reinforce the definitions of these terms with visual supports (diagrams).ELL: As new vocabulary is introduced, be sure to repeat it several times and to allow students to repeat after you as needed. Write the new words as they are introduced and allow enough time for ELLs to check their dictionaries or briefly consult with another student who shares the same primary language if they wish.ratiocircumferencecirclediameterscatter plot

This lesson plan uses Ozobots and their color code commands coding to review Geometry concepts.

In this activity, learners use basic measurements of the Earth and pieces of rock and iron to estimate the mass of the Earth. Learners will calculate mass, volume, and density, convert units, and employ the water displacement method. To calculate an even more accurate estimate of the mass of the Earth, this resource includes optional instructions on how to measure the iron core mass.