In this video David rapidly explains all the concepts in 1D motion ...

In this video David rapidly explains all the concepts in 1D motion and also quickly solves a sample problem for each concept. Keep an eye on the side scroll see how far along you've made it in the review video. Created by David SantoPietro.

In this video David quickly explains each 2D motion concept and does ...

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.

A plot of luminosity vs. time is a ‘light curve’. In this ...

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 learn how engineers gather data and model motion using vectors. They ...

Students learn how engineers gather data and model motion using vectors. They learn about using motion-tracking tools to observe, record, and analyze vectors associated with the motion of their own bodies. They do this qualitatively and quantitatively by analyzing several examples of their own body motion. As a final presentation, student teams act as engineering consultants and propose the use of (free) ARK Mirror technology to help sports teams evaluate body mechanics. A pre/post quiz is provided.

This is a really fun and informative lesson that I do with ...

This is a really fun and informative lesson that I do with my high school Programming/technology class to break up the monotony of beginner programming. However; this lesson can be used and applied in essentially any class and for many purposes, and to address many areas. One of the other really nice things about this lesson is that it can be extended to hit many points including physics, math, and advanced engineering.

Throughout the building period, I would present teams with a challenge (puzzle, build, etc…) and the first team to complete it would get a prize. It could be more modification time, extra materials, etc…)

The materials (including hot glue guns) can be purchased at Wal Mart or a similar store for around $20-25, if ordering through your district isn’t an option. With those purchases, it gives you a lot more materials than needed which can be used for additional similar projects.

This is a really fun and informative lesson that I do with ...

This is a really fun and informative lesson that I do with my high school Programming/technology class to break up the monotony of beginner programming. However; this lesson can be used and applied in essentially any class and for many purposes, and to address many areas. One of the other really nice things about this lesson is that it can be extended to hit many points including physics, math, and advanced engineering.

Throughout the building period, I would present teams with a challenge (puzzle, build, etc…) and the first team to complete it would get a prize. It could be more modification time, extra materials, etc…)

The materials (including hot glue guns) can be purchased at Wal Mart or a similar store for around $20-25, if ordering through your district isn’t an option. With those purchases, it gives you a lot more materials than needed which can be used for additional similar projects.

A physics assignment that allows students to address real-life concepts of distance ...

A physics assignment that allows students to address real-life concepts of distance and displacement using their knowledge of vectors and their own school schedule.

An interactive applet and associated web page that demonstrate how to find ...

An interactive applet and associated web page that demonstrate how to find the perpendicular distance between a point and a line using trigonometry, given the coordinates of the point and the slope/intercept of the line. The applet has a line with sliders that adjust its slope and intercept, and a draggable point. As the line is altered or the point dragged, the distance is recalculated. The grid and coordinates can be turned on and off. The distance calculation can be turned off to permit class exercises and then turned back on the verify the answers. The applet can be printed as it appears on the screen to make handouts. The web page has a full description of the concept of the concepts, a worked example and has links to other pages relating to coordinate geometry. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Students' understanding of how robotic ultrasonic sensors work is reinforced in a ...

Students' understanding of how robotic ultrasonic sensors work is reinforced in a design challenge involving LEGO MINDSTORMS(TM) NXT robots and ultrasonic sensors. Student groups program their robots to move freely without bumping into obstacles (toy LEGO people). They practice and learn programming skills and logic design in parallel. They see how robots take input from ultrasonic sensors and use it to make decisions to move, resulting in behavior similar to the human sense of sight but through the use of sound sensors, more like echolocation. Students design-test-redesign-retest to achieve successful programs. A PowerPoint® presentation and pre/post quizzes are provided.

Students develop and solidify their understanding of the concept of "perimeter" as ...

Students develop and solidify their understanding of the concept of "perimeter" as they engage in a portion of the civil engineering task of land surveying. Specifically, they measure and calculate the perimeter of a fenced in area of "farmland," and see that this length is equivalent to the minimum required length of a fence to enclose it. Doing this for variously shaped areas confirms that the perimeter is the minimal length of fence required to enclose those shapes. Then students use the technology of a LEGO MINDSTORMS(TM) NXT robot to automate this task. After measuring the perimeter (and thus required fence length) of the "farmland," students see the NXT robot travel around this length, just as a surveyor might travel around an area during the course of surveying land or measuring for fence materials. While practicing their problem solving and measurement skills, students learn and reinforce their scientific and geometric vocabulary.

In this activity students practice measuring techniques by measuring different objects and ...

In this activity students practice measuring techniques by measuring different objects and distances around the classroom. They practice using different scales of measurement in metric units and estimation.

In this activity, learners use their hands as tools for indirect measurement. ...

In this activity, learners use their hands as tools for indirect measurement. Learners explore how to use ratios to calculate the approximate height of something that can't be measured directly by first measuring something that can be directly measured. This activity can also be used to explain how scientists use indirect measurement to determine distances between things in the universe that are too far away, too large or too small to measure directly (i.e. diameter of the moon or number of bacteria in a volume of liquid).

Students learn about how ultrasonic sensors work, reinforcing the connection between this ...

Students learn about how ultrasonic sensors work, reinforcing the connection between this sensor and how humans, bats and dolphins estimate distance. They learn the echolocation process sound waves transmitted, bounced back and received, with the time difference used to calculate the distance of objects. Two mini-activities, which use LEGO MINDSTORMS(TM) NXT robots and ultrasonic sensors, give students a chance to experiment with ultrasonic sensors in preparation for the associated activity. A PowerPoint® presentation explains stimulus-to-response pathways, sensor fundamentals, and details about the LEGO ultrasonic sensor. Pre/post quizzes are provided. This lesson and its associated activity enable students to gain a deeper understanding of how robots can take sensor input and use it to make decisions via programming.

Students practice their multiplication skills using robots with wheels built from LEGO® ...

Students practice their multiplication skills using robots with wheels built from LEGO® MINDSTORMS® NXT kits. They brainstorm distance travelled by the robots without physically measuring distance and then apply their math skills to correctly calculate the distance and compare their guesses with physical measurements. Through this activity, students estimate parameters other than by physically measuring them, practice multiplication, develop measuring skills, and use their creativity to come up with successful solutions.

Students learn about video motion capture technology, becoming familiar with concepts such ...

Students learn about video motion capture technology, becoming familiar with concepts such as vector components, magnitudes and directions, position, velocity, and acceleration. They use a (free) classroom data collection and processing tool—the ARK Mirror—to visualize and record 3-D motion. The Augmented Reality Kinematics (ARK) Mirror software collects data via a motion detector. Using an Orbbec Astra Pro 3D camera or Microsoft Kinect (see note below), students can visualize and record a robust set of data and interpret them using statistical and graphical methods. This lesson introduces students to just one possible application of the ARK Mirror software—in the context of a high school physics class. Note: The ARK Mirror is ported to operate on an Orbbec platform. It may also be used with a Microsoft Kinect, although that Microsoft hardware has been discontinued. Refer to the Using ARK Mirror and Microsoft Kinect attachment for how to use the ARK MIrror software with Microsoft Kinect.

Students explore methods employing simple machines likely used in ancient pyramid building, ...

Students explore methods employing simple machines likely used in ancient pyramid building, as well as common modern-day material transportation. They learn about the wheel and axle as a means to transport materials from rock quarry to construction site. They also learn about different types and uses of a lever for purposes of transport. In an open-ended design activity, students choose from everyday materials to engineer a small-scale cart and lever system to convey pyramid-building materials.

Students measure the relative intensity of a magnetic field as a function ...

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.

Students learn about slope, determining slope, distance vs. time graphs through a ...

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.

Rate Type of Unit: Concept Prior Knowledge Students should be able to: ...

Rate

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers. Understand quantity as a number used with a unit of measurement. Solve problems involving quantities such as distances, intervals of time, liquid volumes, masses of objects, and money, and with the units of measurement for these quantities. Understand that a ratio is a comparison of two quantities. Write ratios for problem situations. Make and interpret tables, graphs, and diagrams. Write and solve equations to represent problem situations.

Lesson Flow

In this unit, students will explore the concept of rate in a variety of contexts: beats per minute, unit prices, fuel efficiency of a car, population density, speed, and conversion factors. Students will write and refine their own definition for rate and then use it to recognize rates in different situations. Students will learn that every rate is paired with an inverse rate that is a measure of the same relationship. Students will figure out the logic of how units are used with rates. Then students will represent quantitative relationships involving rates, using tables, graphs, double number lines, and formulas, and they will see how to create one such representation when given another.

Gallery OverviewAllow students who have a clear understanding of the content thus ...

Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Gallery DescriptionsCreate Your Own RateStudents create their own rate problems, given three quantities that must all be used in the problems or the answers.Paper Clip ChallengeStudents think about rate in the context of setting a record for making a paperclip chain.The Speed of Light Students must determine the speed of light so they can figure out how long it will take a light beam from Earth to reach the Moon (assuming it would make it there). They conduct research and perform calculations.Tire WeightStudents connect area and a rate they may not be familiar with, tire pressure, to indirectly weigh a car. They find and add areas and do a simple rate calculation. Please note this problem requires adult supervision for the process of measuring the car tires. If no adult supervision is available, you can provide students with measurements to work with inside the classroom. Do not allow students to work with a car without permission from the owner and adult supervision.Planting Wildflowers Students apply area and length concepts (square miles, acres, and feet) to rectangles, choose and carry out appropriate area conversions, and show each step of their solutions. While specific solution paths will vary, all students who show good conceptualization will make at least one area conversion and show understanding about area even when dimensions and units change. This task allows several different correct solution paths.Train Track Students use information about laying railroad ties for the Union Pacific Railroad. These rates are different from those used elsewhere in the unit, asking how many rails per gang of workers, how long it takes to lay one mile of track, and how many spikes are needed for a mile of track.HeartbeatsStudents will investigate and compare the heartbeats of different animals and their own heartbeat.FoghornStudents use the relationships among seconds, minutes, and hours to find equivalent rates. Each step requires students to express an equivalent rate in terms of these different units of time. In any strong response, students use conversion factors and the given rate to find equivalent rates.

In this lesson, students first watch three racers racing against each other. ...

In this lesson, students first watch three racers racing against each other. The race is shown on a track and represented on a graph. Students then change the speed, distance, and time to create a race with different results. They graph the new race and compare their graph to the original race graph.Key ConceptsA rate situation can be represented by a graph. Each point on a graph represents a pair of values. In today's situation, each point represents an amount of time and the distance a racer traveled in that amount of time. Time is usually plotted on the horizontal axis. The farther right a point is from the origin, the more time has passed from the start. Distance is usually plotted on the vertical axis. The higher up a point is from the origin, the farther the snail has traveled from the start. A graph of a constant speed is a straight line. Steeper lines show faster speeds.Goals and Learning ObjectivesUnderstand that a graph can be a visual representation of an actual rate situation.Plot pairs of related values on a graph.Use graphs to develop an understanding of rates.

In this lesson, students watch a video of a runner and express ...

In this lesson, students watch a video of a runner and express his speed as a rate in meters per second. Students then use the rate to determine how long it takes the runner to go any distance.Key ConceptsSpeed is a rate that is expressed as distance traveled per unit of time. Miles per hour, laps per minute, and meters per second are all examples of units for speed. The measures of speed, distance, and time are all related. The relationship can be expressed in three ways: d = rt, r = dt, t = dr.Goals and Learning ObjectivesExplore speed as a rate that measures the relationship between two aspects of a situation: distance and time.In comparing distance, speed, and time, understand how to use any two of these measures to find the third measure.

Students use their knowledge of rates to solve problems.Key ConceptsGiven any two ...

Students use their knowledge of rates to solve problems.Key ConceptsGiven any two values in a rate situation, you can find the third value.These three equations are equivalent, and they all describe rate relationships:y = rx, r = yx, x = yrAt the beginning of this lesson (or for homework), students will revise their work on the pre-assessment Self Check. Their revised work will provide data that you and your students can use to reassess students' understanding of rate. You can use this information to clear up any remaining misconceptions and to help students integrate their learning from the past several days into a deeper and more coherent whole.The work students do in this lesson and in revising their pre-assessments will help you and your students decide how to help them during the Gallery. In this lesson, students will reveal the depth and clarity of their understanding of rate.Students whose understanding of rate is still delicate should get extra help during the Gallery.Students who feel that they have a robust understanding of rate may choose from any of the problem-solving or deeper mathematics problems in the Gallery.Goals and Learning ObjectivesUncover any partial understandings and misconceptions about rate.Develop a more robust understanding of rate.Identify which Gallery problems to work on.

Four full-year digital course, built from the ground up and fully-aligned to ...

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.

Proportional Relationships Type of Unit: Concept Prior Knowledge Students should be able ...

Proportional Relationships

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Understand what a rate and ratio are. Make a ratio table. Make a graph using values from a ratio table.

Lesson Flow

Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work.

Gallery 1 provides students with additional proportional relationship problems.

The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals.

Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2.

Students determine whether a relationship between two quantities that vary is a ...

Students determine whether a relationship between two quantities that vary is a proportional relationship in three different situations: the relationship between the dimensions of the actual Empire State Building and a miniature model of the building; the relationship between the distance and time to travel to an amusement park; and the relationship between time and temperature at an amusement park.Key ConceptsWhen the ratio between two varying quantities remains constant, the relationship between the two quantities is called a proportional relationship. For a ratio A:B, the proportional relationship can be described as the collection of ratios equivalent to A:B, or cA:cB, where c is positive.Goals and Learning ObjectivesIdentify proportional relationships.Explain why a situation represents a proportional relationship or why it does not.Determine missing values in a table of quantities based on a proportional relationship.

Putting Math to Work Type of Unit: Problem Solving Prior Knowledge Students ...

Putting Math to Work

Type of Unit: Problem Solving

Prior Knowledge

Students should be able to:

Solve problems involving all four operations with rational numbers. Write ratios and rates. Write and solve proportions. Solve problems involving scale. Write and solve equations to represent problem situations. Create and interpret maps, graphs, and diagrams. Use multiple representations (i.e., tables, graphs, and equations) to represent problem situations. Calculate area and volume. Solve problems involving linear measurement.

Lesson Flow

Students apply and integrate math concepts they have previously learned to solve mathematical and real-world problems using a variety of strategies. Students have opportunities to explore four real-world situations involving problem solving in a variety of contexts, complete a project of their choice, and work through a series of Gallery problems.

First, students utilize their spatial reasoning and visualization skills to find the least number of cubes needed to construct a structure when given the front and side views. Then, students select a project to complete as they work through this unit to refine their problem-solving skills. Students explore the relationship between flapping frequency, amplitude, and cruising speed to calculate the Strouhal number of a variety of flying and swimming animals. After that, students explore the volume of the Great Lakes, applying strategies for solving volume problems and analyzing diagrams. Next, students graphically represent a virtual journey through the locks of the Welland Canal, estimating the amount of drop through each lock and the distance traveled. Students have a day in class to work on their projects with their group.

Then, students have two days to explore Gallery problems of their choosing. Finally, students present their projects to the class.

Students first create a diagram that represents the distance a ship drops ...

Students first create a diagram that represents the distance a ship drops in each of a series of locks. Students create their diagrams based on a video of an actual ship traveling through the locks. Students need to use contextual clues in order to determine the relative drops in each of the locks.Key ConceptsStudents are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.Students will:Try a variety of strategies to approaching different types of problems.Devise a problem-solving plan and implement their plan systematically.Become aware that problems can be solved in more than one way.See the value of approaching problems in a systematic manner.Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.Make connections between previous learning and real-world problems.Create efficacy and confidence in solving challenging problems in a real-world setting.Goals and Learning ObjectivesRead and interpret maps, graphs, and diagrams.Solve problems that involve linear measurement.Estimate length.Critique a diagram.

Working With Rational Numbers Type of Unit: Concept Prior Knowledge Students should ...

Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line. Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.

This is three examples of "Type III" documents that I have prepared ...

This is three examples of "Type III" documents that I have prepared for students to write about math. Our school uses the Collins system of writing, but these could be adapted to a variety of classroom settings. The topics could be middle school or early high school topics, and they are set up to allow students to indepedently express their knowledge of the given topics in short essay form.

In addition to the writing prompts, I have included a rubric that students use to peer-edit each others' rough drafts. Students then use this feedback form to make the necessary corrections and submit a subsequent final draft.

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