18.104.22.168 Speed & Direction
Measure and calculate the speed of an object that is traveling in a straight line.
For an object traveling in a straight line, graph the object’s position as a function of time, and its speed as a function of time. Explain how these graphs describe the object’s motion.
MN Standard in Lay Terms
Students should be able to describe the movement of an object that is traveling in a straight line in terms of speed, direction and change of position.
Forces and Motion: Motion is a continual change in position of an object as seen by an observer. A force is any influence that can change the motion of an object, such as its speed or direction. (AAAS Atlas Vol I)
They should also be able to graph that information and analyze such graphs made by others.
MN Standard Benchmarks
22.214.171.124.1 Measure and calculate the speed of an object that is traveling in a straight line.
126.96.36.199.2 For an object traveling in a straight line, graph the object's position as a function of time, and its speed as a function of time. Explain how these graphs describe the object's motion.
The cartoon, from this source can be downloaded and used, free of charge, by individual teacher/educators.
Content Standard B: As a result of their activities in grades 5-8, all students should develop an understanding of properties and changes of properties in matter, motions and forces, transfer of energy. (p.149-155)
- AAAS Atlas:
Motion: Laws of Motion, Volume 1, p. 62-63
4F An unbalanced force acting on an object changes its speed or direction of motion, or both. 4F/M3a
The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass. 4F/H1*
All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion. 4F/H2
Common Core Standards
6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Solve unit rate problems including those involving...constant speed. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5. Summarize numerical data sets in relation to their context, such as by:
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
L.6.6. Acquire and use accurately grade-appropriate general academic and domain-specific words and phrases; gather vocabulary knowledge when considering a word or phrase important to comprehension or expression.
W.6.7. Conduct short research projects to answer a question, drawing on several sources and refocusing the inquiry when appropriate.
SL.6.1. Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 6 topics, texts, and issues, building on others' ideas and expressing their own clearly.
"The words fast and slow refer to the speed of an object. The words short and long refer to time intervals. Students often confuse these two related, but different, concepts.
"Mathematical studies reveal that few children recognize that any point on a measurement scale can serve as a starting point. They tend to read off whatever number is the end point. Even students up through fifth grade have been shown to have this tendency."
"Students often experience difficulty interpreting the slope of a graph and sometimes confuse the height of the graph with the slope. Many students interpret graphs as literal pictures rather than symbolic representations"
"Younger children typically start to describe motion by identifying the direction in which an object moves, without regard to the speed of the object. As the sophistication of their ideas progress, they may use a "snapshot" description, in which they compare the speed of an object at different locations or instants. (In a "snapshot" description, students describe what is essentially a still photograph of an object, without looking at changes) Eventually, older children can be led to describe how the speed of an object is changing at a specific location or instant."
"Many students interpret distance/time graphs as the paths of actual journeys (Kerslake 1981). In addition, students confuse the slope of a graph and the graph's maximum or minimum value and do not know that the slope of a graph is a measure of rate."
Keeley, Paige, Rand Harrington. Uncovering Student Ideas in Physical Science: 25 Formative Assessment Probes. 1. Arlington, VA: National Science Teachers Association, 2010. pp 61. Print.
"Naturally, children's ideas and descriptions of motion tend to be less differentiated than those of a physicist. They tend to see objects either at rest or moving. The period of change is less frequently focused on by children. They use everyday terms such as going faster in ambiguous ways, sometimes referring to the object and at other times referring to the speed increasing with time"
Driver, Rosalind, Squires, Ann, Rushworth, Peter, & Wood-Robinson, Valarie. (2003). Making Sense of Secondary Science. New York, New York: Routeledge.
(188.8.131.52) Students in Ms. M's class are designing cars to roll straight down a narrow ramp using Legos. Students ask to use other materials, but Ms. M continually reminds them that engineers must work within constraints and theirs are the materials in their Lego kits. (Benchmark 184.108.40.206.1)
As the students begin to test their models they notice that some move very slowly or turn to one side or the other rather than going straight down the ramp. Ms. M talks through where the forces, such as friction, are acting upon the car to make it not perform the way they need. Students then return to their group to improve their design.
Once everyone has a car working, Ms. M asks the class to compare the cars. Which ones are the most creative? Which ones are the most attractive? Which ones are the fastest? How do you know? The students suggest a race down the ramp, but as Ms. M points out the ramp is too narrow. The students suggest determining the speed. This leads to a discussion of what is speed and how is it measured.
Someone says "Speed is miles per hour."
"But what does that mean?" Ms. M probes.
The students fall silent. Ms. M explains that speed is something that is measured, but it is made of two measurements: distance and time.
"Would we measure our cars' speeds in MPH?" she asks. When the students respond "no" she asks why not and pushes them with a better measurement of time and distance for their smaller cars. They choose meters per second.
The students mark off a meter from the end of the ramp and record the time it takes the car to go one meter. The data is recorded for each trial. Class data from multiple trials will be recorded on a whiteboard/smartboard . Graphs of both group data and class data will be constructed, displayed and discussed to illustrate the relationship between distance and time.
Suggested Labs and Activities
In this lab, students identify the relationship between speed, time, and distance, by equally spacing dominoes in a straight line on the lab table. A force is applies to the first domino, causing a chain reaction. Students record the amount of time it takes the row of dominoes to fall and record the data. Then they increase the space between each of the dominoes and perform the lab again, recording and noticing time differences.
In this lesson, students learn how to make a graph to measure average speed and calculate the mid-times for personal intervals of student runs, walks, and jogs. (Common Core Math Standard: 6.SP.5. Summarize numerical data sets in relation to their context) Working in groups, one member walks, jogs, or runs in a straight-line path while attempting to maintain a constant speed. The other group members time the runner along the path, and then record and graph the data of each run. ThinkQuest Motion Graph
Students should engage in labs that allow them to demonstrate motion of objects and graph results.
reference point - A stationary or moving object used to compare the position of another object
speed - Distance traveled divided by the time traveled
motion - any change in position over time
acceleration - Rate at which speed changes
direction - A point to or from which an object moves
position - the location of an object
Vernier Go Motion probes provide opportunities to measure position and graph motion in real time.
Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).
Students can time themselves at different intervals on a 100 yd dash and graph the data to see the acceleration at the start and decrease in speed at the end of the run.
Assessment of Students
220.127.116.11.1: Formative: Provide students with a graph depicting motion. Tell the students to act out the motion described by the graph.
18.104.22.168.1: Summative: What information do you need to determine if an object is in motion? Speeding up? Slowing down?
Provide students with a graph and tell the students to indicate if the object is in motion or at rest.
22.214.171.124.2: Summative: Provide students with two graphs depicting motion. Tell the students to compare the position and speed of the objects at different times.
Assessment of Teachers
What impacts the speed and acceleration of an object?
Why is it important for students to not only create, but also analyze graphs depicting motion?
Why is it important for students to perform multiple trials when calculating the motion of an object?
Struggling and At-Risk
Take students out with stopwatches and place them in groups at regular intervals on the sidewalk. Have them time cars that stop at a stop sign, start moving, and continue down the block. Then have them take the data back in the classroom to graph.
While developing Motion concepts with ELL students make sure to
Illustrate and diagram concepts with vocabulary on the board during discussion
Give step-by-step directions for labs
Prepare word walls or glossary sheets with illustrated vocabulary for students to easily access
Summarize discussion and learning more frequently
In setting up groups, pair non-native with native speakers.
Make connections to the students' out of school experiences
Vary instructional delivery to include picture books, video, etc.
Students might research forces involved in operating a roller coaster or an engineered design.
Allow students to research a popular athlete or sport associated with a particular country or culture. As students research, they should specifically look for examples of how reference points, speed, acceleration, and position, are important to the sport. A starting point for research material might be the Exploratorium Sport Science Website.
Utilize multiple labs and repeated trials to demonstrate the process involved in calculating speed and acceleration. Allow students opportunities to demonstrate their understanding with physical manipulatives, paper and pencil, and verbally.
Students should be actively involved in demonstrating or analyzing the motion of objects. Key vocabulary terms, such as position, time, speed, and acceleration should be used in student conversations.
Administrators will see students motivated to learn, asking questions, and drawing on their personal experiences with motion and speed as they connect to lab activities occurring in the classroom.
Help students make connections between science concepts such as position, velocity, and acceleration by using the vocabulary terms in context. For example, point out the speed limit signs on the road, and ask students how long it would take to travel a given number of miles at the posted speed.