Pedagogical overview
- Pedagogical overview
- Big ideas, concepts, facts, & outcomes
- Science content concepts & outcomes
- Inquiry & science process concepts
- Pedagogical overview
- Activities sequence
- Focus questions
- Materials
- Scoring guide suggestions
- Unit activity sequence
- Activity 1 - I spy an object or What's my object
- Activity 2 - What’s my reference object?
- Activity 3 - Challenge - Locate an object without a reference object?
- Activity 4 - Four in a row & Cartesian puzzle
- Activity 5 - Introductory maps - What’s my position
- Activity 6 - Relative position puzzles
- Activity 7 - Spheres motions: What's my track?
- Activity 8 - Sphere crashes with a stationary object
- Activity 9 - Moving sphere hits stationary sphere with different speeds
- Activity 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
- Activity 11 - Bird and cage activity - with more discovery activities Sphere collisions
- Activity 12 - Create a model miniature golf hole
- Lab notes
- Lab note 1 - - I spy an object or What's my object
- Lab note 2 - - What’s my reference object?
- Lab note 3 - - Challenge - Locate an object without a reference object?
- Lab note 4 - Four in a row & Cartesian puzzle
- Lab note 5 - Introductory maps - What’s my position
- Lab note 6 - Relative position puzzles 1-10
- Lab note 7 - Spheres motions: What's my track?
- Lab note 8 - Sphere crashes with a stationary object
- Lab note 9 - Moving sphere hits stationary sphere with different speeds
- Lab note 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
- Lab note 11 - Bird and cage activity - with more discovery activities
- Lab note 12 - Create a model miniature golf hole
- Support materials
A sequence of activities to review and facilitate a deeper understanding of relative position and motion. Information has been heavily influenced by the SCIS (Science Curriculum Study).
- Outline of SCIS science relative position and motion module
- Sample teacher edition pages
The map above describes information for some science dimensions included in this thematic unit for relative position and motion.
The colored bars represent threads and all together represent a piece of yarn. Stars represent activities and the concepts are identified below. Below the chart is an outline for development of relative position and motion with a sequence of possible activities for a learning unit or packet.
Imagine the bands at the top as a piece of yarn and each colored bar as a hair or piece of fiber in the yarn. Each piece of wool yarn can be thought of as a learning sequence with each hair learning sequence, including activities, that are opportunities for learners to conceptualize the targeted facts, relationships, and concepts listed below.
Suppose the list of science dimensions and the facts, relationships, and concepts were unpacked as the information desired for students to learn. Then activities were selected and sequenced to present them with opportunities to construct and learn the information. The yarn across the top is a quick way to see how multiple dimensions are included in the sequence and for which activity.
If the lesson included or relied on other concepts then additional hairs or combinations of hairs would need to be added for each concept represented in an activity. Some would be included for maybe only one activity and other hairs would overlap from one activity to another if the concepts were included in them for students to learn. This would create, as in the case of yarn, hairs that start and stop in the yarn at different places. With hairs starting before and after others, with some overlapping and others separated by other hairs along the length of the yarn. With the entire yarn representing a topic or subject of instruction for a certain period of time.
Of course not all of the concept hairs need to be targeted with instructional activities. If the teacher knows the learner's existing knowledge includes certain information; then the concept hairs are included in the appropriate part of the yarn, but there is no need to target them for instruction, as they are already know by the learner. However, they are necessary to include as that information must be available for learners to use to be successful.
Supporting information
- General planning framework for a general teaching model
- Support for an Instructional Methodology based on a Constructivist Learning Theory
- The Learning Cycle as an instructional methodology, theory or model
- Learning Theory and Developmental Characteristics of Reasoning from Infant - Adult
Background information
This plan is designed for learners who have prior knowledge in cause and effect, use of observations to make inferences, models as explanations for observable and non observable events, and working in groups.
Learners should also have experienced activities with motion, but not necessarily information about relative position and motion. If learners have not had these experiences, then the following activities can be used before this unit.
- Background motion information that would be helpful for learners to have experienced before can be experienced with activities in units in previous grades. Two examples:
- Shadow & the Sun's motion on the playground activity plan and notes - for first grade and up. If learners have not previously experienced these activities, then include them before activities in this unit.
- Motion unit: Spinners: tops, zoomers, twirlers, rollers: wheels, wheels & axles, cups, & spheres ( Primary grades and above) - for second grade and up If learners have not previously experienced these activities, then include them before activities in this unit.
- Review activities for science inquiry and process of observation, property, and inference to review for 4-5 days, before this unit.
- Four day observation - Introductory observation/inference sequence observe three illustrations over four days
- Back view front view with definition of science and S. White comic - observation or inference
- Bird and cage - observation or inference, optical illusion, position and motion
- Foot prints in rock - observation or inference, critical thinking about what happened millions of years ago.
- Play - What's my properties.
- Have learners secretly select an object and ask them to identify it's properties one at a time. Or just start by playing the game.
- Secretly select an object.
- Identify one of it's properties.
- Ask. Who wants to guess what the object is, by identifying another property. They don't guess the object they guess another of its properties and state that property.
- The initial learner then says yes if it is a property of the object or no if it isn't a property of the object.
- Continue taking turns with learners identifying properties until it appears everyone knows the object.
- The sequence of activities in this unit for relative position and motion.
Anticipated learner thinkings & misconceptions
A person's understanding of relative position and motion can be inferred by their ability to locate objects, explaining how objects are located, and how to report objects' movements among different objects.
Learners may or may not visualize spatial orientations. See more on visualization and visual thinking. People who make map apps know there are people who prefer verbal directions and those who prefer visual directions.
Because of this, they provide both options with their apps. However, both ways require skills that can be learned. Unfortunately many schools provide a lot of experience with verbal learning and not so much with visual. This unit provides activities to develop visual skills. and verbal skills in locating objects and describing their motion.
Some misconceptions young learners have.
- Directions relative to me are also relative to others.
- Directions stay the same not matter the location from which they are given.
- Similar directions starting at different places will arrive at the same location.
- An object's motion is viewed similarly by different people at different locations.
Big idea
Observation, inference, and measurement are used to describe the properties of an object's position and its motion relative to a reference object.
Concepts
- An objects position is described relative to a reference object.
- An object's motion is described by its change in position relative to a reference object.
Source concepts & misconceptions
Outcome
- Describe the position and location of stationary and moving objects relative to other objects.
- Describe the position and location of stationary and moving objects from at least two reference points that would cause substantial differences in the descriptions of the location and motion.
- Describe properties that affect an objects motion (gravity, surface, mass, density, flexibility, distribution of matter, air or other medium through which it travels) and how they affect it.
Science concepts: physical, earth, life
Big ideas:
An objects motion depends on the physical properties of the objects and the forces that act on it (gravity, surface, mass, density, flexibility, distribution of matter, air or other medium through which it travels, and interactions with other objects).
Force and Newton's Laws
- Force is a push or pull.
- Objects in a uniform motion tend to stay in that motion unless interacting with an external force (Newton's first law of motion).
- For every action there is an equal and opposite reaction (Newton's third law of motion).
The following is included for background information. Not for younger learners to know.
- Force = mass * acceleration (Newton's second law of motion).
- Momentum = mass * acceleration;
- Acceleration is the same as velocity; or the rate of change of position, or distance/ time - miles per hour (60 miles/hour).
Related concepts
- An object can be moved with a force (push or pull).
- The distance of the motion is related to the size of the force (push or pull).
- Objects near the Earth fall toward the center of the Earth if not acted upon by another force.
- Force, mass, and movement are related.
- The greater the force, the greater the change of direction.
- Friction is a force that can slow an object.
- An object that is not being subjected to a force will continue to move at a constant speed and in a straight line.
- If more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude.
- Unbalanced forces will cause changes in the speed or direction of an object’s motion.
- All objects have a gravitational force that interacts with another objects gravitational force proportional to the masses and distances.
- Electricity and magnetism can exert a force on each other.
- Objects at rest will stay at rest until acted upon by an outside force.
- Objects in motion will stay in motion with the same speed and the same direction (in a straight line) unless acted upon by a force.
- Kinetic energy is the energy an object has because of its motion.
- Potential energy is the stored energy do to its position that may be available if the object is let fall.
Outcome
- Describe how force changes the motion of objects.
- Describe force as a push or pull.
- Describe Newton's first law. Objects at rest will stay at rest until acted upon by an outside force. And Objects in motion will stay in motion with the same speed and the same direction (in a straight line) unless acted upon by a force.
- Describe Describe that a greater force creates increased speed or a longer distance an object travels before stopping.
- Describe the amount of mass in an object as a variable that effects the transfer of energy or the force applied.
- Describe the velocity of an object as a variable that effects the transfer of energy or the force applied.
Inquiry, process, & cross cutting concepts & skills
Inquiry
Big ideas
When I experiment I collect observations that describe how different properties change (become variables) when objects and systems interact. This helps me make claims, explain what is happening, and to predict what might happen in the future. An object's position and motion is one of those properties.
Related concepts and facts
Observation
- Observations of an objects properties can suggest how the object will interact with other objects.
- Observations of an objects properties can suggest what materials were used to make it and how it was made.
- Observational data and reasoning is used to explain interactions.
- Evidence is something that
is observed and can be used to understand what is happening and make predictions
about future changes.
- Models are structures that correspond to real objects, events, or classes of
events.
- Explanations are based on observation derived from experience or experimentation and are understandable.
- Observations help collect information that can be used to answer questions.
- People learn by carefully observing interactions with objects.
- Tools can be used to make better and more accurate observations (magnifiers, camera, ...).
- Observations can be compared through communication of properties.
- Recording observations helps remember specific information.
- When people report different observations they can make more observations to try and find agreement.
- Observation, creativity, and logical argument are used to explain how things work.
- When people disagree on explanations for an observation they usually make more observations to refine their explanations.
- Observations of an object relative to other objects is its position or location.
Properties
- Objects are identified, described, and compared by their properties.
- Objects have many properties.
- Objects may have properties that change and properties that don’t change.
- Properties of objects can be measured using tools such as rulers, balances, and thermometers.
- Properties of matter include: position, motion, form, function, and change.
- Properties and change of properties can be quantified.
- Objects, properties, and events stay the same or happen in similar ways.
- Properties are used to define all objects.
- Definitions change as the properties change.
- Before and after pictures can be used to represent change.
- Object's position or location is a property.
Outcomes
- Make observations and identify properties/ characteristics of an object.
- Describe the location or position of an object as an observable property of the object.
- Describe direction as a property used to locate objects' position.
- Describe the properties of above, below, left, right, front, behind, near, far, close.
- Describe measurement as a property.
- Describe the location or position of an object using the properties of above, below, left, right, front, behind and measurement of near, far, close.
- Identify properties or characteristics of an object and use them to describe, identify, and locate an object.
- Use the location or position of an object as evidence and property in explanations.
Relative position and motions as a cross cutting concept
Locating objects at rest requires a procedure that has a known reference object or point and a directional description with distances of a path from the reference object to the object being located. To describe an object in motion or the motion of an object, a reference object or point is used to describe the path the object takes with a directional description and rate of change.
Related concepts and facts -
- An object's position is relative to a reference position.
- An object's motion is described relative to a reference position.
- Objects are located relative to a reference object.
- The description of an object's position changes from one reference point to another.
- The description of an objects' motion changes from one reference point to another.
- Objects can be located with different combinations of distances and directions from a singular point or multiple points. (one point as a reference object can be used to locate another point or object with a distance and direction.) (An object or point can be located from two know points with a distance and direction from one point and either a distance or a direction from the second point.)
- Objects move in different ways (straight, crocked, circular, and back and forth).
- Objects move fast and slow.
- An object’s motion can be described by tracing and measuring its position over time.
- Motion can be too fast or slow for people to see.
- Objects move steadily or change direction.
- Objects that make sound vibrate.
- Motion of an object can be described by its position, direction of motion, and speed.
- Motion can be measured and represented on a graph.
Outcome
- Describe the position and location of stationary and moving objects relative to other objects.
- Describe the position and location of stationary and moving objects from at least two reference points that would cause substantial differences in the descriptions of the location and motion.
- Describe properties that affect an objects motion (gravity, surface, mass, density, flexibility, distribution of matter, air or other medium through which it travels) and how they affect it.
Other possible concepts
- Explanations derive from evidence.
- Evidence is based on observation.
- Evidence derives from properties, characteristics, and variables.
- Explanation helps us share evidence, models, and explanations (reasoning).
- Sharing evidence, models, and explanations helps us learn from one another.
- People have always tried to explain their ideas with one another.
- Explanations from one person to another require communication (a message being sent and received).
- Errors can occur when communicating.
- Clear explanations give other people information about your discoveries and ideas.
- Repeating messages is a way to avoid miscommunication.
- Information can be communicated in many different ways each of which have advantages and disadvantages.
- Sketches can be used to explain evidence, properties, characteristics, variables, procedures, events, models, ideas, and explanations to the creator and other people.
- Before and after pictures can be used to represent change.
- Numerical data can be used to describe and compare objects and events to the creator and other people.
- Tables and charts can be used to represent objects and events.
- Graphs can be used to identify relationships.
- Explanations are better when specific observable evidence is provided.
- Communication allows other people to agree or disagree with a person’s findings.
History of science and development of technology - perspective of science
See also Concepts & misconceptions also science, math, technology timeline
- People have practiced science and technology for a long time.
- Science develops over time.
- Science investigators such as
Scoring guides suggestions (rubric)
Relative position to locate objects or points (scoring guide)
Top level
- Locating objects at rest requires a procedure that starts with a known reference object or point and a directional description and distances of a path from the reference object to the object being located. To describe an object in motion or the motion of an object, a reference object or point is used from which to describe the path the object takes with a directional description and rate of change.
- Objects can be located relative to two reference points and two distances or a direction and distance.
- Objects can be located with a list of directions.
- Objects are located by the place they occupy.
Lower level
Locate objects on a map (scoring guide)
Top level
- Accurately describe a route on a map from one location to another (distance and direction).
- Objects can be located by starting at a place (reference object) and following a list of directions (distances or directions).
- Identify the coordinate position of a specific object on a map when given the object (Where is the playground located on the map? 5, 4).
- Locate a specific object on a map when given specific coordinates of that object on a map (What is located at 5, 4 on the map? Playground).
- Directions are used to locate objects.
- Identify objects on a map
Lower level
Pedagogical Overview
All procedures are based on the learning cycle theory & methodology and integrates science content, inquiry and process skills. The following sequence includes three sections:
Activities Sequence to provide sufficient opportunities for learners to achieve the outcomes
Make sure learners have the prior knowledge and experiences identified in the background information and start with a week of review. for observation and inference.
Week of review
- Activities to review science inquiry and process of observation, property, and inference. I have used the first week to do the four day observation each day and integrate the others as time allows.
- Four day observation - Introductory observation or inference sequence observe three illustrations over four days
- Back view front view with definition of science and S. White comic - observation or inference
- Bird and cage - observation or inference, optical illusion, position and motion
- Foot prints in rock - observation or inference, critical thinking about what happened millions of years ago when the tracks were made
- Play - What's my properties.
- Have learners secretly select an object and ask them to identify it's properties one at a time. Or just start by playing the game.
- Secretly select an object.
- Identify one of it's properties.
- Ask. Who wants to guess what the object is, by identifying another property. They don't guess the object they guess another of its properties and state that property.
- The initial learner then says yes if it is a property of the object or no if it isn't a property of the object.
- Continue taking turns with learners identifying properties until it appears everyone knows the object.
Week two and beyond
- Activity 1 - What’s my object? or I spy an object
- Activity 2 - What’s my reference object?
- Activity 3 - Challenge - Locate an object without a reference object?
- Activity 4 - Four in a row & Cartesian puzzle - Introduction for maps
- Activity 5 - What’s my position - polar coordinates - Introductory maps
- Activity 6 - Puzzle - Solve relative position puzzles 1-10, record and publish results, share, resolve any differences
- Activity 7 - Spheres motions: What's my track? Introductory relative position and motion sequence - Starts with a review of activities in Rolling spheres and will extend them.
- Activity 8 - Sphere crashes with a stationary object
- Activity 9 - Moving sphere hits stationary sphere with different speeds
- Activity 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
- Activity 11 - Bird and cage activity - with more discovery activities
- Activity 12 - Create a model miniature golf hole (Generative assessment activity)
Extension activities or unit
- Perception illusions memory ...
- Roller coaster & ball run activities
- Ramp investigations
- Motion: force, gravity, acceleration, inertia, friction, & energy Unit with activities & plans
- Cartography - plans and activities fourth grade and up with activities for making a variety of different maps with different methods. Also challenge activities with maps.
Focus question
Unit focus question:
- How do you describe the location of objects? Another city or a landmark within a city?
- How do you describe an object that is in motion?
Sub focus questions:
- What properties are necessary and sufficient to locate an object or position?
- How do objects move?
- What causes the motion?
- What is needed to change its motion?
- How can its motion be changed?
Materials
- Support materials
- Lab notes
- Lab note 1 - What’s my object? or I spy an object
- Lab note 2 - What’s my reference object?
- Lab note 3 - Challenge - Locate an object without a reference object?
- Lab note 4 - Introductory maps - What’s my object?
- Lab note 5 - What’s my position - polar coordinates - Introductory maps
- Lab note 6 - Relative position puzzles 1-10
- Lab note 7 - Spheres motions: What's my track?
- Lab note 8 - Sphere crashes with a stationary object
- Lab note 9 - Moving sphere hits stationary sphere with different speeds
- Lab note 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
- Lab note 11 - Bird and cage activity - with more discovery activities
- Lab note 12 - Create a model miniature golf hole
Lesson Plans
Activity 1 - I spy an object or What's my object
Materials
- Directions
- Lab note
Focus questions:
- How do we locate objects?
Learning outcomes:
- Communicate the location of objects from different reference points.
Suggested procedures overview:
- Put learners in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Play I spy location game until learners understand that every hint must have a reference object. Or it is impossible to play without naming a reference object.
Exploration -
- Ask. Want to play a guessing game of I spy an object? yes
- Explain the directions with example.
Directions for I spy an object:- A person picks an object and the rest of us takes turns trying to guess it.
- No physical descriptions or properties of the object are allowed.
- When it is a players turn they can ask a question using only positions to describe the location of the object.
- Example:
- Is the object above us? Spy's response: no
- Is the object below the ceiling. Spy's response: yes
- Is the object the flag? Spy's response: no
- Is the object right of the clock ...
- When the learners are fairly familiar with playing the game, ask them what is similar about the kinds of words they are using. They are direction words: left, right, up, down, above, below, on top, ...
- If they don't respond, then suggest to continue with the game and write the descriptions on the board.
- Continue the game until there are enough hints on the board for them to describe similarities or patterns for the words in the list.
Invention -
- Ask. What kind of pattern do you notice? We always starts with "The object" then there is a "directional" and then a name of a location.
- Ask. What words are changing and what words are not? The object. Doesn't change. The directional words changes. And the location mostly stays the same.
- Why doesn't the location change? It's usually easier to use the same location to identify an object by eliminating or narrowing the search.
- Introduce reference point as a location, place, or object that is selected and doesn't change in the description.
- Ask. Why? It would be confusing, need to keep it the same for each set of directions. However, it is possible to locate objects with multiple reference points or objects. For example. Its on the bookshelf between A Wrinkle in Time and The Gift Giver.
- Ask. Why is it necessary to change the direction words? changing them to provide more information to eliminate or narrow the search.
- When learners are focused on the position descriptors, suggest that a list of those words be made. in front, on top, up, down, behind, above, below, right, left, diagonal, ...
- Make a list and have the learners sort or classify the words. Location words (for reference) and position words for direction, maybe also distance words far, close, near, six feet ...
- When they are familiar with the descriptors and are comfortable with that part of the game, write an operational definition to use to play the game. Operational definition Start with a location (reference point) then add directions from up or down, left or right, in front or behind, and maybe a distance. Don't worry if it isn't very accurate as it can be modified later.
Discover
- Divide the class into two groups.
- Have one group describe the location of an object from one position in the room and have the second group describe the same object from a different part of the room.
- If they don't notice the difference, then write the descriptors to locate the objects, and point out the differences, and ask. Why are the descriptors different?
- Ask. Would it be possible for an object to be described with opposite words? (In front of ______ and to the right. Behind _______ and to the left.)
- Discuss how and why different descriptors are need for the same objects.
- Repeat the procedure for a different object in the class.
- Continue with objects in the class until the learners get the idea.
Discovery 2
- When you are confident they are constructing the concept, then challenge them to describe the location of a place in the school building from their classroom.
- Next have them describe a location outside the school building or grounds.
Discovery 3
- When they get the idea of this, challenge them by playing the game backwards. for example. Don't tell them the starting location, but give them the description to locate, a place or object, and what the final place or object is. Then ask them if they can identify the starting position. left of starting location, above starting location, and behind starting location. What is the starting location?
- Have them create their own backwards descriptions as a puzzle for their classmates.
- Trade with a partner, solve the puzzle, and then share their discoveries with the class.
- Continue to add descriptors to the list and other significant learnings about how to locate objects and how descriptions change relative to starting position (position of person ...
- Review and edit their operational definitions.
- When is person the reference point or position? Usually every time we give directions when people ask - How do you get to ....
- Ask. Is this statement accurate:
The description of an object's position is a matter of personal perspective. - Have learners explain if this is an accurate statement or not and why they believe it is or is not.
Activity 2 - What's my reference object
Materials:
Focus questions:
- When you need to locate an object or describe an object's location, are there different ways to do it?
Learning outcomes:
- Describe different ways to locate an object from the same reference point.
- Explain. Any object can be used as a reference point, or starting point, and what you choose can make it easier or harder to locate something.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Write different descriptions from different reference points for the same object. Continue until every one knows any object can be used as a reference point or starting point, and what you choose can make it easier or harder to locate something.
Exploration
- Ask. When you need to locate an object or describe an object's location, are there different ways to do it? Yes
- Let's do one.
- For example: Select and object. Clock ... We can locate it as below the ceiling and to the right of the door. We can also locate it as above the desk and to the right of the door.
- Have learners select another object and locate it with different examples of directions.
- Continue till all can use location words accurately to locate different objects in the room.
Invention
- Ask. How many different ways can we locate an object? A lot maybe infinite
- Are some better than others?
- Continue to discuss how and why different descriptors are needed to locate the same objects. It depends on what is used as a reference object (starting point). If you say below the ceiling that only narrows it down much if it is in the room. If you say above the teacher's desk it narrows it down a lot more. If you say above the board, that narrows it down more than above the desk.
- Repeat the procedure for different object in the class.
- Continue with objects in the class until learners are confident and accurate.
Discover
- When you are confident that students are constructing the concept, then challenge them to describe the location of a place in the school from their classroom and then from a different part of the school building or grounds.
- When they get the idea of this, challenge them by playing the game backwards. For example. Don't tell them the starting location, but give them the description to locate a place or object and what the final place or object is. If the clock is to the left, in front, and above this object, what is the object?
- Ask if they can identify the starting object or position.
- Have students create their own backwards descriptions as a puzzle for their classmates, trade with a partner, solve the puzzle, and then share their discoveries with the class.
- Continue to add descriptors to the list and other significant learnings about how to locate objects and how descriptions change relative to starting position (position of person....[is the person the reference position?])
Generalization
- The description of an object's position is a matter of personal perspective. Have students explain if this is an accurate statement or not and why they believe it is or is not.
- Continue with the same ideas only describe a position of an object as it moves...
Activity 3 - Locate an object without a reference object
Materials:
Focus questions:
- Can you locate an object without a reference object?
Learning outcomes:
- Explain why it is impossible to locate or provide directions to an object or place without a reference object.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Challenge them to locate and object without using a reference point. Continue till they agree it is impossible and have them write what they learned in their lab notes.
Exploration
- Ask. Can you locate an object without a reference object?
- Take turns letting each person give directions for an object that doesn't have a reference point or object.
- After each example ask. What is the reference point or object? Give amble wait-time to let them answer. If after 3o seconds or so and they didn't recognize it, then ask, How did you know not to use me as the reference object? What helped you decide how to use the descriptions? If they still don't get it, tell them what the reference object was. Often learners will use themselves as the reference object and not realize they are.
Invention
- Keep asking for examples until they realize it is impossible. In one class I remember one person was sure it was possible and tried for several minutes, then realized it wasn't, sat still and let the other learners continue to try for about five minutes, until they could take it no more. Stood up and said listen, think about it, it's not possible ...
- Ask. Why is it impossible? need a place to start or a place from which to orient.
Discovery
- In following activities
Activity 4 - Introductory maps - Four in a row & Cartesian puzzle
Materials
Focus questions:
- How does a Cartesian coordinate work?
Learning outcomes:
- Locate positions on a Cartesian coordinate map.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Have learners explore how to identify positions on a Cartesian coordinate by playing the game four in a row.
- Have learners practice using a Cartesian coordinate by solving a puzzle.
Exploration
- Ask. What is a Cartesian coordinate? square or rectangular grid.
- Want to play a connect four game using a Cartesian coordinate? yes
- Divide the class into two teams. Assign one team to place X's and the other team to place O's on the intersections of the distances from the X and Y origin on the Cartesian coordinate. For example if they say five, six; then put a mark on the intersection of five right and six up.
Four in a row rules:
- For today's game we are using this 10 X 10 grid.
- May want to make it interesting (and faster) by not using all the whole number intersections. For example allow only even numbers or odd number.
- You have 15 seconds to call a position.
- Must say it as (X, Y).
- No helping (if another person (on your team) calls out, then it's the other team's turn (you lose your turn).
- If you make a mistake, it is the other team's turn.
- And to make it interesting we are only using EVEN numbers.
Invention
- Discuss how to locate objects on a Cartesian coordinate.
- What information is used to locate an object or position on a Cartesian map or gird? two directions and a reference point or position
- Tell. I have a puzzle for you.
- See if you can solve this ... Cartesian puzzle
Discover
- How does what you learned about Cartesian coordinates relate to a map?
- Do you think it is possible to locate objects by using something other than two distances? next lesson we will see.
Activity 5 - What’s my position - polar coordinates - Introductory maps
Materials:
- Blank polar coordinate
- Polar coordinate with only degrees labeled
- Zoo map
- Crack the code
- Where are the flags?
- Lab notes
Focus questions:
- How can we locate an object or place without using two distances and a reference object or point?
Learning outcomes:
- Explain how to locate a position or object from a reference point or position with a direction and a distance.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Play the game: four in a row until learners become really good at locating places on a polar coordinate.
- Challenge them to complete the following
- May want to insert more map activities from the cartography unit of study. See Study Investigation for making maps (Cartography) here or at the end of this unit.
Exploration
- Organize learners into pairs or groups.
- Have learners explore how to identify positions on a polar coordinate by playing the game four in a row.
- Divide the class into two teams. Assign one team to place X's and the other team to place O's on the intersections of degrees and distances on the polar coordinate. For example if they say 180 degrees, five; then put a mark on the polar coordinate at that position.
Four in a row rules:
- For today's game we are using multiples of 5 to 20 for distance and multiples of 30 for degrees. Remember zero is ...
- You have 15 seconds to call a position.
- Must say it as (degrees, distance)
- No helping (if another person (on your team) calls out, then it's the team's turn (lose your turn).
- If make a mistake, it is the other team's turn.
Invention
- Discuss how to locate objects on a polar coordinate. Use a direction (degrees) and distance from a reference point or position.
- Ask. What advantage is there to use a polar coordinate instead of Cartesian coordinates. It is sometimes easier in real life to start from a known location (reference point) and head in a certain direction for a particular distance.
The place you are looking for? go to the intersection (reference point) turn north (direction) and go 5 miles (distance) and it will be on your left.
Discover
Present the following challenge:
Two fourth graders measured the distance of three small flags using the large American flag pole as a reference point, or starting point. Then they marked the position of each flag with a colored dot on a polar coordinate.
When they checked their work they found they used the direction of the blue flag as zero instead of north as zero. They realized that the starting point on their map was okay, but they needed to change the zero direction to north.
When they did they found the blue flag was 30 degrees and, 5 paces so they marked polar coordinate with an X.
On the polar coordinate mark where you think they will place the yellow and red flag.
Explain how did you decided to mark the flags positions?
Activity 6 - Relative position puzzles 1-10
This activity is one of the best I have ever observed a whole class of fourth graders totally on task and cooperating for the entire time it took for every student to solve all the puzzles. Not just once, but every year I used it for many years.
Their focus, cooperations, and persistence in completing the was delightful to see. Additionally, later during the year, I would sometimes over hear them compare this activity to another problem to solve it with comments like. It's like those puzzles where you have to turn it around and over to find all the different ways.
Materials
- Relative position puzzles & pieces - If you prepare them ahead of time put them in envelops and color code them by printing them on different colors of paper or oak tag.
- Lab notes
Focus questions:
- What are the solutions to these Puzzle sequences -
Learning outcomes:
- Solve puzzles 1-10, record and publish results, share, resolve any differences
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Make puzzles available for learners to solve, record, share, and resolve any differences.
Exploration
- Learners work individually or in groups.
- Tell. There are 10 puzzles, one puzzle has a set of pieces that are in an envelop.
- How many different envelops? 10
- Each of you are to solve each puzzle and record your results for each puzzle on a 3x5 index card.
- How many cards will you complete? 10
- There is a box on the table. When you complete a puzzle and card, you are to put the card into the box. If there already is a card in the box for that puzzle then you are to check your solutions with the solutions on the other card or cards if there are more than one.
- If you agree with the solutions, then put a rubber band around all the cards and put them back into the box.
- When you complete all ten puzzles you can read until someone comes to compare cards or until everyone has competed all ten cards.
- There are 25 students here today so how many cards will be in the box when we are all done? 250
- Solve puzzles 1-10, record and publish results, share, resolve any differences
Invention
- Regroup as a class and ask.
- What did you discover from solving the puzzles? Each puzzle piece has four possible ways it could be a solution.
- What did you use to place the pieces? the holes in the pieces
- You used the whole as what? reference points
Discover
We are going to do a set of experiments with spheres and ramps (inclined planes) to learn about motion and force. To help us know what is happening it is good you know about position and motion will be helpful.
The SPHERES could be replaced with hot wheel cars and their ramps, or ball runs made from K'Nex.
Activity 7 - Spheres motion related to speed, mass, and force: What's my track?
Background information:
I have three sets of activities related to rolling spheres;
Tracks of Rolling Spheres (third grade), focus on matching tracks with actions - observation, evidence, cause & effect. qualitative
The activities 7, 8a, 8b, 8c, 9, & 10 here (fourth grade) focus on using tracks as evidence to explain transfer of energy with a hint of Newton. qualitative with a bit of quantitative
Science, mathematics & cooperative activities with K'Nex® in the section:
The Down hill ramp, ... explorations:
- Long Track drift till stop
- Runs from Different Heights
- Hill Vibrations
- Crash and Slide (sixth grade) focus on measurement as quantitative evidence and graphing to explain change and relationships.
Materials
- Spheres of different sizes and masses, paper and carbon paper, ramps
- Lab note speed, Lab notes mass, & Lab notes summary speed & mass
Focus questions:
- How do spheres, with different speeds & different masses, roll?
Learning outcomes:
- Use tracks as evidence to describe how the motions for spheres of different speeds and different masses.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- May want to do Tracks of Rolling Spheres
- Activity - Explore sphere tracks from rolling down a ramp at different speeds and with different masses to explain their motions (4 activities).
Exploration
- Organize learners into pairs or groups.
- May want review the activity Tracks of Rolling Spheres.
- Provide learners with lab note speed, lab notes mass, & lab notes summary speed & mass
- Demonstrate the ramp set up and provide directions to explore different speeds (start position 20 cm - faster; & 10 cm - slower) for the two spheres (large (more mass) & smaller (less mass)).
Directions:
Use a ruler and a piece of wood to make a ramp that is elevated on one end about 10 cm above the table. Position a piece of carbon paper, with the carbon side up, at the bottom of the ramp so spheres will roll across it. Then cover it with a plain sheet of white paper.
- Answer any questions and tell the learners to experiment by releasing the small sphere from 20 and 10 cm, and write their ideas for the questions in their lab notes and then the larger sphere. If they aren't sure for some, they can wait till they get back together as a class.
- Remind them, they will be do four experiments, collect data, and then come back together as a class to share their data.
Setup 20 cm roll small sphere
Position a small sphere 20 cm from the bottom of the ramp. Release the sphere and let it roll down the ramp onto the paper on top of the carbon paper.
- Describe the track.
- What do they say about the sphere’s speed?
- Place an arrow beside the track to indicate the direction sphere is moving and label it small sphere 20 cm.
Setup 10 cm roll small sphere
Now position the same sphere 10 cm from the bottom of the ramp. Reposition the papers so it rolls on a different section of the paper so the two tracks can be compared.
- How are they similar to the first set of tracks?
- How are they different?
- How could the difference be explained?
- What does the distance between dots in a set of tracks say about speed?
- What change in the distance between dots takes place in the direction of motion? Distance between dots decreases with speed.
- Why does this occur? The tracks are made when the sphere bounces on the carbon paper and as it slows down the bounces are closer together
Setup 20 cm roll large sphere
Release a larger sphere from a distance of 20 cm. Reposition the papers so it rolls on a different section of the paper so the three tracks can be compared.
- How are these tracks different from those of the small sphere when it was released from the same height?
- How are they similar?
Setup 10 cm roll large sphere
Release a larger sphere from a distance of 10 cm. Reposition the papers so it rolls on a different section of the paper so the three tracks can be compared.
- How are these tracks different from those of the small sphere when it was released from the same height?
- How are they similar?
Invention
- Regroup as a class and groups share their data.
- Ask. How do the four tracks show a representation of the spheres speed? Distance between dots.
- How do the tracks show a representation of the spheres mass? Size and thickness of dots.
- As a sphere rolls along a table top, what factor(s) act on it to change it’s speed? friction, initial speed, air, gravity pushes down on it to increase its friction with the surface.
- What evidence do you have to support this?
- If this (these) factor(s) was (were) not acting, sketch how the tracks would look. Learners will be surprised the tracks are not solid tracks and will want to discuss what is happening.
- Ask. What do you think would happen?
Discover
- Next activities for collisions.
Activity 8 - Sphere crashes with a stationary object
Materials
- Spheres, ramps, block of wood, paper and carbon paper
- Lab notes
Focus questions:
- How do spheres roll and bounce off stationary objects?
Learning outcomes:
- Describe how spheres travel before and after they collide with a stationary object at different speeds.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Describe how spheres roll at different speeds before and after they collide with a stationary object.
Exploration
- Organize learners into pairs or groups.
- What can you infer from tracks that are a result of a collision between a sphere and a stationary object?
- Use a piece of wood as a stationary object.
- Place it on top of the carbon paper and white papers and hold it firmly as the sphere hits it.
- Release the same sphere from 10 cm, to make a track, then reposition the paper and release the same sphere from 20 cm.
- Draw diagrams for each track and answer the questions in the lab notes that you can.
- Display tracks to prepare for the invention.
Invention
- Regroup as a class and share tracks and answers to questions.
- Use the tracks from the spheres and explain what happened.
- What was different between the speed of a sphere before and after colliding with a stationary object? faster before and slower after
- What happens to the speed? Some of the force from the rolling sphere was transfered to the block of wood causing the sphere to slow down. For every action there is an equal and opposite reaction.
- What evidence supports this? could feel force when holding wood block can see a big change in the distance between track dots
- What affect did the collision have on the direction it was moving? change direction. Opposite reaction
- How did the speed affect the tracks? The dots got closer and lighter as the spheres slowed.
- How do we describe motion? direction, speed ... relative to a reference point and how it is changing
Discover
- Next activities
Activity 9 - Moving sphere hits stationary sphere with different speeds (heights on an incline plane)
Materials
- Spheres, ramps, paper and carbon paper
- Lab notes -
Focus questions:
- How does speed affect how a sphere hits a stationary sphere?
Learning outcomes:
- Describe the effect the change in speed has on the transfer of energy to a stationary sphere. Describe how a faster sphere pushes another sphere farther than when it is hit by a slower one.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Describe how to control all variables except speed to collect data from a moving sphere hitting a stationary one.
Exploration
- Organize learners into pairs or groups.
- Ask. How can we explore what happens when a sphere is hit by another sphere at different speeds? Need to pick two spheres to collide and vary the speeds from run to run. Speed will change by the sphere's position on the ramp. 10 cm 20 cm. Mass of spheres will be controlled by deciding which two spheres will crash (either the one small and one large, or two small ones, or two large ones) and don't change them during the runs. Remember you are changing the speed.
Teacher note: Make sure there are groups that select same size spheres and different sized spheres to have more data for the invention.
Directions
- Pick two spheres to crash. One will be stationary below the ramp and you will vary the speed of the other from run to run. Speed will change by the sphere's position on its ramp. 10 cm 20 cm. Mass of spheres will be controlled by deciding which two spheres will crash (either the one small and one large, or two small ones, or two large ones) and don't change them during the runs. Remember you are changing the speed.
- Place one sphere below the ramp so the sphere coming off the ramp will hit it on the carbon paper.
- Release the sphere and collect the data.
- Change the starting position on the ramp and collect more data.
- Repeat as needed.
Invention
- Regroup as a class and groups share their tracks and explanations.
- Explain.
- What is the motion of each sphere?
- What evidence do you have to support this?
- Where did the spheres collide? between the dots that change directions
- Why isn't there a dot where the spheres collide? because the collision is up off the paper between where the surface of the sphere touches the paper on the table or floor. A radius distance of each sphere.
- Which sphere was faster? Before the collision the one from the ramp, after the collision, depending on how they hit maybe the one that was slower.
- How are the collisions different at different speeds? Faster more energy to transfer. Slower less energy to transfer.
- How do the sphere's speeds compare from before and after colliding. Slow down
- What can be inferred from the tracks that are a result of a collision between two spheres at different speeds that were the same size? Big sphere hit big sphere - ..... small sphere hit small sphere - ......
- What can be concluded? More speed has more energy and more energy is transfered to a sphere being hit.
- How do we describe motion? direction, speed ... relative to a reference point and how it is changing
Discover
- May want to do more collisions with different pairs of spheres, but only changing the speed. Mass will be changed in the next activity.
Activity 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
Materials
- Spheres, ramps, paper and carbon paper
- Lab notes -
Focus questions:
- How does mass affect what happens when spheres collide?
Learning outcomes:
- Describe the effect mass has on the transfer of energy to spheres.
- Describe how a more massive sphere pushes another sphere farther than one with less mass.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Describe how to control all variables except mass to collect data from a colliding spheres.
Exploration
- Organize learners into pairs or groups.
- Ask. How can we explore what happens with spheres when they collide with another sphere of a different mass? Need to pick two sphere to crash into each other and vary their mass from run to run. Mass will change by the selection of the sphere's. Large or small. Speed of the spheres will be controlled by starting them from the same height on the included planes and not changing them during the runs. Remember you are changing the mass.
Directions
- Place two ramps just off opposite edges of the carbon paper so they face each other. Release a sphere from each ramp at the same time.
- Compare the speed of the two spheres before and after colliding. What happens to the speed? Should be close to the same
- What evidence do you have to support this? watching and maybe the tracks suggest they are the same speed.
- How did the collision affect the direction each sphere was going?
Invention
- Regroup as a class and groups share their tracks and explanations.
- Explain.
- What is the motion of each sphere?
- What evidence do you have to support this?
- Where did the spheres collide? between the dots that change directions
- Why isn't there a dot where the spheres collide? because the collision is up off the paper between where the surface of the sphere touches the paper on the table or floor
- Which sphere was faster? Before the collision they should be the same. after the collision, depending on how they hit maybe the smaller one.
- How are the collisions different with different masses?
- How do the sphere's speeds compare from before and after colliding. They more massive one slows and the smaller one may speed up. Depends on the mass difference.
- What can be inferred from the tracks that are a result of a collision between two spheres of different masses that hit at the same speed? Big sphere hit small sphere and ..... small sphere hit large sphere and ......
- What can be inferred from the tracks that are a result of a collision between two spheres of different masses that were traveling at the same speed? small sphere hit large sphere and ..... ; large sphere hit small sphere and .....
- What can be concluded? More mass has more energy (momentum) and more energy is transfered to the sphere being hit.
- How do we describe motion? direction, speed ... relative to a reference point and how it is changing
Discover
- May want to do more collisions with different pairs of spheres, changing whatever is desired.
- How does what we learned about collisions apply to vehicles?
Activity 11 - Bird and cage activity - with more discovery activities
Materials
Focus questions:
- How can the motion of the spinner be explained based on your observations?
Learning outcomes:
- Describe how the motion and observation contradict each other and explain how it can happen.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the focus questions.
- Activity - Make the bird and cage spinner, spin it, observe, and describe how the motion and observation contradict each other; and explain how it can happen.
Exploration
- Organize learners into pairs or groups.
- Tell. Use the pattern and make the bird cage spinner.
- Spin them, observe, and complete the following in your group:
- Describe the motion.
- Describe your observations.
- Explain how the motion and observation contradict each other.
Invention
- Regroup as a class and have groups report the spinners motion, their observations, and explanations.
- Conclude the relative position of the cage and the bird continually face in the opposite direction.
- However, since the motion is faster than the eye can interpret the separation of each on one side the two appear to be in the same location at the same time. Or they appear to be in the same position at the same time.
Discover
How can you use what you learned to analyze other objects in motion?
Balls, vehicles, planes, moons, planets,
Example!
Jae was riding a bike and throwing a ball up in the air and catching it.
- How would you describe the motion from Jae's point of view? The ball goes straight up and down. Jae's point of view.
- If you are standing along the path, Jae is traveling, how would you describe the motion of the ball from your point of view? The ball is traveling in sine wave pattern (roller coaster hills and valleys).
More!
- How do you describe the Earth's movement around the Sun? Movement of the Earth and moon system around the Sun? All the planets in the solar system around the Sun? Movement of the solar system through the Milky Way galaxy?
- How do you describe the movement of balls and cars down inclined planes mathematically? The exchange of momentum when objects crash and transfer energy?
Activity 12 - Generative assessment - Creating a Miniature Golf Hole
Materials
- Golf ball, cardboard, different objects (plastic, wood, rubber, sponge, Styrofoam, metal, ...), glue, tape (masking & duct), ...
- Location for each hole. The authors provided large cardboard boxes or trays (≈ 3 foot by 4 foot) to create their miniature golf hole. While an alternative would be to provide space in a rec room, playground, or gym to assemble their miniature golf hole, the problem of how to engineer the hole needs to be solved.
- Standard golf hole is 4.2 inches.
- USGA standard golf ball size is around 1.68 inches, it is not the same everywhere.
- Lab notes -
Focus questions:
- How does an engineer test materials and use the data to design a miniature golf hole?
Learning outcomes:
- Describe how force can be used to create a miniature golf hole where it is possible to make a hole in one with a bounce shot.
Suggested procedures overview:
- Put students in groups, focus their attention, and assess their initial understanding of the challenge.
- Activity - Pose the challenge, share materials, and ask if they can explain how to test the materials to see how golf balls bounce off them and use that information to design a miniature golf hole.
Exploration
- Organize learners into pairs or groups.
- Pose the challenge: Design a miniature golf hole where it is possible to make a hole in one by bouncing the golf ball off two different objects.
- Share materials.
- Ask if they can explain how to test the materials to see how golf balls bounce off them. Generative assessment to see if learners will suggest how to control all variables except the type of material.
- Design a fair test to bounce balls off different materials. Set up a ramp to roll a golf ball down to hit a piece of each material and measure how far it bounces. Control the height of the ramp, where the ball starts each time, the placement of the object, the angle the golf ball hits it, and how to measure the distance. Do three trials for each material, average the roll, and graph the results.
- Review a design process.
- Use the data and other information to design a miniature golf hole.
Invention
- Regroup as a class and have groups demonstrate their miniature golf hole.
- Could have a tournament, record everyones score and find the class average for each hole and the total for the entire course.
- Discuss what they learned about design and how different material's elasticity transfers the motion of the golf ball.
- What forces acted on the ball? push with the club, bounce off the objects,
- When the ball bounces off the objects is it a push or a pull? the ball pushes into the object, and object contracts or the wall pushes back depending of the elasticity of the different materials.
- How can you improve your design?
- How can you make it more challenging, but not impossible.
- What did you learn about designing?
- What did you learn about engineering?
Lab Notes for activities
Lab notes 1 - I spy an object
Materials
- Lab notes
Focus questions:
- How do you get good at the game?
Challenge
Identify what words are helpful when playing I spy an object and write a procedure on how to play.
- Directions for I spy an object:
- A person picks an object and the rest of the class take turns trying to guess it.
- No physical descriptions or properties of the object are allowed.
- When it is a players turn they can ask a question using only positions to describe the location of the object.
- Example:
- Is the object above us? Spy's response: no
- Is the object below the ceiling. Spy's response: yes
- Is the object the flag? Spy's response: no
- Is the object right of the clock ...
List helpful words.
Write a procedure that would be helpful to find the object with less questions.
Lab notes 2 - What's my reference object
Materials
- Lab notes
Focus questions:
- What is a reference object?
- How do we select them?
Challenge
Pick an object in the room and locate it from two different places.
1.
2.
Locate an object outside your room locate it from two different places.
1.
2.
Think of a starting place and stopping place. Create a set of backwards directions.
Write what you learned about reference points.
Lab notes 3 - Locate an object without a reference object
Materials
- Lab not4es
Focus questions:
- Can you locate an object without a reference point?
Challenge
Locate an object without a reference point.
Describe what you learned.
Lab notes 4 - Introductory maps - Four in a row & Cartesian puzzle
Materials
Focus questions:
How does a Cartesian coordinate work?
Challenge:
Play four in a row
What is the solution for the Cartesian puzzle?
What did you learn about a Cartesian coordinate system.
Lab notes 5 - What’s my position - polar coordinates
Materials
Challenge
Explain how to locate a position or object from a reference point or position with a direction and a distance.
Describe how to play four in a row on a polar coordinate.
What is the solution for crack the code?
Where are the flags?
Locate three animals on the zoo map.
Lab notes 6 - Relative position puzzles 1-10
Materials
- 10 3x5 cards
- set of Relative position puzzles
Challenge
- There are 10 puzzles, each puzzle has a set of pieces that are in an envelop
- You are to solve each puzzle and record your results for each puzzle on a 3x5 index card.
- When you complete a puzzle and card, put the card into the box. If there already is a card in the box for that puzzle then you are to check your solutions with the solutions on the other card or cards if there are more than one.
- If you agree with the solutions, then put a rubber band around all the cards and put them back into the box.
- When you complete all ten puzzles you can read until someone comes to compare cards or until everyone has competed all ten cards.
Solutions:
Lab notes 7a - Spheres motion related to speed, mass, and force: What's my track?
Materials
- Spheres of different sizes and masses, paper and carbon paper, ramp
- Lab notes
Challenge
Use tracks as evidence to describe how the motions for spheres of different speeds roll.
Different speeds - 20 cm roll small sphere
Position a small sphere 20 cm from the bottom of the ramp. Release the sphere and let it roll down the ramp onto the paper on top of the carbon paper.
Describe the track. Place an arrow beside the track to indicate the direction sphere is moving and label it small sphere 20 cm.
What do they say about the sphere’s speed?
Different speeds - 10 cm roll small sphere
Now position the same sphere 10 cm from the bottom of the ramp. Reposition the papers so it rolls on a different section of the paper so the two tracks can be compared.
Describe the track. Place an arrow beside the track to indicate the direction sphere is moving and label it small sphere 10 cm.
How are they similar to the first set of tracks?
How are they different?
How could the difference be explained?
What does the distance between dots in a set of tracks say about speed?
What change in the distance between dots takes place in the direction of motion?
Why does this occur?
Lab notes 7b - Spheres motion related to speed, mass, and force: What's my track?
Materials
- Spheres of different sizes and masses, Paper and carbon paper, Ramp, Lab notes
Challenge
Use tracks as evidence to describe how the motions for spheres of different masses roll.
Different masses
Setup 20 cm roll large sphere
Position a large sphere 20 cm from the bottom of the ramp. Release the sphere and let it roll down the ramp onto the paper on top of the carbon paper.
Draw and describe the track. Place an arrow beside the track to indicate the direction the sphere is moving and label it large sphere 20 cm.
What do they say about the sphere’s speed?
Setup 10 cm roll large sphere
Now position the same sphere 10 cm from the bottom of the ramp. Reposition the papers so it rolls on a different section of the paper so the two tracks can be compared.
Draw and describe the track. Place an arrow beside the track to indicate the direction the sphere is moving and label it large sphere 20 cm.
How are they similar to the first set of tracks?
How are they different?
How could the difference be explained?
What does the distance between dots in a set of tracks say about speed?
What change in the distance between dots takes place in the direction of motion?
Why does this occur?
Lab notes 7c - Spheres motion related to speed, mass, and force: What's my track?
Materials
- Tracks from 10 cm small sphere, 20 cm small sphere, 10 cm large sphere, 20 cm large sphere,
- Lab notes
Challenge
Use tracks as evidence to compare how the motions for spheres of different speeds and masses roll.
Summary
How do the tracks show a representation of the sphere's speed?
How do the tracks show a representation of the sphere's mass?
As a sphere rolls along a table top, what factor(s) act on it to change it’s speed?
What evidence do you have to support this?
If this (these) factor(s) was (were) not acting, sketch how the tracks would look.
Explain why do you think this would happen.
How do we describe motion?
Lab notes 8 - Sphere crashes with a stationary object
Materials
- Sphere, Paper and carbon paper, Ramp, Lab notes
Challenge
What can you infer from tracks that are a result of a collision between a sphere and a stationary object?
Directions
- Use a piece of wood as a stationary object.
- Place it on top of the carbon paper and white papers and hold it firmly as the sphere hits it.
- Release the same sphere from 10 cm, to make a track, then reposition the paper and release the same sphere from 20 cm.
Diagrams for 10 cm run and collision
Diagrams for 10 cm run and collision
What was different between the speed of a sphere before and after colliding with a stationary object?
What happens to the speed?
What evidence supports this?
What affect did the collision have on the direction it was moving?
How did the speed affect the tracks?
How do we describe motion?
Lab notes 9 - Moving spheres hits stationary sphere with different speeds (heights on an incline plane)
Materials
- Spheres, Paper and carbon paper, Ramp, Lab notes
Challenge
Explore collisions of a stationary sphere being hit by spheres at different speeds.
Directions
- Pick two spheres to crash. One will be stationary below the ramp and you will vary the speed of the other from run to run. Speed will change by the sphere's position on its ramp. 10 cm 20 cm. Mass of spheres will be controlled by deciding which two spheres will crash (either the one small and one large, or two small ones, or two large ones) and don't change them during the runs. Remember you are changing the speed.
- Place one sphere below the ramp so the sphere coming off the ramp will hit it on the carbon paper.
- Release the sphere and collect the data.
- Change the starting position on the ramp and collect more data.
- Repeat as needed.
Run 1
Draw tracks, label directions, and write the speed of the two spheres before and after colliding.
Run 2
Summary questions
What happens to the speed after a collision?
What evidence do you have to support this?
How did the collision affect the motion of the spheres?
What direction is each sphere going?
What evidence do you have to support this?
Where did the spheres collide?
Why isn't there a dot where the spheres collide?
Which sphere was faster?
How are the collisions different at different speeds?
How do the sphere's speeds compare from before and after colliding.
What can be inferred from the tracks that are a result of a collision between two spheres at different speeds that were the same size?
What can be inferred from the tracks that are a result of a collision between two spheres at different speeds that were different size?
What can be concluded?
How do we describe motion?
Lab notes 10 - Spheres with different masses hit each other after rolling down an include plane from the same height
Materials
- Spheres, Paper and carbon paper, Ramp, Lab notes
Challenge
Explore collisions of spheres at different speeds.
Directions
- Pick two spheres with different masses to crash into each other and keep the speeds the same from run to run (sphere's position on the ramp) Speed of spheres will be controlled by deciding where the two spheres will start on the ramp and not changed from run to run. Remember you are changing mass.
- Place two ramps just off opposite edges of the carbon paper so they face each other. Release the spheres from each ramp at the same time.
- If need to collect more data, do so.
Run 1
Draw tracks, label directions, and write the speed of the two spheres before and after colliding.
Run 2
Summary questions
What happens to the speed after a collision?
What evidence do you have to support this?
How did the collision affect the direction each sphere was going?
What direction is each sphere going?
What evidence do you have to support this?
Where did the spheres collide?
Why isn't there a dot where the spheres collide?
Which sphere was faster?
How are the collisions different at different speeds?
How do the sphere's speeds compare from before and after colliding.
What can be inferred from the tracks that are a result of a collision between two spheres at different speeds that were the same size?
What can be inferred from the tracks that are a result of a collision between two spheres at different speeds that were different size?
What can be concluded?
How do we describe motion?
Lab notes 11 - Bird and cage activity - with more discovery activities
Materials
Challenge
Put the bird in the cage!
Want more?
How can you use what you learned to analyze other objects in motion?
Balls, vehicles, planes, moons, planets,
Example!
Jae was riding a bike and throwing a ball up in the air and catching it.
- How would you describe the motion from Jae's point of view? Jae's point of view.
- If you are standing along the path, Jae is traveling, how would you describe the motion of the ball from your point of view?
More!
- How do you describe the Earth's movement around the Sun? Movement of the Earth and moon system around the Sun? All the planets in the solar system around the Sun? Movement of the solar system through the Milky Way galaxy?
- How do you describe the movement of balls and cars down inclined planes mathematically? The exchange of momentum when objects crash and transfer energy?
Lab notes 12 - Creating a Miniature Golf Hole
Materials
- Golf ball, cardboard, different objects (plastic, wood, rubber, sponge, ...), glue, tape (masking & duct),
Challenge
Explore with different materials to see how a golf ball bounces off of them. Use your discoveries to design a miniature golf hole and demonstrate how to make a hole in one.
Data
Material | trial 1 | trial 2 | trial 3 | average | class average |
---|---|---|---|---|---|
Wood | |||||
Plastic | |||||
Rubber | |||||
Sponge | |||||
Plan
Support materials
Cartesian coordinate
Cartesian puzzle
Polar coordinate
Zoo map
Challenge
Select three animals you would like to see and write their name and direction.
1.
2.
3.
Where are the flags?
Challenge:
Two fourth graders measured the distance of three small flags using the large American flag pole as a reference point, or starting point. They measured and marked the position of each flag with a colored dot on a polar coordinate.
When they checked their work they found they used the direction of the blue flag as zero instead of north as zero. They realized that the starting point on their map was okay, but they needed to change the zero direction to north.
When they did they found the blue flag was 30 degrees and, 5 paces so marked their polar map with an X.
On the polar coordinate mark where you think they will place the yellow and red flag.
Explain how did you decided to mark the flags positions?
Crack the code
Challenge
Crack the code:
(140, 15) (60, 10) (120, 5) (30, 15) (300, 10)
(90, 14) (0, 0)
(330, 10) (30, 10) (300, 15)
(120, 10) (260, 15) (70, 15) (340 15) (170, 15) (210, 10)
Write one of your own and exchange with another person and crack each other's code!
Bird and Cage pattern
Relative position puzzles
Make some relative position questions to be solved by the different O's on this page!
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