- 1. Final Review (5/24/07-6/12/07)
- 2. Momentum (5/7/07-5/18/07)
- 3. Light (4/23/07-5/4/07)
- 4. Oscillation and Waves (4/3/07-4/13/07
- 5. Electricity (3/11/07-4/2/07)
- 6. Heat (2/27/07-3/9/07)
- 7. Operations (01/16/07-02/16/07)
- 8. Number (01/03/07-01/12/07)
- 9. Energy (12/01/06-12/21/06)
- 10. Force (11/07/06-11/30/06)
- 11. Vectors (10/26/06-11/06/06)
- 12. Linear Motion (9/27/06-10/24/06)
- 13. Units (9/7/06-9/26/06)

- Recognize rate-of-change relationships in many parts of mechanics
- Be able to recognize a rate of change relationship in a new context
- Recognize that physics quantities describe state, change in state (motion), and change in motion of objects, and that the relationship between any two levels involves rate of change.
- Given a graph of position, figure out what the velocity and acceleration graphs must look like.

- Read graphs of position, velocity, acceleration, force, energy, and other physics concepts.
- Identify rate of change as the slope of a graph, and determine what the rate of change graph will look like for any given graph.
- Find the area under a graph to determine the change in another graph.
- Read stacked graphs, such as energy graphs.

- Add, subtract, and multiply vectors.
- Use vectors in equations as momenta or velocities.
- Resolve an angled vector into components using trigonometry.

- Relate force to other physics quantities such as energy, momentum, and acceleration.
- Know Newton's three laws and see how to apply them to various situations.
- Draw a force diagram for an object, resolving any angled forces, and determine the net force.

- Recognize that for a quantity to be
**conserved**means that the total amount of it never changes. - Apply the laws of conservation of energy, mass, and momentum to various situations.
- Apply conservation of energy to problems involving a graph of energy versus position.
- Apply conservation of energy to problems involving universal gravitation.

- Recognize that heat is really kinetic energy of molecules, and temperature is average kinetic energy.
- Recognize that phase change involves molecules gaining enough energy to have a higher level of freedom.
- Calculate the heat capacity and heat content of various materials, and use this to find an equilibrium temperature when two are mixed.

- Recognize that all matter is made up of atoms, and that atoms contain both protons (positively charged) and electrons (negatively charged). Know that only electrons can move.
- Determine how charged objects will behave around each other, using the rule that like charges repel and opposites attract.
- Explain the phenomena of polarization, conduction, induction, and triboelectrification.

- Recognize and relate period, frequency, wavelength, and wave speed.
- Understand how the wavelength of a wave defines its interaction with other objects.
- Recognize the various parts of the electromagnetic spectrum and their effects, sources, and uses.

- Review the equations we used in mechanics (force, energy, and linear motion) and solve problems using them.
- Calculate momentum: p = mv
- Recognize that momentum will be
**conserved**, meaning that the total amount of momentum in any situation is fixed.

- Recognize that because momentum is always conserved, when an object breaks up or two objects stick together, the momentum of the whole is the sum of the momenta of the parts.
- Use vectors in solving collision and explosion problems.
- Review vectors, including drawing them.

- Recognize that force is the rate of cchange of momentum: F = Δp/Δt.
- Recognize that a large momentum will require a bigger force or a longer time to stop.
- Determine the direction of force in a collision, and recognize it as the mechanism of transfering momentum between the objects.

- Recall that energy is also conserved.
- Determine how much energy is lost to heat in a collision in which the start and end state are known.
- Solve problems using just energy and momentum conservation, then verify them in other ways.

- Determine the
**center of mass velocity**as the velocity that would result from an inelastic collision. - Figure out what will happen in an elastic collision by first finding this, then bouncing the objects back to preserve their energy.
- Recognize and apply conceptual rules for 1D collisions between balls of smaller, greater, or equal masses.

- Recognize that a 2D elastic collision really only happens in one component; the other is unchanged.
- Calculate the result of a 2D elastic collision.

- If a stationary object is struck by a moving one, the behavior of both after the collision depends on whether the stationary object is heavier, lighter, or the same mass as the other.
- Apply collision rules to determine the approximate result of one dimensional and two dimensional collisions.

- Calculate momentum and recognize that it is conserved.
- Relate momentum to other mechanical properties such as force and energy.
- Determine the result of one and two dimensional collisions, elastic and inelastic.

- Recognize that light is a type of wave.
- Know that the medium that light travels through is electric and magnetic fields, which allows light to go through space, where there is no matter to oscillate.
- Know that light always travels at a speed of 3×10
^{8}m/s.

- Recognize that visible light is just a tiny part of the entire spectrum of frequencies of electromagnetic radiation.
- Recognize the order of the parts of the spectrum, and know what we use each part for.
- Understand the relationship between wavelength and frequency and recognize that wavelength relates to the size of the object producing a wave.

- Waves are produces by oscillation and make objects oscillate. Know the causes and effects of light:
- Oscillation of electrons in large objects like an antenna (radio)
- Molecular motion, like rotation of water molecules (microwave) or heat vibration (infrared through ultraviolet)
- Electrons within an atom moving between energy levels (infrared through x-ray)
- Transfomations within the nucleus of an atom (gamma rays)

- Recognize that light is emitted in discrete packets called
**photons**. - Find the energy of a photon: E = hf, where h = 6.626×10
^{-34}J/Hz - Relate photon energy to the energy level transitions in an atom.
- Recognize that higher frequencies are more energetic and therefore more dangerous.

- Recognize that all objects "glow" with a wavelength dependent on their temperature.
- Recognize that because the energy of individual molecules varies, thermal radiation produces a broad, continuous spectrum of frequencies.
- Calculate the peak wavelength of thermal emission: λ = .0029 / T, for T in Kelvins

- Understand the basic principal of reflection: a light ray reflects back from a mirror at the same angle it hit.
- Trace out the paths of rays of light hitting a mirror of any shape, by duplicating angles.
- Recognize that certain mirror
**focus**parallel light beams to a certain**focal point**. - Use parallel rays and rays through the center of a mirror to locate the image of an object.

- Recognize that light travels more slowly in water or glass than it does in air.
- Recognize that this changes the wavelength, not the frequency, of the light.
- Recognize that because of this, light that comes in at an angle needs to bend its angle.
- Understand that light going into a less dense material will bend toward the surface, and light going into a more dense material will bend away.

- Recognize that light is an electromagnetic wave that travels with a speed of 3×10
^{8}m/s - Identify the different parts of the electromagnetic spectrum and our uses for them.
- Identify characteristics such as wavelength, frequency, energy, temperature, and size of emitters and receivers, and how they are related.
- Trace the path of light rays in reflection and refraction.

- A situation is in equilibrium if it is balanced and unchanging.
- An equilibrium is unstable if a slight change will cause it to fall out of equilibrium.
- If a situation is in stable equilibrium,
**and**there is something (like inertia) that causes it to constantly swing**past**that equilibrium, we say that it will**oscillate**: move back and forth. - Rate of oscillation is measured with two values: the
**period**, or how long it takes to oscillate once, and the**frequency**, or how many times it oscillates in a second.

- When a harmonic oscillator is connected to something else oscillating at that same frequency, it will also start to oscillate.
- There are many examples of this in our daily life, such as swinging on a swing set.
- This results in energy being transfered from one oscillator to the other.

- Recognize four properties of a wave: period, frequency, wavelength, and wave speed.
- Understand that a wave is like a moving oscillation.
- Use the ideas of wavelength to discuss similar situations like people walking.

- Recognize that a standing wave forms when a medium is bounded at both ends and the total distance a wave has to travel to return to its start position is a multiple of its wavelength.
- Identify the
**nodes**and**antinodes**in a standing wave. - Classify standing waves as mode 1, mode 2, etc. based on the number of nodes and antinodes.
- Relate the wavelength of the standing wave to the length of the rope.

- Understand the difference between
**transverse**and**longitudinal**waves. - Recognize that sound can travel through any type of matter, not just air.
- Recognize that sound travels faster in denser materials.
- Calculate the frequency of a standing wave in a simple musical instrument.

- Measure and relate the characteristics of waves and oscillation - period, frequency, wavelength, speed
- Determine what sort of standing wave can form in a medium based on the characteristics of the ends.
- Relate the concept of waves, standing waves, and resonance to real-life situations.

- Recognize that matter is comprised of protons (positive charge), fixed in place, which form the structure of the matter, and electrons (negative charge), which are free to move.
- Recognize that most objects are neutrally charged because each electron in them is paired with a proton.
- Recognize that two objects with the same sort of charge will be pushed away from each other, while two objects with the same sort of charge will be attracted.
- Recognize that some objects have a greater hold on their electrons than others, and might steal electrons from other objects as a result.

- Recognize that matter is comprised of protons (positive charge), fixed in place, which form the structure of the matter, and electrons (negative charge), which are free to move.
- Recognize that individual electrons will try to run toward a positively charged object or away from a negatively charged one.
- Understand that some materials, such as metals, allow electrons to be freely conducted around, while others fix electrons in place.

- Recognize that matter is comprised of protons (positive charge), fixed in place, which form the structure of the matter, and electrons (negative charge), which are free to move.
- Recognize that individual electrons will try to run toward a positively charged object or away from a negatively charged one.
- Explain how polarization results in neutrally charged objects being attracted to positively charged ones.

- Recognize that matter is comprised of protons (positive charge), fixed in place, which form the structure of the matter, and electrons (negative charge), which are free to move.
- Recognize that individual electrons will try to run toward a positively charged object or away from a negatively charged one.
- Understand that charging by induction is just separating the parts of a polarized object.
- Understand why it is necessary to break contack while still polarized for induction to happen.

- Understand that matter is made up of huge numbers of protons (+) and electrons (-) and that they are attracted to each other while repelling from the same type.
- Use these concepts to explain triboelectrification, conduction, polarization, and induction.
- Identify situations in which each of these phenomena occur, and track charge throughout a process.

- Understand that batteries produce a potential difference, and current flows from high to low voltage.
- Understand that only the
**difference**in potential between two points is relevant when trying to figure out where and how fast electrons flow. - Find the potential at each node in a circuit, and identify the direction of electron flow through each wire.

- Apply Ohm's law to find the current, voltage, or resistance of any component given the other quantities.
- Recognize that Ohm's law is saying that the amount of current depends on a slope: the amount of voltage drop per ohm of resistance.
- Understand that many resistors in a line combine their resistance, but that separate branches each draw their own current from the same voltage.

- Visualize electrical current as similar to water in a pipe or stream.
- Recognize that when two currents flow together or one current splits, the total current coming in must equal the total current going out from that point.
- Solve problems using Ohm's law and this current relationship.

- Find the Thevenin equivalent resistance of any collection of resistors.
- Recognize that in general, two resistors in parallel will have less resistance than either alone, while two resistors in series will have the combined resistance of each alone.
- Relate resistors to traffic jams - recognize that when two paths are open, the conductances add, while when two traffic jams are on the same street, the resistances add.

- Use equivalent resistance to determine the current going into a circuit.
- Use Ohm's law to relate the current, resistance, and voltage drop across a path.
- Use the current law to relate the currents in different paths.
- Given a circuit, find the current through each path by a combination of these methods.

- Understand Ohm's Law, Kirchoff's Laws, and Thevenin equivalents, and know where to apply each.
- Solve circuits using any combination of the above.
- Understand what voltage, current, and resistance are and what values for each are expected in real-life circuits.
- Solve electrostatics problems and identify examples of triboelectrification, conduction, polarization, and induction.

- Recognize that what we sense as hot or cold is really our nerves telling us that heat is traveling into our out of our skin.
- Recognize that heat will travel from a warmer object to a cooler one.
- Understand that when two objects are at the same temperature, heat stops flowing, and we say that they are
**in thermal equilibrium.**

- Understand that
**temperature**is what we use to measure how hot or cold an object is. - Recognize that as time goes on, objects that are in contact will want to equalize their temperatures.
- Know some factors, such as insulation, amount of area in contact, and difference in temperature, that affect how quickly heat flows.
- Convert between the three main temperature scales: °F, °C, and K.

- Recognize that temperature is how much kinetic energy
**each**molecule in an object has, whereas heat energy is the**total**kinetic energy of**all**the molecules. - Relate temperature, number of molecules, and total heat energy, using simplified units.
- Using simplified units, calculate the equilibrium temperature, when two objects are put together, by calculating how much heat energy there is in each object and spreading that out over all the molecules in the two objects.

- Understand that
**heat capacity**determines how much heat it takes to change the temperature of an object by 1 °C. - Understand that different materials have different
**specific heat capacities**that determine how much heat capacity an object of that material has per kilogram. - Calculate the total amount of heat energy present in an object by multiplying its heat capacity by its temperature in Kelvins.
- Calculate the equilibrium temperature of two objects by dividing their total heat by their total heat capacity.

- Recognize that some materials allow heat to transfer more easily.
- Recognize that a thicker barrier is a better insulator, and that the more area something has, the faster heat transfers out of it.
- Calculate the rate of heat loss across a given barrier, and relate this to change in temperature.

- Matter can exist in an of three phases: solid, liquid, or gas.
- In a liquid, the molecules are more free to move around than they are in a solid, and in a gas they are the freest of all.
- Energy is required to give molecules this freedom.
- The energy required to melt or boil one kilogram of a material is called the
**specific heat of melting**or of**boiling.**

- Recognize that heat is a type of energy, in the form of vibration of atoms, that will transfer from hotter objects to colder ones.
- Understand that temperature is based on the average kinetic energy of one molecule.
- Convert between the various temperature scales.
- Use heat capacity to relate temperature to heat energy. The heat capacity of an object is how much energy it takes to raise that object's temperature by one degree Celsius.
- Relate heat energy to power, calculating the power escaping through a wall or using the power produced by something to figure out how much a room will be heated.
- Recognize situations where matter is changing phase, and know that during a phase change, the temperature remains constant and the energy is used to break bonds rather than to heat molecules.

- Be comfortable using a number line, and understand the meaning of both positive and negative numbers.
- Think about addition as shifting a number in one direction or the other, and figure out what addition is needed to shift one number to another.
- Recognize function notation, and be able to write and use functions for simple addition transformations.

- Recognize that an
**inverse**function is a way to find out what the input was given the output. - Write an inverse function by reversing the function's steps in the reverse order.
- Recognize that addition and subtraction are inverses.
- Be aware that I can push a number through a function backwards instead of explicitly writing out the inverse function.

- Make use of the
*associative property*: two operations of the same kind that follow each other in a function may be combined. - Make use of the
*transitive property*: a function from**A**to**B**can be combined with one from**B**to**C**to make one from**A**to**C**. - Recognize how both of these properties follow intuitively from the properties of the number line and the meaning of a function.
- Use some combination of these two properties, and the concept of inverse functions, to solve word problems.

- Solve problems by labeling numbers and drawing out functions on a number line.
- Understand and make use of reversibility and the associative and transitive properties
- Practice extracting from a word problem a functional description of how numbers are related.

- Identify what "feature" of an object is the number involved in a comparison
- Translate between mathematical and conversational language
- Use a number line to model a situation

- Practice writing, using, reversing, and combining change functions.
- Recognize that I cannot combine two similar operations unless they are right next to each other
- Use the distributive property to rearrange a function by pushing an addition "through" a multiplication

- Write a function that reflects the number line across any given point
- Recognize how this can be used in solving word problems

- Work comfortably with the concepts of function, input and output, and the number line.
- Recognize reflection and shift relations among the numbers in a word problem.
- Apply reversibility and the transitive, distributive, and associative properties to combine and simplify functions.

- Be able to express as a function any relationship between two numbers that represent the same feature.
- Visualize functions as transformations on the number line, and explain them as relationships in English.
- Combine and simplify functions using the rules of mathematics.

- Recognize that a graph shows a relationship between two numbers.
- Use a graph both forward and backwards to find the value of one number corresponding to some value of another.
- Use graphs and functions interchangeably in processing numbers.

- Given a function, represent it as a table or graph
- Recognize the identity and negation function and functions
- Use a graph as a relationship to which the transitive property may be applied

- Describe the transformation needed to get from the identity graph to a given graph.
- Recognize what the effect will be when I use the transitive property to join two function graphs.

- Be able to visualize the effect of a transformation on a number line, and determine what transformation would have a given effect.
- Recognize that transformations that can happen on a number line can be applied to either axis of a graph.
- Recognize the effects of transformations on a graph, and write transformations to have a desired effect.
- Relate this to the form of a function graph.

- FInd the slope of a graph that goes through the origin
- Recognize that this can be shifted up or down with addition
- Write the function form of any linear graph

- Recognize that if two numbers in a problem refer to
**different sorts of things**, I need to figure out how many of one are worth how many of the other. - Use a relationship like this as a starting point to determine a function or its graph.

- Recognize that multiplication changes my numbers from dealing with one ting to dealing with another.
- Identify whether an addition is in units of one or the other type of thing by where it is in the function.
- "Push" an addition forward through a multiplication by multiplying, or backwards by dividing.

- Understand how to apply order of operations when simplifying an algebraic expression.
- Convert from an algebraic expression to function notation and back.
- Use what you know about function notation to aid in solving and simplifying expressions.

- Determine how much of one thing is worth how much of another, and create a function from that.
- Use and convert between various ways of representing a relationship: function, graph, transformation, word problem, symbolic notation.
- Apply the transitive, associative, and distributive properties to combine and simplify relations.

- Given two points, determine the function relating them.
- Describe transformations in terms of scaling, flipping, and shifting.
- Given a function, represent it as a transformation, a graph, a word problem, and an equation.

- Make measurements, estimating one decimal point beyond what your scale shows
- Estimate where on a ruler or number line a given number would fall
- Answer word problems involving length and measurement

- Figure out the value of unlabeled tick marks on a number line
- Convert comfortably from fractions to decimals
- Understand what it means to have a decimal number as the numerator of a fraction

- Be comfortable measuring things in inches or meters, using fractions and decimals
- Confidently locate numbers on a number line
- Understand that a number can be represented in many different ways, and all sorts of numbers live together on the number line

- Recognize the difference between measuring division and sharing division and know when to use which one
- Understand the meaning of the integer and decimal parts of the answer to a division, and know how they relate to the remainder
- Understand fractions in several different ways showing different interpretations of division

- Measure a position on a number line by counting how many marks it is over from a label and adding the count times the size of a mark.
- Use the "measurement" sort of division to solve word problems, particularly when there is a remainder involved.
- Recognize that in a division result, the whole number part times the size of a group gives the number of objects in full groups, whereas the decimal part times the size of a group gives the amount in the last, partial group.
- Solve problems where a known length needs to be broken up according to a certain rule.

- Recognize that division changes what sort of thing I am dealing with
- When doing a division problem, carefully identify what is the total amount, the size of a group, and the number of groups
- Understand the meaning of the integer and decimal parts of the answer to a division, and know how they relate to the remainder

- Practice identifying what in a word problem is the total, number of parts, and size of a part.
- Practice working with remainders and with fractional answers.

- Understand continued fractions as a process for measuring
- Convert into and out of continued fraction notation
- Use the concept of continued fractions to gain a more robust understanding of what a fraction is

- Energy is the capacity to do work; it makes something "dangerous."
- A moving object has kinetic energy.
- An object lifted above the ground has potential energy.
- The total amount of energy in any situation doesn't change over time.

- The more weight an object has and the higher up it is, the more potential energy it has.
- The equation for this is
*PE*, where the subscript "g" stands for "gravitational"._{g}= mgh - Solve problems involving figuring out how much kinetic or potential energy changes when an object moves from one position to another.

- Recognize that kinetic energy is bigger for an object with bigger mass or faster velocity.
- Calculate kinetic energy:
*KE = ½mv²* - Solve problems that involve finding the speed of a projectile at various heights, and vice versa.

- Read an energy graph, determining the total, potential, and kinetic energy at any position.
- Determine how far an object will roll on an energy graph.
- Determine when an object is moving quickly, slowly, or stopped on an energy graph.

- Read the potential, kinetic, and total energy off of an energy graph.
- Describe when on an energy graph the object is speeding up or slowing down.
- Read a graph with multiple types of potential energy added together.
- Recognize the shape of gravitational potential on a height-versus-energy graph.

- Use a know portion of an energy graph, and information about where on the graph an object rolls to and from, to trace out the potential of the unknown part.

- Recognize that pushing an object while it moves some distance changes its energy.
- Identify situations where the work is positive or negative.
- Use the rate-of-change equation F = ΔE / Δs.

- Recognize that a force will cause the total energy line of an object to slope.
- Recognize that the slope of a hill is the force needed to roll the object up it.
- Determine the work being done on an object at various points on a graph by the slope of its total energy.

- Recognize that friction will give the total energy line a downward slope equal to the friction force.
- Determine where on a grap an object acted on by friction will stop.
- Determine using the rate of change equation or a graph how far the object will roll, in total, before stopping.

- Draw a graph of force versus position, given a graph of energy.
- Draw an energy graph given the force graph.
- Use an energy graph generated in this way to answer questions about the object's potential and kinetic energy at various points in its journey.

- Use equations to find potential and kinetic energy, and relate these with the law of conservation of energy.
- Use the work-force relationship to solve problems where the total energy of an object is changing.
- Use graphs to represtne problems where an object has a varying amount of potential, kinetic, and total energy as it moves from position ot position.
- Be able to generate a force graph from an energy graph and vice versa.

- Recognize that mass gives an object
**inertia**, a tendency to resist acceleration. - Understand in terms of inertia why heavier objects (car, bowling ball) are harder to move than lighter ones (bicycle, baseball).
- Know Newton's first law, that the motion of an object changes only if there is a force exerted on it.

- Know Newton's second law: F = ma
- When looking at an equation, be able to say how a change in one variable will change another variable
- Recognize newton's second law as an expression, mathematically, of what we know about inertia

- Draw force diagrams with forces in the horizontal and vertical directions.
- Determine the net force from a force diagram.
- Determine the missing forces in a force diagram, given the net force.
- Recognize that the net force is what is used in Newton's second law.
- Recognize that no acceleration means a net force of zero.

- Be familiar with the idea of μ, the coefficient of friction, representing how sticky a surface is.
- Know how μ relates the friction force and the normal force.
- Recognize that pressing two surfaces together more increases the force required to slide them past each other, and that the normal force is the force with which two surfaces are pushed together.
- Be able to solve out force diagrams involving normal, gravity, friction, and applied forces, acting in either the vertical or the horizontal direction.

- Recognize that the trig functions give a
**ratio**between two sides of a**right**triangle. - Recognize that the angles of a triangle sum to 180°, so that if one is a right angle the other two must add up to 90°.
- Be able to solve for any side of a right triangle given one side and one of the acute angles.

- Given an angle, construct a useful triangle on which to apply trig.
- Given a force and the angle at which it is pulling, "resolve" it into and components.
- Find the net force when several angled forces are added.

- Given a force diagram with many forces, some of them at an angle, determine the net force, or the strength of any missing force.
- Recognize that any part of an object has its own force diagram, and must balance individually.
- Be aware of the ways that friction and normal forces are deceptively intertwined.

- Be able to find the strength of a force, given one of its components.
- Be able to find the net force from acceleration and use that to solve a force diagram.

- Identify what sort of forces are acting on an object: gravity, normal, tension, friction, applied.
- Recognize that forces add as vectors, and find the net force.
- Using trigonometry, find a componnt given the full force, or find the force given a component.

- Know and apply Newton's third law.
- Be able to sketch the force diagrams for several objects, given the requirement of matching force pairs.
- By recognizing force pairs, determine in what way several objects must be in contact with each other.

- Know and apply Newton's three laws.
- Draw force diagrams representing any given situation.
- Use equations to find the acceleration, coefficient of friction, and gravity force.
- Balance a force diagram, resolving forces into components as needed.

- Lab introduces the concept of vectors as directions.
- A vector has two components, x and y. It changes both coordinates of my position.
- Be comfortable with adding head-to-tail.
- Be able to separate out components and add them each up individually.

- Recognize that a vector is merely a description of how much the x and y coordinates of something change by.
- Determine the vector between two given (x, y) points.
- Add vectors, recognizing that the components add separately.
- Add vectors graphically by head-to-tail placing.

- Determine change for vector quantities and for coordinates.
- Recognize that position, velocity, and acceleration are vectors.
- Subtract vectors algebraically and graphically.
- Be very careful to follow the distributive property.

- Be able to scale a vector graphically or algebraically.
- Find rate of change of a vector.
- Use vectors in simple equations.
- Recognize that time is a "scalar".

- Use separation of components to determine when a projectile will hit the ground.
- Use the free fall graphs then dealing with projectiles.
- Recognize that in the horizontal direction, the speed of a projectile is constant.

- Determine the vector difference between two (x, y) positions.
- Add, subtract, and scale vectors.
- Use vectors in the motion equations, recognizing that position, velocity, and acceleration are vectors and time is a scalar.
- Solve projectile motion problems.

- Create a position versus time graph representing a person's motion.
- Read position and time data from a graph.
- Relate the shape of a graph to the motion of an object.

- Determine from a position graph at what time an object was moving forward, backwards, changing direction, or standing still.
- Determine the velocity of an object by finding the slope of a position graph.
- Recognize that velocity contains information about both speed and direction, whereas speed has no direction.

- Recognize acceleration and direction of acceleration in a graph.
- Be able to describe an object in a graph as speeding up or slowing down.

- Read graphs of position, velocity, and acceleration versus time.
- Connect what you knwo about velocity and acceleration on position graphs to velocity and acceleration graphs.
- Recognize that all three graphs are dealing with the same times.

- Recognize what sort of story is being told by a position graph with multiple objects.
- Be able to recognize when two objects meet, how far apart they are at some time, and how much of a difference in time there is between when they reach somme position.
- Be able to make a multiple-object graph that tells a given story.

- Determine the
**change**in a variable by subtracting the final value from the initial. - Determine the rate of change of one variable with respect to another, by dividing the change in the first variable by the change in the second variable.
- Recognize that slope is a rate of change.
- Recognize that velocity is the rate of change of position, and that acceleration is the rate of change of velocity.

- Use the average velocity equations to determine how far an object will move while accelerating, given its start and end velocities.
- Solve for any variable in the joined equation, given the other variables' values.
- Relate these equations to what you know about graphs.

- Use the equation Δs = v
_{i}Δt + ½aΔt² - Recognize that the equations for determining displacement from acceleration require that you be dealing with a time of constant acceleration.
- Recognize how this equation relates to graphs, and be able to plot the position graph it predicts.

- Practice using the seven linear motion equations.
- Be able to identify which variable(s) are present in a problem statement.
- Be able to quickly (in one line) solve any equation for any variable.

- Use the free fall acceleration of -9.8 m/s² in dealing with problems with thrown or released objects.
- Be comfortable dealing with both horizontal and vertical motion.

- Review and organize all the equations we have used in linear motion
- Know how to choose which equation to use in a problem
- Deal comfortably with problems that ask you to use two or more equations in series to arrive at the answer

- Use the free fall displacement and velocity graphs to answer questions
- Be able to translate the requirements of a problem into a set of statements about the graph of an object's motion
- Understand why this is a powerful tool

- Determine the slope of a graph.
- Use slope to find velocity from a position graph and acceleration from a velocity graph.
- Determine slope even at a point where the graph is not a straight line, by drawing a tangent.

- Understand and use graphs of position, velocity, and acceleration versus time.
- Generate the other two graphs from any one of these (and appropriate starting conditions).
- Answer questions that require you to read several graphs, connecting them through the time coordinate.

- Read information from graphs, including position, time, and sign of acceleration and velocity.
- Generate the other graphs from any one of acceleration, velocity, or position.
- Use the linear motion equations, and pick intelligently which to use.

- Solve a word problem using either graphs or equations.
- Think carefully about what our various linear motion relationships do and do not allow you to deduce.

- Be aware of how you use scientific problem solving in your everyday life.
- Devise a
**hypothesis**and an**experiment**to test it, and**predict**what should happen if your hypothesis is true. - The purpose of a scientific experiment is to be able to test a hypothesis by comparing the predicted result to the actual result.

- Using the Unitary game, practice thinking about what combinations of units are needed to make other units.
- Practice multiplying, dividing, and canceling algebraic expressions made up of variables.

- Recognize that in Unitary, playing a card represents multiplying by its units, and playing a card upside-down represents dividing by it.
- Be able to generate an equation from a string of Unitary plays.
- Using skills from Unitary, be able to predict an equation that will link values with known units.

- Pick out of a problem what physics quantities you have values for, and what their units are.
- In any quantitative (numerical) problem, list out what you have, what you want, what equation you will use, and what the answer is.
- In the absence of any better way to solve the problem, be able to create an equation that puts together those units to get the sort of units you want.

- Guess what physics quantities might matter in an experiment, by imagining what would happen if you changed that quantity. You will get much better at this later in the year, once you actually understand intuitively what all these quantities mean!
- Set up an experiment to compare actual measured results to the results predicted by a hypothesis equation generated through dimensional analysis.
- Revise that equation by adding a constant factor to make the predictions match the results.

(Use dimensional analysis to predict an equation for how long it takes a weight on the end of a string to swing once)

(When I pluck an end of a stretched string, a little kink or "pulse" shoots along the string and bounces back toward me when it hits the other end. Use dimensional analysis to find an equation for how long this takes.)

- Be aware that rather than names, we usually use one-letter variables to represent physics quantities, possibly with other letters attached to further describe them.
- Evaluate a mathematical expression involving both numbers and units, by working out first the numbers, then the units.
- Be aware that when squaring or square rooting an expression, both units and numbers are affected.
- Use units to check yourself for mathematical errors.

- Convert using the factor-label procedure.
- Be able to do this even when complex units are involved.
- Be aware that all measurements in physics must be converted to kg, m, and s.
- Know that 1 m = 100 cm, 1 kg = 1000 g.

- Solve an equation for any given variable.
- Know how to reverse any operation.
- Use order of operations to figure out what the last thing done to a variable was.
- Use a given physics equation to solve for any one of the variables in it.

- Use
**dimensional analysis**to determine what equation relates some quantities, based on how their units go together. - Use
**factor-label conversion**to convert any simple or complex measurement into a standard kg-m-s units. - Use
**symbolic manipulation**to solve any equation for any variable.