content standard from MST (one or more of the seven):
one-Students will use mathematical analysis, scientific inquiry,
and engineering design, as appropriate, to pose questions, seek
answers, and develop solutions.
will understand mathematics and become mathematically confident
by communicating and reasoning mathematically, by applying mathematics
in real-world settings, and by solving problems through the integrated
study of number systems, geometry, algebra, data analysis, probability
Students will understand and apply scientific concepts, principles
and theories pertaining to the physical setting and living environment
and recognize historical ideas in science.
Students will apply technological knowledge and skills to design,
construct, use and evaluate products and systems to satisfy human
and environmental needs.
Students will understand the relationships and common themes that
connect mathematics, science and technology and apply the themes
to these and other areas of learning.
standards (what you want your students to know or be able to do)
- Use algebraic
and geometric representations to describe and compare data.
- Apply algebraic
and geometric concepts and skills to the solution of problems.
- Use various
means of representing and organizing observations and interpret
the organized data.
problem situations symbolically by using algebraic expressions,
sequences, tree diagrams, geometric figures and graphs.
appropriate representations to facilitate the solving of a problem.
the appropriate tools for measurement.
- Use trigonometry
as a method to measure indirectly.
- Apply proportions
to scale drawings in order to compute indirect measurements.
and predict different patterns of motion of objects.
appropriate tools, instruments and equipment and use them correctly
to process materials, energy and information.
- Find and
use mathematical models that behave in the same manner as processes
standards (how you will know that they know--how good is good
- Daily checks
for understanding in the form of questions, quizzes and activities.
and completeness of laboratory experiments.
problem solving and evaluation grade.
Content standards or outcomes for your unit: Be sure to identify
all the constructs you will be assessing. They should help your students
achieve the above
scalars and vectors in terms of direction.
add, subtract and scalar multiply vectors to find the desired
Resultant (or Equilibrant, in the case of vector forces).
forces and the three kinematical quantities of acceleration,
velocity and displacement as scaled arrows, whose length is
proportional to a magnitude and whose orientation is that of
the given vectors orientation.
and contrast the parallelogram method vs. the head-to-tail method
of adding vectors.
a given vector into components, pairs of components and finally
two mutually perpendicular and independent component pair.
the given equations for finding the scalar magnitudes of x-
and y-component vectors.
the given equations to find a vector from its x- and y-components.
the effects the angle between two vectors has on their resultant.
component force vectors in a pendulum, an inclined plane, a
ladder, and a plane in flight.
Performance measures for your unit: Describe how you will know
that you have achieved your unit outcomes. Attach all instruments or assessment
activities (see Chapter 7).
completion of the three laboratory experiments and exercises,
- A passing
grade on the evaluation, attached.
exercises to be graded on the accuracy and completion of all
tables, diagrams, graphs and questions. Units and vector direction
are stressed in these labs.
of error between actual results and experimental results is
the basis for accuracy in these labs.
activity Laboratory Exercises
of scalar and vector quantities Intro to vector representation
- Vector Operations
- A+B paralleogram
method Displacement vector lab
- A+B head-to-tail
- Problem solving
session Plane and boat velocities
- Vector components
- Force components
(Equilibrant, Resultant) Expt. 6- Combining forces
- Resolution perpendicular
- Vector resolution
and trigonometric methods Expt. 7- Boom Lab
- Evaluation on
List all scientific quantities that the students know and ask if they
have a direction.
Negating and scaling a given vector.
Utilize forces required to move a heavy piano.
Stress importance of this method because of its use in adding many vectors
method is limited to two vectors).
Homework problems solved by students at board.
Draw a large vector on board and ask what vectors could have composed
Set-up an equilibrium situation and analyze forces.
Show the proof of perpendicular vector resolution.
Reinforce trigonometric method as the more useful of the two methods.