| OUTCOME/
ESSENTIAL
QUESTION |
|
|
|
|
Begin
Fireworks Unit (Algebra)
How can I solve a complicated problem with
mathematical models?
How can I predict how high and how far my rockets
will travel? How
will I know how long it will take to reach the top
of its path? |
|
Solving
quadratic equations algebraically.
Interpreting graphs of quadratic equations.
Model real situations with quadratic equation. |
|
Distinguish
between linear and quadratic functions.
Distinguish between graphs of linear and quadratic
functions.
Review concept of factoring from area model.
Be able to factor quadratic expressions, including
perfect squares and when leading coefficient is not
one.
Use zero multiplication property and factoring to
solve quadratic equations.(N.B2.K3)
Recognize some quadratic equations as unfactorable.
Complete the square on a quadratic function to put
in vertex form. |
|
|
Finish Fireworks Unit
Begin Orchard Hideout Unit (Geometry)
How can the growth of trees be predicted over time?
When will the trees grow to the point that
there is no line of sight to the outside of my
orchard? |
|
Coordinate geometry formulas for segments and
circles.
Creating simpler situation as strategy to solve
complex problem.
Explore relationships between circles and lines.
Proof
|
|
Find x intercepts of a quadratic equation in standard form and in
vertex form.
Analyze coefficients of a quadratic equation for
placement of vertex, concavity and symmetry.
(G.B4.K7)
Review geometry from Shadows Unit.
Discover and identify a set of points meeting a
specific geometric condition.
Develop and use distance formula.
Define distance from point to a line.
Use similar triangles to find distance from a point
to a line.
Develop and use midpoint formula.
Develop concept of sector and best line of sight. |
|
Homework, classwork, presentations, observations, POW's,
assessments, portfolio
Homework, classwork, observation, POW's |
|
Continue Orchard Hideout
Begin Meadows or Malls? Unit
(Algebra)
How can a city make a decision about how to use some
land left to them, working with several constraints?
How can I represent a situation with more than 3
variables since I can't graph it? |
|
Develop formulas for circumference and area of circle
Develop concept of pi
as irrational number.
Logic and Proof
Review concept of Linear Programming in 2 variables.
Review writing constraints symbolically. |
|
Use concept of circle and distance formula to derive equation of
a circle with center at (a,b) with radius r.
Use completing the square to put equation of circle
into standard form.
A.B2.K1
Define inscribed circles and polygons.
Define circumscribed circles and polygons.
(G.B1.K8)
Use similarity to discover ratio between
circumference and radius and ratio between area and
radius squared.
Review trig functions to find area and perimeter of
regular polygons.
Work with converses of conditionals and
biconditional to develop proof.
Generalize pattern to find area and circumference
formulas for circles.
Synthesize concepts to solve unit problem.
Write constraints using variables and inequalities.
Review general strategy to solve max/min problems
Review concept of feasible region.
Find intersections without graphing. |
|
Homework, classwork, presentations, observations, POW's,
assessments, portfolio
Homework, classwork, observation |
|
| Continue Meadows or Malls? Unit |
|
Linear Programming in 3 or more variables
Develop elimination method to solve systems of
equations in 2 or more variables.
Continue to develop ways to count all possible
combinations. |
|
Generalize corner point principle to
more than 2 variables.
Identify intersection of 2 distinct lines as a
unique point unless they are parallel.
Identify intersection of two planes as a line unless
they are parallel.
Identify possible intersections of 3 planes.
Use elimination method to solve equations in 2 or
more variables.
Develop 3 dimensional coordinate system.
Be able to graph linear equations and inequalities
in 3 dimensional space and identify points of
intersection.
Be able to solve systems in 2 or 3 variables by
substitution, graphing or elimination.
Count the number of possible combinations of
intersections of constraints. |
|
|
| Continue Meadows or Malls? Unit |
|
Develop matrices to organize data.
Use matrices to represent system of equations. |
|
Identify intersecting, inconsistent and dependent systems of
equations.
Solve system of 4 equations and 4 unknowns.
Find the equation of a line between 2 points using a
system of equations.
Find the equation of a quadratic function through 3
points using a system of equations.
Develop concept of matrix, rows and columns
Define matrix addition and subtraction.
Define matrix multiplication.
Define compatible matrices srt an operation.
Write the matrix equation that could represent a
system of equations.
Use calculator to add, subtract and multiply
matrices.
|
|
| Homework, Classwork, observations, presentations, POW's |
|
Finish Meadows or Malls? Unit
Begin Small World, Isn't It?
Unit (Algebra)
When will the world's population be so crowded we
will all be squashed up against each other? How can
I use math to model this situation? |
|
Develop concept of inverse matrix
Use matrix equations to solve unit problem.
Rate of change
Slope and Linear Functions
Proof |
|
Be able to find the inverse of a 2x2 matrix without the
calculator.
Use the inverse matrix to solve a system of 2
equations and 2 unknowns.
Generalize the method to solve larger systems.
Find the inverse matrix for larger systems using the
calculator.
Synthesize the skills of the unit to solve the unit
problem.
Calculate average rates of change
Use % to describe rate of change wrt original value
Use step functions to model situations
Use linear functions to approximate step functions
Formalize concept of slope as rate of change of
dependent variable compared to independent variable.
Find equations of lines given a point and the slope
or two points.
Review similarity and properties of parallel lines.
Justify the independence of the slope of a line from
the choice of points. |
|
| Homework, Classwork, observation, participation, presentations,
POW's, assessments, portfolio. |
|
| Continue Small World, Isn't It? Unit |
|
Derivatives
Exponential growth -- Looking at situations modeled
by exponential functions.
Logarithmic functions
The number e
Compound interest
Sums of arithmetic series |
|
Work with equations that represent real world situations
throughout the unit.
Calculate rates of change using non-linear
functions.
Develop concept of secant lines and tangent lines.
Calculate instantaneous speed
Calculate average growth of area over time.
Define derivative of a function as instantaneous
rate of change of y wrt x or as the slope of the
tangent line at (a,b)
Analyzing special cases:
absolute value function causes derivative to
be undefined when x = 0
Review sigma notation to represent sums.
Be able to identify arithmetic sequences, initial
term, common difference.
Derive formula for nth sum.
Use recursive formula to model population growth
Use exponential function to model population growth.
Review logarithms
Review rules for evaluating exponential expressions.
Use the derivative to analyze graph wrt tilt,
turning point (point of inflection)
Introduce notation f'(x) and y'
Define e as the limit of the compounding process (1
+ 1/n)^n
Define natural logarithm
|
|
| Homework,
Classwork, observation, participation,
presentations, POW's, |
|
Finish Small World Unit
Introduce Pennant Fever Unit
(Data)
How can I calculate probability of a certain team
winning the pennant?
How can I count all the possibilities of
win/loss records?
|
|
Probability
Area and Tree Diagrams
Counting Principles
Pascal's Triangle
Binomial Distribution
and Theorem
Statistical reasoning |
|
connect f(x) = e^x to its derivative
Use area and tree diagrams to calculate probability
of events.
Use simulation to help understand a problem.
Review finding expected value.
Use probability to evaluate null hypothesis.
Review concept of equally likely events.
Be able to calculate the probability of a sequence
of events
|
|
|
| Continue Pennant Fever Unit |
|
|
Develop a mathematical model for a complex probability problem
Be able to calculate permutations and combinations
without a calculator.
Introduce notation nPr and nCr
Use factorial notation n!
Be able to state difference between permutations and
combinations.
Analyze special cases for nCr and nPr, ie when r = o
and when r = n-r
Distinguish between sampling with replacement and
sampling without replacement when calculating
probabilities.
Use combinatorial coefficient in process of solving
linear programming problems.
Use probability and combinatorial coefficients to
evaluate a null hypothesis.
Introduce the term bias and compare with random
events. |
|
| Hmk,
classwork, POW's,
presentations, observation |
|
| Finish Pennant Fever Unit |
|
| Develop the binomial theorem |
|
Identify pattern in problems such as (a + b)^n
Define concept of cumulative probability
Be able to find patterns in Pascal's triangle
Identify where the binomial coefficients are
embedded in Pascal's triangle.
Be able to use the binomial theorem to calculate
binomial coefficients.
Define binomial distribution
Synthesize skills developed in the unit to solve the
unit problem. |
|
| Hmk, classwork, assessments, POW's, portfolio |
|