Transcript Slide 1 - Images

Unit 1 Plan Math 2
Key Learning(s):
Analyzes the graphs of and solves
quadratic equations and
inequalities by factoring, taking
square roots, and using the
quadratic formula.
Topic: Quadratics and Complex
Numbers
Unit Essential Question(s):
How do I determine characteristics of a
quadratic function algebraically and
graphically?
Concept 1
Imaginary and Complex
Numbers
Concept 2
Horizontal Shifts of
Quadratic Functions
Days: 3
Days: 1
Essential Question:
How do I represent
the square root of a
negative number? How
do I simplify and
perform operations
using complex
numbers?
Vocabulary:
Vertex, Vertex form,
Horizontal Shift
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
graph paper, learning
tasks, and graphic
organizers
Concept 3
Converting from
Standard to Vertex
Form
Concept 4
Solving Quadratic
Equations by
Factoring
Concept 5
Quadratic Formula and
the Discriminant
Days: 2
Days: 1
Essential Question:
How do I graph
transformations of
quadratic functions?
How do I know when
to shift a parabola
from left to right
based on the
equation?
Essential Question:
How do I convert a
quadratic equation
from standard to
vertex form?
Essential Question:
How do I solve
quadratic equations
by factoring when the
leading coefficient is
not 1?
Essential Question:
How do I solve
quadratic equations
using the quadratic
formula? How do I use
the discriminant to
determine the nature
of roots?
Vocabulary:
Vertex, Horizontal
Shift
Vocabulary:
Vertex Form
Vocabulary:
Vocabulary:
Discriminant,
Quadratic Formula,
Nature of Roots
Days: 2
Unit 1 Plan Math 2
(Pg. 2)
Key Learning(s):
Analyzes the graphs of and solves
quadratic equations and
inequalities by factoring, taking
square roots, and using the
quadratic formula.
Topic: Quadratics and Complex
Numbers
Unit Essential Question(s):
How do I determine characteristics of a
quadratic function algebraically and
graphically?
Concept 6
Partial Sums of Arithmetic Series
Concept 7
Solving Quadratic Inequalities
Days: 1
Days: 1
Essential Question:
How can arithmetic sequences be expressed
and manipulated as functions?
Essential Question:
How do I solve quadratic inequalities
algebraically and by using a graphing
calculator?
Vocabulary:
Vocabulary:
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
graph paper
Unit 2 Plan Math 2
Key Learning(s):
Students will learn how to:
Determine side lengths of special
right triangles and apply
trigonometric ratios to right
triangles.
Concept 1
Constant ratios in
similar right triangles
Days: 1.5
Topic: Right Triangle Trigonometry
Grade: 10
Optional
Instructional Tools:
Unit Essential Question(s):
How do I determine side lengths of
special right triangles? How do I apply
sine, cosine, and tangent to solve
problems involving right triangles?
Concept 2
Special right
triangles
Days: 3
Graph paper, graphic
organizers, graphing
calculators or utility
Concept 3
Defining and using
trigonometric ratios
Concept 4
Using trigonometric
functions for
complementary angles
Concept 5
Introduction to
inverse trigonometric
functions
Days: 3
Days: 3
Days: 1
Evaluation: 1.5
Essential Question:
How do I use constant
ratios to solve similar
right triangles?
Essential Question:
How do I determine
side lengths of 30°60°- 90° triangles
and 45°- 45°- 90°
triangles?
Essential Question:
How do I use sine,
cosine, and tangent
to find missing
information in right
triangles?
Essential Question:
How do I use the
relationship between
trigonometric
functions and
complementary
angles?
Essential Question:
How do I use the
inverse trigonometric
functions on my
graphing calculator to
find angles given their
sines, cosines, or
tangents?
Vocabulary:
Similar right triangles,
Ratios
Vocabulary:
30°- 60°- 90°
triangles, 45°- 45°90° triangles
Vocabulary:
Sine, cosine,
tangent,
trigonometric ratio,
trigonometric
function
Vocabulary:
Complementary
Vocabulary:
Unit 3 Plan Math 2
Key Learning(s):
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Parts of a circle
Angle measures in a circle
Chords, tangents, and secants
Arc lengths and areas of sectors
Volume and surface area of
spheres
Concept 1
Parts of a Circle
Topic: Circles and Spheres
Grade: 10
Optional
Instructional Tools:
Unit Essential Question(s):
How do I find the measures of special segments
and angles of a circle?
How do I use and apply properties of circles to
solve various problems?
Concept 2
Angle Measures in a
Circle
Concept 3
Segments of Circles
Graphic organizers,
calculators, random
stuff ; )
Concept 4
Arc Length and Area
of a Sector
Concept 5
Volume and Surface
Area of a Sphere
Days: 4
Days: 1.5
Days: 2
Days: 2
Days: 3.5
Essential Question:
Essential Question:
Essential Question:
Essential Question:
Essential Question:
How do I distinguish among
the special segments and
angles associated with a
circle?
How do I find the
measures of various
angles formed by
intersecting segments
inside or tangent to a
circle?
How do I use triangle
similarity to understand
properties of
intersecting chords,
tangents, and secants of
circles?
How do I use the
properties of circles to
solve problems involving
the length of an arc and
the area of a sector?
How do I use and apply
surface area and volume of
a sphere? How do I
determine the effect on
surface area and volume of
changing the radius and
diameter of a sphere?
Vocabulary:
Vocabulary:
Vocabulary:
Vocabulary:
Vocabulary:
Central angle, inscribed
angle, vertex, intercepted
arc
Chord, secant, tangent, point
of tangency, central angle,
inscribed angle, intercepted
arc, similar triangles, AA
similarity
Arc length,
circumference, area of a
circle, area of a sector,
exact values, approximate
values
Radius, diameter, sphere,
surface area, volume,
circumference
Center, diameter, radius, secant,
chord, tangent, point of tangency,
central angle, inscribed angle, arc,
major arc, minor arc, semicircle
Evaluation of Unit: 1.5
days
Unit 4 Plan Math 2
Topic: Statistics
Key Learning(s):
Unit Essential Question(s):
Analyzing data by looking at
standard deviation, normal
distribution, and sample and
population distributions
Concept 1
Means, Variances, and
Standard Deviations
How do I use measures of variability and normal
distributions to analyze data?
Concept 2
The Empirical Rule
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
Graph paper, and
Learning tasks
Concept 3
The Golden Ratio
Days: 3.5
Days: 1.5
Days: 2.5
Essential Question:
How do we calculate and
interpret the relationship
among mean, variance, and
standard deviation in
problem solving?
Essential Question:
How do I determine when and how to use
empirical rule to interpret the mean and
standard deviation given a distribution of
data values?
Essential Question:
How do I make inferences on populations
and their samples using mean and
standard deviation?
Vocabulary:
Mean, Mean deviation,
Standard deviation,
Variance, Frequency ,
Frequency distribution
Vocabulary:
Empirical rule, Normal distribution,
Standard deviation, Mean, Dotplot,
Outlier, Center, Shape, Skewedness,
Symmetrical, Spread
Vocabulary:
Golden ratio, Standard deviation, Mean,
Dotplot, Sample, Population, Random
sample, Probability
Unit 4 Plan Math 2
(Pg.2)
Key Learning(s):
Analyzing data by looking at
standard deviation, normal
distribution, and sample and
population distributions
Concept 4
Comparing Population Means and
Standard Deviations
Days: 6
Topic: Statistics
Grade: 10
Optional
Instructional Tools:
Unit Essential Question(s):
How do I use measures of variability and
normal distributions to analyze data?
Concept 5
Comparing Sample and Population
Distributions
Days: 6
Graphing calculator,
Graph paper, and
Learning tasks
Concept 6
Non-Normal Distributions
Days: 6
Evaluation of Unit: 2
Essential Question:
How do I make conclusions about
data using the comparison of mean
and standard deviation?
Essential Question:
How do I make conclusions about
data based on comparing the sample
versus the population mean and the
sample versus the population
distribution?
Essential Question:
How do I determine if data has a nonnormal distribution and how do I use this
information to make conclusions about
the data?
Vocabulary:
Scatterplot, Mean, Population,
Stem-and-leaf plot, Standard
deviation, Least squares regression
line, Correlation coefficient
Vocabulary:
Mean, Population, Random Sample,
Scatterplot, Standard deviation,
Stem and leaf plot
Vocabulary:
Normal distribution, Non-normal
distribution, Dotplot, Mean, Median,
Standard deviation, Interquartile range,
Outliers
Unit 5 Plan Math 2
Key Learning(s):
Students will learn how to:
Identify and graph piecewise,
inverse, and exponential
functions.
Solve exponential equations and
inequalities.
Topic: Piecewise, Inverse, and
Exponential Functions
Unit Essential Question(s):
How do I describe and use piecewise,
inverse, and exponential functions?
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
Graph paper, Learning
tasks, Graphic
organizers
Concept 1
Piecewise Functions
Concept 2
Points of
Discontinuity
Concept 3
Floor Functions
Concept 4
Ceiling Functions
Concept 5
Solving Exponential
Equations and
Inequalities
Days: 2
Days: 1
Days: 1
Days: 2
Days: 2
Essential Question:
How do I identify,
describe, and graph
piecewise functions?
Essential Question:
How do I identify
points of
discontinuity in
piecewise functions?
Essential Question:
How do I graph a
greatest integer
function? How do I
determine if a
piecewise function is
a floor function?
Essential Question:
How do I determine
if a piecewise
function is a ceiling
function?
Essential Question:
How do I use
properties of
exponents to simplify
algebraic expressions
and solve exponential
equations and
inequalities?
Vocabulary:
Piecewise function
Vocabulary:
Point of discontinuity
Vocabulary:
Step function, Floor
function, Greatest
integer function
Vocabulary:
Step function, Ceiling
function
Vocabulary:
Unit 5 Plan Math 2
(Pg. 2)
Key Learning(s):
Topic: Piecewise, Inverse, and
Exponential Functions
Unit Essential Question(s):
Students will learn how to:
Identify and graph piecewise,
inverse, and exponential
functions.
Solve exponential equations and
inequalities.
How do I describe and use piecewise,
inverse, and exponential functions?
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
Graph paper, Learning
tasks, Graphic
organizers
Concept 6
Transformations of Exponential
Functions
Concept 7
Geometric Sequences
Concept 8
Inverse Functions
Concept 9
Composition of Functions
Days: 2
Days: 2
Days: 5
Days: 2
Evaluation of Unit: 2 days
Essential Question:
How do I graph
transformations of exponential
functions?
Essential Question:
How do I use the common
ratio in a geometric
sequence with exponential
functions?
Essential Question:
How do I determine the
inverses of linear,
quadratic, and power
functions? How do I
describe the graphs of
inverse functions?
Essential Question:
How do I use composition
of functions to verify that
functions are inverses of
each other?
Vocabulary:
Vocabulary:
Common Ratio, Geometric
Sequence
Vocabulary:
Inverse function, Oneto-oneness
Vocabulary:
Composition of functions
Unit 6 Plan Math 2
Topic: Finding the Best Model
Key Learning(s):
Unit Essential Question(s):
Analyzing data and finding a model
that best fits the data
Solving Absolute value equations
and inequalities
How do I find a model that best fits a set of data?
How do I solve absolute value equations and
inequalities? How do I describe relationships using
causation and correlation?
Grade: 10
Optional
Instructional Tools:
Graphing calculator,
Graph paper, Learning
tasks, and Graphic
organizers
Concept 1
Solving Absolute Value
Equations and Inequalities
Concept 2
Choosing Appropriate Models for a Set
of Data
Concept 3
Correlation and Causation
Days: 3
Days: 5
Days: 3.5
Essential Question:
How do I solve absolute
value equations and
inequalities both
algebraically and
graphically?
Essential Question:
How do I determine the best fitting
model for a set of data using visual
approximation, median-median line, and
least squares regression?
Essential Question:
How do I use the correlation coefficient
to determine the strength and direction
of a linear relationship? How do I
distinguish between correlation and the
causation between two quantitative
variables?
Vocabulary:
Vocabulary:
Extrapolation, Interpolation, Linear
regression line, Least Squares
Regression line, Median-median line,
Method of finite differences, Quadratic
regression, Regression curve
Vocabulary:
Correlation coefficient, Correlation,
Causation