Number, Number Sense
and Operations

(Based
on State of Ohio
Curriculum
Standards)

1. Determine what properties hold for matrix addition and matrix
multiplication; e.g., use examples to show addition is commutative and when
multiplication is not commutative.


Modeling
and Solving TwoStep Equations Solve a
two‑step equation using a cup‑and‑counter model. Use step‑by‑step feedback to
diagnose and correct incorrect steps.

Solving Formulas for any Variable Choose
the correct steps to solve a formula for a given variable. Use the feedback to
diagnose incorrect steps.

Solving TwoStep Equations Choose the
correct steps to solve a twostep equation. Use the feedback to diagnose
incorrect steps.

2. Determine what properties hold for vector addition and
multiplication, and for scalar multiplication.


Vectors Manipulate the magnitude and direction
of two vectors to generate a sum and learn vector addition. The x and y
components can be displayed, along with the dot product of the two vectors.

3. Represent complex numbers on the complex plane.


Math
Dictionary animation for kids This is an outstanding website
allowing you to explore a comprehensive view of math with many examples
4 Star

4. Use matrices to represent given information in a problem
situation.


5. Model, using the coordinate plane, vector addition and scalar
multiplication.


Vectors
Manipulate the magnitude and direction of two
vectors to generate a sum and learn vector addition. The x and y components
can be displayed, along with the dot product of the two vectors.

6. Compute sums, differences and
products of matrices using paper and pencil calculations for simple cases,
and technology for more complicated cases.


Matrices:
An Introduction This study guide
from Encyclopedia Britannica covers a discussion of the basic aspects of
matrices, including labeling, equality of two matrices, and addition,
subtraction, and multiplication of matrices.

7. Compute sums, differences, products and quotients of complex
numbers.


Points in the Complex
Plane  Activity A
Identify the imaginary and real coordinates of a point in the complex plane.
Drag the point in the plane and investigate how the coordinates change in
response.

8. Use fractional and negative exponents as optional ways of
representing and finding solutions for problem situations; e.g., 272/3 =
(271/3)2 = 9.


Mathway
This a step by step math solver for General Math, Geometry, Algebra, Pre
Algebra, Trigonometry, Precalculus, Calculus. A great program to
show students step by step directions and also allow a teacher to create
a presentation to be used on their LSD projector. This is a great
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instruction. 4 Star

9. Use vector addition and scalar multiplication to solve
problems.


Vectors:
An Introduction This Study Guide
from Encyclopedia Britannica discusses the topics of scalar and vector
quantities, quality of vectors, vector addition and subtraction, multiplying
a vector by a scalar, component form of vectors, algebraic vector
arithmetic, and calculating magnitude and direction.

Vectors Manipulate the magnitude and direction
of two vectors to generate a sum and learn vector addition. The x and y
components can be displayed, along with the dot product of the two vectors.

Measurement

1. Determine the number of significant digits in a measurement.


2. Use radian and degree angle measures to solve problems and
perform conversions as needed.

 Smart
Board Lesson Created by
: LAURIE FOUTS
SB

Mathway
This a step by step math solver for General Math, Geometry, Algebra, Pre
Algebra, Trigonometry, Precalculus, Calculus. A great program to
show students step by step directions and also allow a teacher to create
a presentation to be used on their LSD projector. This is a great
tool for facilitating and allowing at teacher to better present their
instruction. 4 Star

3. Derive a formula for the surface area of a cone as a function
of its slant height and the circumference of its base.


Surface and Lateral Area of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface
area changes. Use the dynamic net of the solid to compute the lateral area and
the surface area of the solid.

Surface and Lateral Area of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area
changes. Use the dynamic net of the solid to compute the lateral area and the
surface area of the solid.

4. Calculate distances, areas, surface areas and volumes of composite
threedimensional objects to a specified number of significant digits.


Mathway
This a step by step math solver for General Math, Geometry, Algebra, Pre
Algebra, Trigonometry, Precalculus, Calculus. A great program to
show students step by step directions and also allow a teacher to create
a presentation to be used on their LSD projector. This is a great
tool for facilitating and allowing at teacher to better present their
instruction. 4 Star

5. Solve realworld problems involving area, surface area,
volume and density to a specified degree of precision.


Density
Experiment: Slice and Dice Drop a chunk of
material in a beaker of water and observe whether it sinks or floats. Cut the
chunk into smaller pieces of any size, and observe what happens as they are
dropped in the beaker. The mass and volume of each chunk can be measured as a
clear understanding of density, buoyancy, and floatation is investigated.

Density Laboratory With a scale to measure
mass, a graduated cylinder to measure volume, and a large beaker of liquid to
observe floatation, the relationship between mass, volume, density, and
floatation can be investigated. The density of the liquid in the beaker can be
adjusted, and a variety of objects can be studied during the investigation.

Density via Comparison Using four beakers
of different liquids with a known density, try to determine the density of a
variety of unknown objects. Compare the buoyancy of each object in each beaker
to determine an approximate value of density without knowing the mass or
volume of the objects.

Determining Density via Water Displacement Drop
objects in a beaker that is filled with water and measure the water that flows
over the edge. Using Archimedes principle, the amount of water displaced by
the floating objects and the water displaced when you force the object under
water, will allow you to determine the density of the objects.

Prisms and Cylinders  Activity A Vary the
height and base‑edge or radius length of a prism or cylinder and examine how
its three‑dimensional representation changes. Determine the area of the base
and the volume of the solid. Compare the volume of a skew prism or cylinder to
the volume of a right prism or cylinder.

Pyramids and Cones  Activity A Vary
the height and base‑edge or radius length of a pyramid or cone and examine how
its three‑dimensional representation changes. Determine the area of the base
and the volume of the solid. Compare the volume of a skew pyramid or cone to
the volume of a right pyramid or cone.

Geometry and Spatial
Sense

1. Use polar coordinates to specify locations on a plane.


Points
in Polar Coordinates Identify the polar
coordinates of a point. Drag the point in the plane and investigate how its r
and theta coordinates change in response. Compare its Cartesian coordinates.

2. Represent translations using vectors.


Rotations,
Reflections and Translations Rotate,
reflect, and translate a figure in the plane. Compare the translated figure to
the original figure.

Translations Translate a figure horizontally and
vertically in the plane and examine the matrix representation of the
translation.

Vectors Manipulate the magnitude and
direction of two vectors to generate a sum and learn vector addition. The x
and y components can be displayed, along with the dot product of the two
vectors.

3. Describe multiplication of a vector and a scalar graphically
and algebraically, and apply to problem situations.


Vectors:
An Introduction
This Study Guide
from Encyclopedia Britannica discusses the topics of scalar and vector
quantities, quality of vectors, vector addition and subtraction, multiplying
a vector by a scalar, component form of vectors, algebraic vector
arithmetic, and calculating magnitude and direction.

4. Use trigonometric relationships to determine lengths and
angle measures; i.e., Law of Sines and Law of
Cosines.


Mathway
This a step by step math solver for General Math, Geometry, Algebra, Pre
Algebra, Trigonometry, Precalculus, Calculus. A great program to
show students step by step directions and also allow a teacher to create
a presentation to be used on their LSD projector. This is a great
tool for facilitating and allowing at teacher to better present their
instruction. 4 Star

Law of Sines
This web site
uses an animated slideshow to explain the Law of Sines,
and then demonstrates using the property to solve a problem. Be sure to
click the "Pause" button as needed if the slideshow moves too
quickly.

Law of Cosines for Obtuse Triangles
This web site
uses an animated slideshow to explain the Law of Cosines for Obtuse
Angles, and then demonstrates using the property to solve a problem. Be
sure to click the "Pause" button as needed if the slideshow
moves too quickly.

Law of
Cosines for Acute Triangles
This web site
uses an animated slideshow to explain the Law of Cosines for Acute
Triangles. Be sure to click the "Pause" button as needed if
the slideshow moves too quickly.

The
Sine Rule
This is an
excellent interactive tutorial that uses animations and audio
explanations to clearly teach the Sine Rule and show several sample
problems. Be sure to click the "Play Audio" button to hear the
commentary.

5. Identify, sketch and classify the cross sections of
threedimensional objects.


Slicing
Platonic Solids  Virtual Manipulative
This online
activity allows you to slice five different platonic solids with a
plane. The solids can be rotated and the plane's height changed. The
resulting shape from the cross section is displayed to the side.

Patterns, Functions
and Algebra

1. Identify and describe problem situations involving an
iterative process that can be represented as a recursive function; e.g.,
compound interest.


2. Translate a recursive function into a closed form expression
or formula for the nth term to solve a problem situation involving an
iterative process; e.g., find the value of an annuity after 7 years.


3. Describe and compare the characteristics of the following
families of functions: quadratics with complex roots, polynomials of any
degree, logarithms, and rational functions; e.g., general shape, number of
roots, domain and range, asymptotic behavior.


Cubic Function Activity Explore a cubic
function, along with the associated Center of Rotation. Vary the coefficients
of the equation and examine how the graph changes in response.

FourthDegree Polynomials  Activity A Compare
the equation of a fourth‑degree polynomial to its graph. Vary the coefficients
of the equation and investigate how the graph changes in response.

General Form of a Rational Function Compare the
equation of a rational function to its graph. Multiply or divide the numerator
and denominator by linear factors and explore how the graph changes in
response.

Logarithmic Functions  Activity A Compare the
equation of a logarithmic function to its graph. Change the base of the
logarithmic function and examine how the graph changes in response. Use the
line y = x to compare the associated exponential function.

Logarithmic Functions: Translating and Scaling
Vary the values in the equation of a logarithmic function and
examine how the graph is translated or scaled. Connect these transformations
with the domain of the function, and the asymptote in the graph.

Quadratic and Absolute Value Functions Compare
the graph of a quadratic or absolute‑value function to its equations. Vary
the coefficients of the equation and explore how the graph changes in
response.

Quadratics in Factored Form Investigate the
factors of a quadratic through its graph and through its equation. Vary the
roots of the quadratic and examine how the graph and the equation change in
response.

Quadratics in Polynomial Form  Activity A
Compare the graph of a quadratic to its equation in polynomial form. Vary
the coefficients of the equation and explore how the graph changes in
response.

Rational Functions Compare the graph of a
rational function to its equation. Vary the terms of the equation and
explore how the graph is translated and stretched as a result. Examine the
domain on a number line and compare it to the graph of the equation.

Roots of a Quadratic Find the root of a
quadratic using its graph or the quadratic formula. Explore the graph of the
roots and the point of symmetry in the complex plane. Compare the axis of
symmetry and graph of the quadratic in the real plane.

4. Identify the maximum and minimum points of polynomial,
rational and trigonometric functions graphically and with technology.


Cosine Function Compare the graph of the cosine
function with the graph of the angle on the unit circle. Drag a point along
the cosine curve and see the corresponding angle on the unit circle.

Cubic Function Activity Explore a cubic
function, along with the associated Center of Rotation. Vary the coefficients
of the equation and examine how the graph changes in response.

FourthDegree Polynomials  Activity A Compare
the equation of a fourth‑degree polynomial to its graph. Vary the coefficients
of the equation and investigate how the graph changes in response.

General Form of a Rational Function Compare the
equation of a rational function to its graph. Multiply or divide the numerator
and denominator by linear factors and explore how the graph changes in
response.

Rational Functions Compare the graph of a
rational function to its equation. Vary the terms of the equation and explore
how the graph is translated and stretched as a result. Examine the domain on a
number line and compare it to the graph of the equation.

Roots of a Quadratic Find the root of a
quadratic using its graph or the quadratic formula. Explore the graph of the
roots and the point of symmetry in the complex plane. Compare the axis of
symmetry and graph of the quadratic in the real plane.

Sine Function Compare the graph of the sine
function with the graph of the angle on the unit circle. Drag a point along
the sine curve and see the corresponding angle on the unit circle

Tangent Function Compare the graph of the
tangent function with the graph of the angle on the unit circle. Drag a point
along the tangent curve and see the corresponding angle on the unit circle.

5. Identify families of functions with graphs that have rotation
symmetry or reflection symmetry about the yaxis, xaxis or y = x.


Holiday
Snowflake Designer Fold paper and cut in a
certain way to make symmetrical snowflakes with six sides (similar to what can
be found in nature) or with eight sides (an easier folding method). This
simulation allows you to cut virtual paper on the computer screen with round
dot or square dot "scissors" of various sizes before using physical paper.

6. Represent the inverse of a function symbolically and
graphically as a reflection about y = x.


Absolute Value with Linear Functions  Activity B
Explore and compare the graphs of y = f(x) and y = f(x). By comparing the
graphs of these functions to the graph of y = f(x), you will see how absolute
value can affect the input and output values of linear functions.

7. Model and solve problems with matrices and vectors.


Matrices:
An Introduction
This study guide
from Encyclopedia Britannica covers a discussion of the basic aspects of
matrices, including labeling, equality of two matrices, and addition,
subtraction, and multiplication of matrices.

Matrices: Equations and Systems of Equations
This study guide
from Encyclopedia Britannica covers a discussion of inverse matrices,
determinants, matrix equations, and simultaneous equations.

Vectors Manipulate the magnitude and direction
of two vectors to generate a sum and learn vector addition. The x and y
components can be displayed, along with the dot product of the two vectors

8. Solve equations involving radical expressions and complex
roots.


Roots
of a Quadratic Find the root of a quadratic
using its graph or the quadratic formula. Explore the graph of the roots and
the point of symmetry in the complex plane. Compare the axis of symmetry and
graph of the quadratic in the real plane.

9. Solve 3 by 3 systems of linear equations by elimination and
using technology, and interpret graphically what the solution means (a point,
line, plane, or no solution).


Modeling Linear Systems  Activity A
Experiment with a system of two lines representing a cat‑and‑mouse chase.
Adjust the speeds of the cat and mouse and the head start of the mouse, and
immediately see the effects on the graph and on the chase. Connect real‑world
meaning to slope, y‑intercept, and the intersection of lines.

Solving Linear Systems by Graphing Compare a
system of equations in standard form or in slope‑intercept form to its graph.
Examine the graph and table of values. Determine the solutions to the system.

Special Types of Solutions to Linear Systems
Compare a system of equations in standard form to its graph. Examine the graph
and table of values. Determine the solutions to the system.

Systems of Linear Equations  Activity A
Solve a system of linear equations by graphing and finding the intersection of
the lines of the equations. Create a system of equations, examine its graph,
matrix, and table of values, and determine the solution of the system.

10. Describe the characteristics of the graphs of conic
sections.


Conic Flyer Similar to
Function Flyer, but allows the manipulation of the constants and
coefficients of all the types of conic section equations on a coordinate
plane by changing those numbers using a slider bar.

11. Describe how a change in the value of a constant in an
exponential, logarithmic or radical equation affects the graph of the
equation.


Data Analysis and
Probability

1. Design a statistical experiment, survey or study for a
problem; collect data for the problem; and interpret the data with
appropriate graphical displays, descriptive statistics, concepts
of variability, causation, correlation and standard deviation.


2. Describe the role of randomization in a welldesigned study,
especially as compared to a convenience sample, and the generalization of
results from each.


3. Describe how a linear transformation of univariate
data affects range, mean, mode and median.


4. Create a scatterplot of bivariate data, identify trends, and find a function to
model the data.


Correlation Explore the relationship between
the correlation coefficient of a data set and its graph. Fit a line to the
data and compare the leastsquares fit line.

Scatter Plots  Activity A Examine the
scatter plot for a random data set with negative or positive correlation.
Vary the correlation and explore how correlation is reflected in the scatter
plot and the trend line.

Solving Using Trend Lines Examine the scatter
plots for a data related to weather at different latitudes. The Gizmo
includes three different data sets, one with negative correlation, one
positive, and one with no correlation. Compare the least squares best‑fit
line.

Scatterplot Activity
This interactive
activity from Encyclopedia Britannica is a statistical tool to explore
the relationships between two data sets. Ranges can be set independently
and data points entered by hand or loaded from sample sets. Displays an
updated regression line and summary statistics.

Scatterplot  Virtual Manipulative
This online
activity allows the user to create scatterplot
by adding points to a grid, and then calculates and displays the line of
best fit. The grid size can be changed fit any activity, and one
suggested activity is explained on the site.

Scatterplots  Excel activity
This is an Excel
spreadsheet activity for individual students or the whole class. As the
user enters ordered pairs, the spreadsheet graphs a scatterplot,
creates a line of best fit, and displays its equation (in linear or
polynomial form).

5. Use technology to find the Least Squares Regression Line, the
regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of
these statistics in the context of the problem situation.


Correlation
Explore the relationship between the correlation coefficient of a data set and
its graph. Fit a line to the data and compare the leastsquares fit line.

Linear Functions Determine if a relation is a
function from the mapping diagram, ordered pairs, or graph. Use the graph to
determine if it is linear.

Solving Using Trend Lines Examine the scatter
plots for a data related to weather at different latitudes. The Gizmo includes
three different data sets, one with negative correlation, one positive, and
one with no correlation. Compare the least squares best‑fit line.

6. Use technology to compute the standard deviation for a set of
data, and interpret standard deviation in relation to the context or problem
situation.


7. Describe the standard normal curve and its general
properties, and answer questions dealing with data assumed to be normal.


8. Analyze and interpret univariate
and bivariate data to identify patterns, note
trends, draw conclusions, and make predictions.


Solving
Using Trend Lines Examine the scatter plots for
a data related to weather at different latitudes. The Gizmo includes three
different data sets, one with negative correlation, one positive, and one with
no correlation. Compare the least squares best‑fit line.

Correlation
Explore the relationship between the correlation coefficient of a data set and
its graph. Fit a line to the data and compare the leastsquares fit line.

9. Evaluate validity of results of a study based on
characteristics of the study design, including sampling method, summary
statistics and data analysis techniques.


10. Understand and use the concept of random variable, and
compute and interpret the expected value for a random variable in simple
cases.


11. Examine statements and decisions involving risk; e.g.,
insurance rates and medical decisions.

