Number, Number
Sense and Operations 
(Based on State of Ohio
Curriculum Standards) 
1.
Connect physical, verbal and symbolic representations of irrational
numbers; e.g., construct square root of 2 as a hypotenuse or on a number
line.


Comparing and Ordering IntegersCompare
and order integers using draggable points on a number line. Also explore
the opposites of numbers on the number line.

Square RootsExplore
the meaning of square roots using an area model.
Use the side length of a square to
find the square root of a decimal number or a whole number.

2.
Explain the meaning of the nth root. 

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

3.
Use factorial notation and computations to represent and solve problem
situations involving arrangements. 

4.
Approximate the nth root of a given number greater than zero between
consecutive integers when n is an integer; e.g., the 4th root of 50 is
between 2 and 3. 

Measurement 
1.
Explain how a small error in measurement may lead to a large error in
calculated results. 

2.
Calculate relative error. 

3.
Explain the difference between absolute error and relative error in
measurement. 

4.
Give examples of how the same absolute error can be problematic in one
situation but not in another; e.g., compare “accurate to the nearest foot”
when measuring the height of a person versus when measuring the height of a
mountain. 

5.
Determine the measures of central and inscribed angles and their associated
major and minor arcs. 

Chords and ArcsExplore
the relationship between a central angle and the arcs it intercepts. Also
explore the relationship between chords and their distance from the
circle's center.

Inscribing AnglesResize
angles inscribed in a circle. Investigate the relationship between
inscribed angles and the arcs they intercept.

Geometry and Spatial Sense 
1.
Formally define and explain key aspects of geometric figures, including:
a. interior and exterior angles of polygons;
b. segments related to triangles (median, altitude, midsegment);
c. points of concurrency related to triangles (centroid, incenter,
orthocenter, circumcenter);
d. circles (radius, diameter, chord, circumference, major arc, minor arc,
sector, segment, inscribed angle). 
 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

Classifying
Quadrilaterals  Activity AApply
constraints to a quadrilateral, and then reshape and resize it. Classify
the figure by its constraints. Explore the differences between the
different kinds of quadrilaterals.

Classifying Quadrilaterals  Activity BApply
constraints to a quadrilateral, and then reshape and resize it. Classify
the figure by its constraints. Explore the differences between the
different kinds of quadrilaterals.

Triangle Angle Sum  Activity AMeasure
the angles of a triangle and find the sum.

Concurrent Lines, Medians, and AltitudesExplore
the relationships between perpendicular bisectors, the circumscribed
circle, angle bisectors, the inscribed circle, altitudes, and medians
using a triangle that can be resized and reshaped.

Chords and ArcsExplore
the relationship between a central angle and the arcs it intercepts. Also
explore the relationship between chords and their distance from the
circle's center.

Circle: Circumference and AreaResize
a circle and compare its radius, circumference, and area.

Inscribing AnglesResize
angles inscribed in a circle. Investigate the relationship between
inscribed angles and the arcs they intercept.

Holiday Snowflake DesignerFold
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.

ReflectionsReshape and
resize a figure and examine how its reflection changes in response. Move
the line of reflection and explore how the reflection is translated.

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

2.
Recognize and explain the necessity for certain terms to remain undefined,
such as point, line and plane. 

3.
Make, test and establish the validity of conjectures about geometric
properties and relationships using counterexample, inductive and deductive
reasoning, and paragraph or twocolumn proof, including:
a. prove the Pythagorean Theorem;
b. prove theorems involving triangle similarity and congruence;
c. prove theorems involving properties of lines, angles, triangles and
quadrilaterals;
d. test a conjecture using basic constructions made with a compass and
straightedge or technology. 

Pythagorean
Theorem  Virtual Manipulative
This online activity allows
you to demonstrate the proof of the Pythagorean Theorem using area models
that can be manipulated.

Biconditional StatementMake
a biconditional statement from a given definition using word tiles. Use
both symbolic form and standard English form.

Conditional Statement
Make a conditional
statement from a given fact using word tiles. Use both symbolic
form and standard English form.

Geoboard: The Pythagorean TheoremBuild
right triangles in an interactive geoboard and build squares on the sides
of the triangles to discover the Pythagorean Theorem.

Proving Triangles CongruentApply
constraints to two triangles. Then drag the vertices of the triangles
around and determine which constraints guarantee congruence.

Pythagorean Theorem  Activity BExplore
the Pythagorean Theorem using a dynamic right triangle. Examine a visual,
geometric application of the Pythagorean Theorem, using the areas of
squares on the sides of the triangle.

Biconditional StatementMake
a biconditional statement from a given definition using word tiles. Use
both symbolic form and standard English form.

Area of Parallelograms  Activity AExamine
and manipulate the graph of a parallelogram or triangle and find its area.

Construct Parallel and Perpendicular LinesConstruct
parallel and perpendicular lines using a straightedge and compass. Use
step‑by‑step explanations and feedback to develop understanding of the
construction.

4.
Construct right triangles, equilateral triangles, parallelograms,
trapezoids, rectangles, rhombuses, squares and kites, using compass and
straightedge or dynamic geometry software.

 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

Classifying Quadrilaterals  Activity BApply
constraints to a quadrilateral, and then reshape and resize it. Classify
the figure by its constraints. Explore the differences between the
different kinds of quadrilaterals.

Constructing Congruent Segments and AnglesConstruct
congruent segments and angles using a straightedge and compass. Use
step‑by‑step explanations and feedback to develop understanding of the
construction.

Parallelogram ConditionsApply
constraints to a dynamic quadrilateral. Then drag its vertices around.
Determine which constraints guarantee that the quadrilateral is always a
parallelogram.

Special Quadrilaterals
Apply constraints to a
quadrilateral and determine what type of quadrilateral results.

5.
Construct congruent figures and similar figures using tools, such as
compass, straightedge, and protractor or dynamic geometry software. 

Congruent
Triangles  Virtual Manipulative
This online activity allows
you to manipulate virtual angles and segments to learn what does and does
not guarantee congruent triangles. The methods covered include SSS, SAS,
ASA, and SSA

Congruence in Right TrianglesApply
constraints to two right triangles. Then drag their vertices around under
those conditions. Determine under what conditions the triangles are
guaranteed to be congruent.

Proving Triangles CongruentApply
constraints to two triangles. Then drag the vertices of the triangles
around and determine which constraints guarantee congruence.

6.
Identify the reflection and rotation symmetries of two and
threedimensional figures. 

7.
Perform reflections and rotations using compass and straightedge
constructions and dynamic geometry software. 

Math
Manipulatives  Flips, Slides, and Turns
This online activity from
Encyclopedia Britanica allows the user to place geometric figures and then
apply reflections, rotations, and translations to them.

Rotation
Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a rotation to them. You
can do this on your own, or go through three premade activities.

Reflection
Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a reflection to them. You
can do this on your own, or go through three premade activities

8.
Derive coordinate rules for translations, reflections and rotations of
geometric figures in the coordinate plane. 

Translation
Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a translation to them. You
can do this on your own, or go through three premade activities.

Rotation
Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a rotation to them. You
can do this on your own, or go through three premade activities.

Reflection
Transformation  Virtual Manipulative
This online activity allows
you to place pattern blocks on a grid and apply a reflection to them. You
can do this on your own, or go through three premade activities.

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

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

9.
Show and describe the results of combinations of translations, reflections
and rotations (compositions); e.g., perform compositions and specify the
result of a composition as the outcome of a single motion, when applicable. 

Multiple
Transformations  Virtual Manipulative
This online activity allows
you to apply two consecutive transformations to pattern blocks, including
translations, reflections, and rotations. You can work on your own, or go
through two premade activities.

ReflectionsReshape and
resize a figure and examine how its reflection changes in response. Move
the line of reflection and explore how the reflection is translated.

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

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

10.
Solve problems involving chords, radii and arcs within the same circle. 

Patterns, Functions and Algebra 
1.
Define function formally and with f(x) notation. 

Smart Board Algebra Lesson This
lesson has examples and videos.
Smart board manipulativeSB

Algebra Tiles –
Visualize multiplying and factoring algebraic expressions using
tiles.
Algebra Tile manipulative





Student Resources for Algebra
 Outstanding web
site for teachers and students.

2.
Describe and compare characteristics of the following families of functions:
square root, cubic, absolute value and basic trigonometric functions; e.g.,
general shape, possible number of roots, domain and range. 

Cubic
Functions: Graphing
This study guide from
Encyclopedia Britannica covers an overview of cubic functions. Includes
sections on creating graphs by transformation, using a sign diagram,
finding turning points, the factor theorem, graphing a cubic function by
factoring, and using a TI83 graphical calculator.

Cosine FunctionCompare
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 ActivityExplore
a cubic function, along with the associated Center of Rotation.

Functions Involving Square RootsCompare
the graph of a function involving square roots to its equation. Vary the
coefficients of the equation and investigate how the graph changes in
response.

Inequalities Involving Absolute
ValuesSolve an inequality involving absolute
values using a graph of the absolutevalue function.

Radical FunctionsCompare
the graph of a radical function to its equation. Vary the terms of the
equation.

Sine FunctionCompare
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 FunctionCompare
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.

3.
Solve equations and formulas for a specified variable; e.g., express the
base of a triangle in terms of the area and height. 
 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

Perimeter, Circumference, and Area 
Activity BResize a rectangle, circle, or square
and find its perimeter or circumference and
area.

4.
Use algebraic representations and functions to describe and generalize
geometric properties and relationships. 

Ellipse  Activity ACompare
the equation of an ellipse to its graph. Vary the terms of the equation of
the ellipse and examine how the graph changes in response.

Hyperbola  Activity ACompare
the equation of a hyperbola to its graph. Vary the terms of the equation
of the hyperbola.
 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 simple linear and nonlinear equations and inequalities having square
roots as coefficients and solutions. 

Modeling OneStep Equations  Activity ASolve
one‑step equations using an area model. Drag tiles into two bins, each
representing a side of the equation, and isolate an x‑tile on one side.

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

Solving Equations By Graphing Each SideSolve
an equation by graphing each side and finding the intersection of the
lines. Vary the coefficients in the equation and explore how the graph
changes in response.

Solving Linear Inequalities using Addition and Subtraction
Solve a linear inequality.
Graph the solution on a dynamic number line.

Solving Linear Inequalities using Multiplication and
Division
Solve an inequality
involving multiplication and division. Graph the solution on a
number line.

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

Square RootsExplore
the meaning of square roots using an area model. Use the side length of a
square to find the square root of a decimal number or a whole number.

6.
Solve equations and inequalities having rational expressions as coefficients
and solutions. 

Modeling OneStep Equations  Activity ASolve
one‑step equations using an area model. Drag tiles into two bins, each
representing a side of the equation, and isolate an x‑tile on one side.

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

Solving Linear Inequalities using Addition and Subtraction
Solve a linear inequality.
Graph the solution on a dynamic number line.

Solving Linear Inequalities using Multiplication and
DivisionSolve an
inequality involving multiplication and division. Graph the solution on a
number line.

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

7.
Solve systems of linear inequalities. 

Linear Programming  Activity AUse
the graph of the feasible region to find the maximum or minimum value of
the objective function. Vary the coefficients of the objective function
and vary the constraints. Explore how the graph of the feasible region
changes in response.

Solving Linear Inequalities using Addition and Subtraction
Solve a linear inequality.
Graph the solution on a dynamic number line.

Solving Linear Inequalities using Multiplication and
DivisionSolve an
inequality involving multiplication and division. Graph the solution on a
number line.

Systems of Linear Inequalities (Slopeintercept form) 
Activity ACompare
a system of linear inequalities to its graph. Vary the coefficients and
inequality symbols in the system and explore how the boundary lines,
shaded regions, and the intersection of the shaded regions change in
response.

8.
Graph the quadratic relationship that defines circles. 

CirclesCompare
the graph of a circle with its equation. Vary the terms in the equation
and explore how the circle is translated and scaled in response.

9.
Recognize and explain that the slopes of parallel lines are equal and the
slopes of perpendicular lines are negative reciprocals. 

Slope  Activity BExplore
the slope of a line, and learn how to calculate slope. Adjust the line by
moving points that are on the line, and see how its slope changes.

10.
Solve realworld problems that can be modeled using linear, quadratic,
exponential or square root functions. 

Exponential Functions  Activity AExplore
the graph of an exponential function. Vary the coefficient and base of the
function and investigate the changes to the graph of the function.

Functions Involving Square RootsCompare
the graph of a function involving square roots to its equation.

Linear FunctionsDetermine
if a relation is a function from the mapping diagram, ordered pairs, or
graph.

Quadratic and Absolute Value FunctionsCompare
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 FormInvestigate
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 ACompare
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.

Radical FunctionsCompare
the graph of a radical function to its equation. Vary the terms of the
equation. Explore how the graph is translated and stretched by the changes
to the equation.

Roots of a QuadraticFind
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.

11.
Solve realworld problems that can be modeled, using systems of linear
equations and inequalities. 

Linear Programming  Activity AUse
the graph of the feasible region to find the maximum or minimum value of
the objective function.

Modeling Linear Systems  Activity AExperiment
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.

Special Types of Solutions to Linear SystemsCompare
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 Inequalities (Slopeintercept form) 
Activity ACompare
a system of linear inequalities to its graph. Vary the coefficients and
inequality symbols in the system and explore how the boundary lines,
shaded regions, and the intersection of the shaded regions change in
response.

12.
Describe the relationship between slope of a line through the origin and the
tangent function of the angle created by the line and the positive xaxis. 

Slope  Activity BExplore
the slope of a line, and learn how to calculate slope. Adjust the line by
moving points that are on the line, and see how its slope changes.

Tangent FunctionCompare
the graph of the tangent function with the graph of the angle on the unit
circle.

Tangent RatioReshape
and resize a right triangle and examine how the tangent of angle A
changes.

Data Analysis and
Probability 
1.
Describe measures of center and the range verbally, graphically and
algebraically. 
 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

BoxandWhisker PlotsConstruct
a box‑and‑whisker plot to match a line plots, and construct a line plot to
match a box‑and‑whisker plots.

Describing Data Using StatisticsInvestigate
the mean, median, mode, and range of a data set through its graph.

Line PlotsBuild
a data set using a line plot. Find its mean, median, mode, and range.
Change the data values by dragging the points, and watch how the mean,
median, mode, and range change (or, in some cases, do not change).

Mean, Median and ModeBuild
a data set and find the mean, median, and mode. Explore the mean, median,
and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs
stacked under a bar of variable height.

2.
Represent and analyze bivariate data using appropriate graphical displays (scatterplots,
parallel boxandwhisker plots, histograms with more than one set of data,
tables, charts, spreadsheets) with and without technology. 

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).

BoxandWhisker PlotsConstruct
a box‑and‑whisker plot to match a line plots, and construct a line plot to
match a box‑and‑whisker plots.

CorrelationExplore
the relationship between the correlation coefficient of a data set and its
graph.

HistogramsChange
the values in a data set and examine how the dynamic histogram changes in
response.

Populations and SamplesCompare
sample distributions drawn from population distributions. Predict
characteristics of a population distribution based on a sample
distribution and examine how well a small sample represents a given
population.

Scatter Plots  Activity AExamine
the scatter plot for a random data set with negative or positive
correlation.

Solving Using Trend LinesExamine
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.

3.
Display bivariate data where at least one variable is categorical. 

BoxandWhisker PlotsConstruct
a box‑and‑whisker plot to match a line plots, and construct a line plot to
match a box‑and‑whisker plots. Manipulate the line plot and examine how
the box‑and‑whisker plot changes. Then manipulate the box‑and‑whisker plot
and examine how the line plot changes.

Describing Data Using StatisticsInvestigate
the mean, median, mode, and range of a data set through its graph.

HistogramsChange
the values in a data set and examine how the dynamic histogram changes in
response.

Line PlotsBuild
a data set using a line plot. Find its mean, median, mode, and range.
Change the data values by dragging the points, and watch how the mean,
median, mode, and range change (or, in some cases, do not change).

Scatter Plots  Activity AExamine
the scatter plot for a random data set with negative or positive
correlation.

StemandLeaf PlotsBuild
a data set and compare the line plot of the data set to the stem‑and‑leaf
plot.

4.
Identify outliers on a data display; e.g., use interquartile range to
identify outliers on a boxandwhisker plot. 

Statistics  Deviation from the Mean
This study guide from
Encyclopedia Britannica covers several lessons on stats such as range,
interquartile range, box and whisker plots, and more.

Box Plot and Histogram  Virtual
Manipulative
This online interactive
activity generates a box plot and a histogram for data provided. You can
choose from several premade sets of topical data, or you can enter new
data or change the data there. Several measures of the data are given as
well.

BoxandWhisker PlotsConstruct
a box‑and‑whisker plot to match a line plots, and construct a line plot to
match a box‑and‑whisker plots. Manipulate the line plot and examine how
the box‑and‑whisker plot changes. Then manipulate the box‑and‑whisker plot
and examine how the line plot changes.

5.
Provide examples and explain how a statistic may or may not be an attribute
of the entire population; e.g., intentional or unintentional bias may be
present. 

6.
Interpret the relationship between two variables using multiple graphical
displays and statistical measures; e.g., scatterplots, parallel
boxandwhisker plots, and measures of center and spread. 

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).

Mean, Median and ModeBuild
a data set and find the mean, median, and mode. Explore the mean, median,
and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs
stacked under a bar of variable height.

7.
Model problems dealing with uncertainty with area models (geometric
probability). 

Geometric Probability  Activity ARandomly
throw darts at a target and see what percent are "hits." Vary the size of
the target and repeat the experiment. Study the relationship between the
area of the target and the percent of darts that strike it

8.
Differentiate and explain the relationship between the probability of an
event and the odds of an event, and compute one given the other. 

Binomial Probabilities
Find the probability of a
number of successes or failures in a binomial experiment using a
tree diagram, a bar graph, and direct calculation.

Geometric Probability  Activity ARandomly
throw darts at a target and see what percent are "hits." Vary the size of
the target and repeat the experiment. Study the relationship between the
area of the target and the percent of darts that strike it
